mit quantum physics phd

Principal investigators , senior research staff , post-docs , graduate students , group alums , undergraduate students , and visting researchers.

Principal Investigators

Professor Isaac Chuang

MIT Professor of Physics and EECS; Principal Investigator, MIT RLE Quanta Group.

Prof. Chuang is a pioneer in the field of quantum information science. His experimental realization of two, three, five, and seven quantum bit quantum computers using nuclear spins in molecules provided the first laboratory demonstrations of many important quantum algorithms, including Shor's quantum factoring algorithm. The error correction, algorithmic cooling, and entanglement manipulation techniques he developed provide new ways to obtain complete quantum control over light and matter, and lay a foundation for possible large-scale quantum information processing systems. Prof. Chuang came to MIT in 2000 from IBM, where he was a research staff member. He received his doctorate in Electrical Engineering from Stanford University, where he was a Hertz Foundation Fellow. Prof. Chuang also holds two bachelors and one masters degrees in Physics and Electrical Engineering from MIT, and was a post-doctoral fellow at Los Alamos National Laboratory and the University of California at Berkeley. He is the author, together with Michael Nielsen, of the textbook Quantum Computation and Quantum Information. [ichaung_[at]_mit.edu]

Dr. John Chiaverini

Senior Technical Staff at Lincoln Laboratory; Principal Investigator at MIT.

John Chiaverini is a Senior Technical Staff member at MIT Lincoln Laboratory where he leads the trapped-ion team, and he is a Principal Investigator in MIT's RLE. His current research interests include architectures, integrated technologies, and new methodologies for trapped-ion quantum information processing. John did postdoctoral research at NIST in Boulder and was a staff member at Los Alamos National Lab before coming to Lincoln and MIT. He received his PhD in physics from Stanford University and his BS in physics from Case Western Reserve University. [john.chiaverini_[at]_ll.mit.edu]

Post-Doctoral Researchers

Dr. Yuan Liu

MIT post-doctoral researcher.

Interests: quantum algorithms and quantum error correction, electronic structure theory, chemical physics. yuanliu_[at]_mit.edu

Dr. Ethan Clements

Interests: experiments with trapped ions, precision measurements, quantum networks, quantum sensing, and quantum information processing. eclement_[at]_mit.edu

Dr. Eleanor Crane

Goal: quantum simulation using error-corrected universal fermion-boson quantum computers. Works towards theoretical aspects of this with circuit QED, ion traps, donors in silicon, etc. Enjoys adventures, whatever the nature. Grew up in a superposition of England and France. emc2_[at]_mit.edu

Graduate Students

MIT PhD Student with the Quanta Group.

Focused on experiment (metastable qubits, omg architecture, qudits) and related theory. I carry out my experiments primarily at MIT Lincoln Laboratory with John Chiaverini's ion trapping group, but collaborate closely with the MIT campus efforts as well. I'm interested in new qubit (and qudit) encoding schemes and how to manipulate them. In my free time, I enjoy hiking, playing the saxophone, and watching Ohio State football. [debry_[at]_mit.edu]

Arkopal Dutt

Interested in the theory of quantum computation and quantum computing assisted sensing. [arkopal_[at]_mit.edu]

Felix Knollmann

I am an experimentalist focused on integrating photonic devices into ion traps and using quantum information techniques to enhance quantum sensing. Beyond the lab, I aim to improve scientific communication. In my free time, you will find me cycling, skiing, climbing or competing in triathlons. [fwk_[at]_mit.edu]

John Martyn

I'm interested in developing computational methods for studying quantum systems, both with quantum algorithms (quantum signal processing, Hamiltonian simulation) and classical algorithms (tensor networks, quantum Monte Carlo, and machine learning). Outside of physics, I enjoy skateboarding and filmmaking. [jmmartyn_[at]_mit.edu]

Gabriel Mintzer

MIT Graduate Researcher with the Quanta Group.

I am a current EECS master’s student (and former physics/CS undergraduate student) at MIT with a concentration in AI and machine learning. In lab, I previously worked on restoring the room-temperature ion-trap system to an operational state and then maintaining and operating it to run experiments. I now work on simulating trapped-ion systems, as well as designing and optimizing algorithms for quantum computing on such systems, for which I often employ machine learning. Outside of lab, I enjoy practicing dance; teaching science; listening to and playing music; learning languages (currently Japanese); solving MIT-Mystery-Hunt-type puzzles; watching anime and donghua; reading, especially science fiction; traveling to new places; and hiking on mountain trails. [gmintzer_[at]_mit.edu]

Interests: quantum algorithms, computational complexity, and adversarial models in quantum computation.

I am interested in developing new classes of quantum algorithms and proving concrete complexity separations for useful computational problems with an eye on relevance in the near-term. I want to answer questions about how can a quantum computer can efficiently prove it is solving a quantum problem specified (as specified), to a lower-power verifier, and further convert quantum information theoretic results to constructive proofs. [zmr_[at]_mit.edu]

Zachary Chin

Interests: quantum algorithms, quantum chemistry, and quantum sensing with trapped ions.

Xiaoyang Shi

Interests in trapped ion experiment; AMO physics; Quantum computing. [shix_[at]_mit.edu]

Jasmine Sinanan-Singh

Interests: continuous variable quantum computing experiment/theory. [jsinanan_[at]_mit.edu]

My research primarily focuses on quantum computing and quantum information theory, specifically fault-tolerant and quantum error correction, entanglement and state purification. Additionally, I explore the connections between quantum information, many-body physics, AMO theory, and high-energy physics. As a Harbinite, I have a fondness for Boston's winters. In my free time, I enjoy conlanging, jamming on the piano with some jazz and classical tunes, eating, and hitting the tennis courts. [ladmon_[at]_mit.edu]

Theory. [johnblue_[at]_mit.edu]

Theory. [aktan_[at]_mit.edu]

Undergraduates

Bianca Hanly

MIT Undergraduate Student with the Quanta Group.

Interests: trapped ion experiments and continuous variable quantum computing (CVQC)

Interests: theory

Agustin Valdes Martinez

Interests: working on experimental efforts with the MIT Lincoln Laboratory team

Juan Angel Luera

Interests: experiment

Kartik Pingle

Group alums, dr. sho sugiura.

Former MIT post-doctoral researcher, now at NTT Research

Interests in condensed matter systems and the application of quantum information to ground state estimation by quantum computation.

Dr. Susanna Todaro

Former MIT post-doctoral researcher with the Quanta Group, now a Senior Quantum Scientist at Oxford Ionics

Post-doc working on CVQC and metastable qubit experiments. B.S. Harvey Mudd (2012) / Ph.D. NIST Boulder (February 2020). Love to dig deep into the experimental weeds. In my free (?) time, I'm a fan of stress baking, kickboxing, and the X-Men. [stodaro_[at]_mit.edu]

Curtis Northcutt

Graduated MIT PhD Student with the Quanta Group, now CEO and co-founder at Cleanlab

Interests: Machine Learning, Weak Supervision, and Human Intelligence.

My research focuses on two goals: (1) dataset uncertainty estimation, (2) the synergy of artificial intelligence to augment human intelligence. To this end, I established confident learning, a family of theory and algorithms for characterizing, finding, and learning with label errors in datasets, and cleanlab, the official Python framework for machine learning and deep learning with noisy labels in datasets. Some of the places I've worked at include Google AI Research (2019), Oculus Research (2018), Amazon AI (2017), Facebook AI Research (2016), Microsoft Research (2014), MIT Lincoln Lab (2013), and NASA (2009). I enjoy mountaineering, hiking, biking, and rapping. My favorite rapper is PomDP the PhD rapper. [cgn_[at]_mit.edu]

Garrett Simon

Graduated MIT Masters Student with the Quanta Group at MIT Lincoln Laboratory, now with US Army Cyber

Interests: Experiment.

I am interested in identifying and measuring experimental noise sources in cryogenic trapped ion systems. [gsimon_[at]_mit.edu]

Dr. Jules Stuart

(Graduated) MIT PhD Student with the Quanta Group, now a post-doc at NIST Ion Storage

Interests: Experiments (Lincoln Laboratory)

I'm interested in applying classical technology in quantum applications, and I'm always wondering what gadgets we will be able to cram into an ion trap next. Outside of the lab, I enjoy checking out concerts, running and playing video games. [jstuart_[at]_mit.edu]

More alums (under construction)

Kenneth brown ( pi at duke ), david leibrandt ( pi at ucla , formerly ion storage group at nist), philip richerme ( pi at indiana university ), andrew houck ( pi at princeton ), david schuster ( pi at stanford ), guang hao low ( senior researcher at microsoft quantum ), theodore yoder ( research staff at ibm quantum ), robert clark ( principal research scientist at georgia tech research institute ), samuel buercklin, nolan hedglin, chris pearson, waseem bakr, tongyan lin, christalee bieber, andrew cross, jaroslaw labaziewicz, hyeyoun chung, ruth shewmon, stephan schulz, beni yoshida, paul antohi, samuel ocko, tony hyun kim, nathan lachenmyer, shankari rajagopal, shannon wang, zachary fisher, hans andersen, spencer nichols, peter herskind, michael walsh, lucy archer, alana lidawer, yousef alowayed, michael turek, kai aichholz, tessa green, joaquin maury, matthew tancik, amira eltony, kuan-yu lin, alex dalzell, jessica pointing, ryuji takagi, anthony badea.

2023 © MIT RLE Quanta Group; MIT Bldg. 26.

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Department of Physics

The Department of Physics offers undergraduate, graduate, and postgraduate training, with a wide range of options for specialization.

The emphasis of both the undergraduate curriculum and the graduate program is on understanding the fundamental principles that appear to govern the behavior of the physical world, including space and time and matter and energy in all its forms, from the subatomic to the cosmological and from the elementary to the complex.

The Department of Physics strives to be at the forefront of many areas where new physics can be found. Consequently, the department works on problems where extreme conditions may reveal new behavior: from clusters of galaxies or the entire universe to elementary particles or the strings that may be the substructure of these particles; from collisions of nuclei at relativistic velocities that make droplets of matter hotter than anything since the Big Bang to laser-cooled atoms so cold that their wave functions overlap, resulting in a macroscopic collective state, the Bose-Einstein condensate; and from individual atoms to unusual materials, such as high-temperature superconductors and those that are important in biology. Pushing the limits provides the opportunity to observe new general principles and test theories of the structure and behavior of matter and energy.

Bachelor of Science in Physics (Course 8)

Minor in physics, minor in astronomy, undergraduate study.

An undergraduate degree in physics provides an excellent basis not only for graduate study in physics and related fields, but also for professional work in such fields as astrophysics, biophysics, engineering and applied physics, geophysics, management, law, or medicine. The undergraduate curriculum offers students the opportunity to acquire a deep conceptual understanding of fundamental physics. The core departmental requirements begin this process. The student then chooses one of two options to complete the degree: the focused option is designed for students who plan to pursue physics as a career, and is an excellent choice for students who want to experience as deep an engagement as possible with physics; the flexible option also provides a very strong physics framework, and gives students who may want to pursue additional academic interests the flexibility to do so. Both programs prepare students very well for graduate studies in physics, as well as for a variety of academic or research-related careers. Either option provides a considerable amount of time for exploration through electives. Students proceed at the pace and degree of specialization best suited to their individual capacities. Both options lead to the same degree: the Bachelor of Science in Physics.

Physics: Focused Option

This option—which includes three terms of quantum mechanics, 36 units of laboratory experience, and a thesis—is ideal preparation for a career in physics.

In the second year, students take:

Important skills for experimentation in physics may be acquired by starting an Undergraduate Research Opportunities Program (UROP)  project.

In the third year, students normally take laboratory subjects:

Students should also begin to take the restricted elective subjects, one in mathematics and at least two in physics. The mathematics subjects 18.04 Complex Variables with Applications , 18.075 Methods for Scientists and Engineers , and 18.06 Linear Algebra are particularly popular with physics majors. Topical elective subjects in astrophysics, biological physics, condensed matter, plasma, and nuclear and particle physics allow students to gain an appreciation of the forefronts of modern physics. Students intending to go on to graduate school in physics are encouraged to take the theoretical physics sequence:

An important component of this option is the thesis, which is a physics research project carried out under the guidance of a faculty member. Many thesis projects grow naturally out of UROP projects. Students should have some idea of a thesis topic by the middle of the junior year. A thesis proposal must be submitted before registering for thesis units and no later than Add Date of the fall term of the senior year.

A relatively large amount of elective time usually becomes available during the fourth year and can be used either to deepen one's background in physics or to explore other disciplines.

Physics: Flexible Option

This option is designed for students who wish to develop a strong background in the fundamentals of physics and then build on this foundation as they prepare for career paths that may or may not involve a graduate degree in physics. Many students find an understanding of the basic concepts of physics and an appreciation of the physicist's approach to problem solving an excellent preparation for the growing spectrum of nontraditional, technology-related career opportunities, as well as for careers in business, law, medicine, or engineering. Additionally, the flexible option makes it more possible for students with diverse intellectual interests to pursue a second major in another department.

The option begins with the core subjects:

Students round out their foundation material with either an additional quantum mechanics subject ( 8.05 Quantum Physics II ) or a subject in relativity ( 8.20 Introduction to Special Relativity or 8.033 Relativity ). There is an experimental requirement of 8.13 Experimental Physics I or, with the approval of the department, a laboratory subject of similar intensity in another department, an experimental research project or senior thesis, or an experimentally oriented summer externship. An exploration requirement consists of one elective subject in physics. Students can satisfy the departmental portion of the Communication Requirement by taking two of the following subjects:

The department and the Subcommittee on the Communication Requirement may accept substitution of one of the department's two required CI-M subjects with a CI-M subject in another department if it forms a natural part of the student's physics program.

Students following this option must also complete a focus requirement—three subjects forming one intellectually coherent unit in some area (not necessarily physics), subject to the approval of the department and separate from those used by the student to satisfy the HASS requirement. Areas of focus chosen by students have included astronomy, biology, computational physics, theoretical physics, nanotechnology, history of science, science and technology policy, philosophy, and science teaching. Some students may choose to satisfy their experimental and exploration requirements in the same area as their focus; others may opt for greater breadth by choosing other fields to fulfill these requirements.

Although students may choose this option at any time in their undergraduate career, many decide on the flexible major during their sophomore year in order to have enough time to craft a program that best suits their individual needs. Specific subject choices for the experimental and focus requirements require the written approval of the Flexible Program coordinator, Dr. Sean P. Robinson.

The Minor in Physics provides a solid foundation for the pursuit of a broad range of professional activities in science and engineering. The requirements for a Minor in Physics are as follows: 

Students should submit a completed Minor Application Form to Physics Academic Programs, Room 4-315. The Physics Department's minor coordinator is Shannon Larkin. See Undergraduate Education for more information on minor programs .

The Minor in Astronomy , offered jointly with the Department of Earth, Atmospheric, and Planetary Sciences, covers the observational and theoretical foundations of astronomy. For a description of the minor, see Interdisciplinary Programs.

Additional information concerning degree programs and research activities may be obtained by contacting the department office , Room 4-315, 617-253-4841.

Master of Science in Physics

Doctor of philosophy, graduate study.

The Physics Department offers programs leading to the degrees of Master of Science in Physics and Doctor of Philosophy.

Admission Requirements for Graduate Study

Students intending to pursue graduate work in physics should have as a background the equivalent of the requirements for the Bachelor of Science in Physics from MIT. However, students may make up some deficiencies over the course of their graduate work.

The normal degree program in the department leads to a PhD in Physics. Admission to a master's degree program in Physics is available only in special cases (e.g., US military officers). The requirements for the Master of Science in Physics are the same as the General Degree Requirements listed under Graduate Education. A master's thesis must represent a piece of independent research work in any of the fields described below, and must be carried out under the supervision of a department faculty member. No fixed time is set for the completion of a master's program; two years of work is a rough guideline. There is no language requirement for this degree.

Candidates for the Doctor of Philosophy or Doctor of Science are expected to enroll in those basic graduate subjects that prepare them for the general examination, which must be passed no later than in the seventh term after initial enrollment. Students are required to take two subjects in the candidate's doctoral research area (specialty requirement) and two subjects outside the candidate's field of specialization (breadth requirement). In addition, all students in the first year of the PhD program must enroll in two semesters of 8.398, a seminar specifically for first-year students. Half of the breadth requirement may be satisfied through a departmentally approved industrial internship. The doctoral thesis must represent a substantial piece of original research, carried out under the supervision of a department faculty member.

The Physics Department faculty members offer subjects of instruction and are engaged in research in a variety of fields in experimental and theoretical physics. This broad spectrum of activities is organized in the divisional structure of the department, presented below. Graduate students are encouraged to contact faculty members in the division of their choice to inquire about opportunities for research, and to pass through an apprenticeship (by signing up for Pre-Thesis Research) as a first step toward an engagement in independent research for a doctoral thesis.

Research Divisions

Faculty and students in the Department of Physics are generally affiliated with one of several research divisions:

• Astrophysics
• Experimental Nuclear and Particle Physics
• Atomic Physics, Biophysics, Condensed Matter Physics, and Plasma Physics
• Theoretical Nuclear and Particle Physics

Much of the research in the department is carried out as part of the work of various interdisciplinary laboratories and centers, including the Center for Materials Science and Engineering, Francis Bitter Magnet Laboratory, Haystack Observatory, Laboratory for Nuclear Science, Microsystems Technology Laboratories, MIT Kavli Institute for Astrophysics and Space Research, Plasma Science and Fusion Center, Research Laboratory of Electronics, and Spectroscopy Laboratory. Additional information about interdisciplinary laboratories and centers can be found under Research and Study . These facilities provide close relationships among the research activities of a number of MIT departments and give students opportunities for contact with research carried out in disciplines other than physics.

Additional information on degree programs, research activities, admissions, financial aid, teaching and research assistantships may be obtained by contacting the department office , Room 4-315, 617-253-4851.

Faculty and Teaching Staff

Deepto Chakrabarty, PhD

Professor of Physics

Head, Department of Physics

Lindley Winslow, PhD

Associate Head, Department of Physics

Raymond Ashoori, PhD

Edmund Bertschinger, PhD

Claude R. Canizares, PhD

Bruno B. Rossi Distinguished Professor Post-Tenure in Experimental Physics

Paola Cappellaro, PhD

Ford Professor of Engineering

Professor of Nuclear Science and Engineering

(On leave, spring)

Arup K. Chakraborty, PhD

John M. Deutch Institute Professor

Robert T. Haslam (1911) Professor in Chemical Engineering

Professor of Chemistry

Core Faculty, Institute for Medical Engineering and Science

Isaac Chuang, PhD

Professor of Electrical Engineering

Janet Conrad, PhD

William Detmold, PhD

(On leave, fall)

Matthew J. Evans, PhD

Mathworks Physics Professor

Peter H. Fisher, PhD

Thomas A. Frank (1977) Professor of Physics

Associate Vice President for Research Computing and Data

Joseph A. Formaggio, PhD

Anna L. Frebel, PhD

Liang Fu, PhD

Nuh Gedik, PhD

Donner Professor of Physics

Jeff Gore, PhD

Alan Guth, PhD

Victor F. Weisskopf Professor in Physics

Aram W. Harrow, PhD

Jacqueline N. Hewitt, PhD

Julius A. Stratton Professor

Scott A. Hughes, PhD

Robert L. Jaffe, PhD

Otto (1939) and Jane Morningstar Professor Post-Tenure of Science

Professor Post-Tenure of Physics

Pablo Jarillo-Herrero, PhD

Cecil and Ida Green Professor of Physics

John D. Joannopoulos, PhD

Francis Wright Davis Professor

Steven G. Johnson, PhD

Professor of Mathematics

David I. Kaiser, PhD

Germeshausen Professor of the History of Science

Mehran Kardar, PhD

Francis L. Friedman Professor of Physics

Wolfgang Ketterle, PhD

John D. MacArthur Professor

Patrick A. Lee, PhD

William and Emma Rogers Professor

Yen-Jie Lee, PhD

Class of 1958 Career Development Professor

Leonid Levitov, PhD

Hong Liu, PhD

Nuno F. Loureiro, PhD

Herman Feshbach (1942) Professor of Physics

Nergis Mavalvala, PhD

Curtis (1963) and Kathleen Marble Professor

Dean, School of Science

Richard G. Milner, PhD

Leonid A. Mirny, PhD

Richard J. Cohen (1976) Professor in Medicine and Biomedical Physics

Ernest J. Moniz, PhD

Cecil and Ida Green Distinguished Professor

Professor Post-Tenure of Engineering Systems

William D. Oliver, PhD

Henry Ellis Warren (1894) Professor

Professor of Electrical Engineering and Computer Science

Christoph M. E. Paus, PhD

Miklos Porkolab, PhD

David E. Pritchard, PhD

Cecil and Ida Green Professor Post-Tenure of Physics

Krishna Rajagopal, PhD

William A. M. Burden Professor of Physics

Gunther M. Roland, PhD

Sara Seager, PhD

Class of 1941 Professor of Planetary Sciences

Professor of Aeronautics and Astronautics

Robert A. Simcoe, PhD

Tracy Robyn Slatyer, PhD

Marin Soljačić, PhD

Iain Stewart, PhD

Otto (1939) and Jane Morningstar Professor of Science

Washington Taylor IV, PhD

Max Erik Tegmark, PhD

Jesse Thaler, PhD

Member, Institute for Data, Systems, and Society

Samuel C. C. Ting, PhD

Thomas D. Cabot Institute Professor

Senthil Todadri, PhD

Mark Vogelsberger, PhD

Vladan Vuletić, PhD

Lester Wolfe Professor

Xiao-Gang Wen, PhD

Cecil and Ida Green Professor in Physics

Frank Wilczek, PhD

Herman Feshbach (1942) Professor Post-Tenure of Physics

Michael Williams, PhD

Boleslaw Wyslouch, PhD

Barton Zwiebach, PhD

Martin Wolfram Zwierlein, PhD

Associate Professors

Joseph George Checkelsky, PhD

Associate Professor of Physics

Riccardo Comin, PhD

Netta Engelhardt, PhD

Nikta Fakhri, PhD

Thomas D. and Virginia W. Cabot Associate Professor of Physics

Daniel Harlow, PhD

Philip Harris, PhD

Or Hen, PhD

Erin Kara, PhD

Kiyoshi Masui, PhD

Michael McDonald, PhD

Max Metlitski, PhD

Phiala E. Shanahan, PhD

Class of 1957 Career Development Professor

Julien Tailleur, PhD

Salvatore Vitale, PhD

Assistant Professors

Soonwon Choi, PhD

Assistant Professor of Physics

Anna-Christina Eilers, PhD

Richard J. Fletcher, PhD

Ronald Garcia Ruiz, PhD

Long Ju, PhD

Sarah Millholland, PhD

Lina Necib, PhD

Shu-Heng Shao, PhD

Eluned Smith, PhD

Andrew Vanderburg, PhD

Visiting Associate Professors

Ibrahim I. Cissé, PhD

Visiting Associate Professor of Physics

Senior Lecturers

Peter Dourmashkin, PhD

Senior Lecturer in Physics

Erik Katsavounidis, PhD

Mohamed Abdelhafez, PhD

Lecturer in Physics

Byron Drury, PhD

Sean P. Robinson, PhD

Senior Technical Instructor of Physics

Alex Shvonski, PhD

Michelle Tomasik, PhD

Technical Instructors

Rosi Anderson, BS

Technical Instructor of Physics

Caleb C. Bonyun, MS

Aidan MacDonagh, BSE

Senior Technical Instructor of Digital Learning

Christopher Miller, BS

Aaron Pilarcik, MS

Joshua Wolfe, BS

Research Staff

Senior research scientists.

Earl S. Marmar, PhD

Senior Research Scientist of Physics

Jagadeesh Moodera, PhD

Richard J. Temkin, PhD

Professors Emeriti

John Winston Belcher, PhD

Class of 1922 Professor Emeritus

Professor Emeritus of Physics

George B. Benedek, PhD

Alfred H. Caspary Professor Emeritus of Physics

Professor Emeritus of Biological Physics

Ahmet Nihat Berker, PhD

William Bertozzi, PhD

Robert J. Birgeneau, PhD

Hale V. Bradt, PhD

Wit Busza, PhD

Min Chen, PhD

Bruno Coppi, PhD

Edward Farhi, PhD

Cecil and Ida Green Professor Emeritus of Physics

Daniel Z. Freedman, PhD

Professor Emeritus of Mathematics

Jerome I. Friedman, PhD

Institute Professor Emeritus

Jeffrey Goldstone, PhD

Thomas J. Greytak, PhD

Lester Wolfe Professor Emeritus of Physics

Lee Grodzins, PhD

Erich P. Ippen, PhD

Elihu Thomson Professor Emeritus

Professor Emeritus of Electrical Engineering

Paul Christopher Joss, PhD

Marc A. Kastner, PhD

Donner Professor of Science Emeritus

Vera Kistiakowsky, PhD

Professor Emerita of Physics

Daniel Kleppner, PhD

Lester Wolfe Professor Emeritus

Stanley B. Kowalski, PhD

J. David Litster, PhD

Earle L. Lomon, PhD

June Lorraine Matthews, PhD

John W. Negele, PhD

William A. Coolidge Professor Emeritus

Irwin A. Pless, PhD

Saul A. Rappaport, PhD

Robert P. Redwine, PhD

Lawrence Rosenson, PhD

Paul L. Schechter, PhD

William A. M. Burden Professor Emeritus in Astrophysics

Rainer Weiss, PhD

James E. Young, PhD

Undergraduate Subjects

8.006 exploring physics using python (new).

Prereq: None. Coreq: 6.100L ; or permission of instructor U (Fall) 2-0-1 units

Reviews and reinforces 6.100L topics, making connections and studying interesting physical systems (from abstract knowledge of concepts to modeling, coding, and evaluating results) that are relevant to physicists. Classes are active and interactive. Students apply programming skills to introductory physics problems and explore the role of simulations on physics. Limited to 12.

8.01 Physics I

Prereq: None U (Fall) 3-2-7 units. PHYSICS I Credit cannot also be received for 8.011 , 8.012 , 8.01L , ES.801 , ES.8012

Introduces classical mechanics. Space and time: straight-line kinematics; motion in a plane; forces and static equilibrium; particle dynamics, with force and conservation of momentum; relative inertial frames and non-inertial force; work, potential energy and conservation of energy; kinetic theory and the ideal gas; rigid bodies and rotational dynamics; vibrational motion; conservation of angular momentum; central force motions; fluid mechanics. Subject taught using the TEAL (Technology-Enabled Active Learning) format which features students working in groups of three, discussing concepts, solving problems, and doing table-top experiments with the aid of computer data acquisition and analysis.

J. Formaggio, P. Dourmashkin

8.011 Physics I

Prereq: Permission of instructor U (Spring) 5-0-7 units. PHYSICS I Credit cannot also be received for 8.01 , 8.012 , 8.01L , ES.801 , ES.8012

Introduces classical mechanics. Space and time: straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics. Designed for students with previous experience in 8.01 ; the subject is designated as 8.01 on the transcript.

8.012 Physics I

Prereq: None U (Fall) 5-0-7 units. PHYSICS I Credit cannot also be received for 8.01 , 8.011 , 8.01L , ES.801 , ES.8012

Elementary mechanics, presented in greater depth than in 8.01 . Newton's laws, concepts of momentum, energy, angular momentum, rigid body motion, and non-inertial systems. Uses elementary calculus freely; concurrent registration in a math subject more advanced than 18.01 is recommended. In addition to covering the theoretical subject matter, students complete a small experimental project of their own design. First-year students admitted via AP or Math Diagnostic for Physics Placement results.

M. Soljacic

8.01L Physics I

Prereq: None U (Fall, IAP) 3-2-7 units. PHYSICS I Credit cannot also be received for 8.01 , 8.011 , 8.012 , ES.801 , ES.8012

Introduction to classical mechanics (see description under 8.01 ). Includes components of the TEAL (Technology-Enabled Active Learning) format. Material covered over a longer interval so that the subject is completed by the end of the IAP. Substantial emphasis given to reviewing and strengthening necessary mathematics tools, as well as basic physics concepts and problem-solving skills. Content, depth, and difficulty is otherwise identical to that of 8.01 . The subject is designated as 8.01 on the transcript.

P. Jarillo-Herrero

8.02 Physics II

Prereq: Calculus I (GIR) and Physics I (GIR) U (Fall, Spring) 3-2-7 units. PHYSICS II Credit cannot also be received for 8.021 , 8.022 , ES.802 , ES.8022

Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric currents, magnetic fields and Ampere's law. Magnetic materials. Time-varying fields and Faraday's law of induction. Basic electric circuits. Electromagnetic waves and Maxwell's equations. Subject taught using the TEAL (Technology Enabled Active Learning) studio format which utilizes small group interaction and current technology to help students develop intuition about, and conceptual models of, physical phenomena.

J. Belcher, I. Cisse

8.021 Physics II

Prereq: Calculus I (GIR) , Physics I (GIR) , and permission of instructor U (Fall) 5-0-7 units. PHYSICS II Credit cannot also be received for 8.02 , 8.022 , ES.802 , ES.8022

Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric currents, magnetic fields and Ampere's law. Magnetic materials. Time-varying fields and Faraday's law of induction. Basic electric circuits. Electromagnetic waves and Maxwell's equations. Designed for students with previous experience in 8.02 ; the subject is designated as 8.02 on the transcript. Enrollment limited.

J. Checkelsky

8.022 Physics II

Prereq: Physics I (GIR) ; Coreq: Calculus II (GIR) U (Fall, Spring) 5-0-7 units. PHYSICS II Credit cannot also be received for 8.02 , 8.021 , ES.802 , ES.8022

Parallel to 8.02 , but more advanced mathematically. Some knowledge of vector calculus assumed. Maxwell's equations, in both differential and integral form. Electrostatic and magnetic vector potential. Properties of dielectrics and magnetic materials. In addition to the theoretical subject matter, several experiments in electricity and magnetism are performed by the students in the laboratory.

8.03 Physics III

Prereq: Calculus II (GIR) and Physics II (GIR) U (Fall, Spring) 5-0-7 units. REST

Mechanical vibrations and waves; simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations, and normal modes; vibrations of continuous systems; reflection and refraction; phase and group velocity. Optics; wave solutions to Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhofer diffraction, and gratings.

Y-J. Lee, R. Comin

8.033 Relativity

Prereq: Calculus II (GIR) and Physics II (GIR) U (Fall) 5-0-7 units. REST

Einstein's postulates; consequences for simultaneity, time dilation, length contraction, and clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy, and mass; particle collisions. Relativity and electricity; Coulomb's law; magnetic fields. Brief introduction to Newtonian cosmology. Introduction to some concepts of general relativity; principle of equivalence. The Schwarzchild metric; gravitational red shift; particle and light trajectories; geodesics; Shapiro delay.

8.04 Quantum Physics I

Prereq: 8.03 and ( 18.03 or 18.032 ) U (Spring) 5-0-7 units. REST Credit cannot also be received for 8.041

Experimental basis of quantum physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, deBroglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials and introduction to hydrogenic systems.

8.041 Quantum Physics I

Prereq: 8.03 and ( 18.03 or 18.032 ) U (Fall) 2-0-10 units. REST Credit cannot also be received for 8.04

Blended version of 8.04 using a combination of online and in-person instruction. Covers the experimental basis of quantum physics: Mach-Zender interferometers, the photoelectric effect, Compton scattering, and de Broglie waves. Heisenberg uncertainty principle and momentum space. Introduction to wave mechanics: Schroedinger's equation, probability amplitudes, and wave packets. Stationary states and the spectrum of one-dimensional potentials, including the variational principle, the Hellmann-Feynman lemma, the virial theorem, and the harmonic oscillator. Basics of angular momentum, central potentials, and the hydrogen atom. Introduction to the Stern-Gerlach experiment, spin one-half, spin operators, and spin states.

8.044 Statistical Physics I

Prereq: 8.03 and 18.03 U (Spring) 5-0-7 units

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third laws of thermodynamics. Numerous examples illustrating a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices. Concurrent enrollment in 8.04 is recommended.

8.05 Quantum Physics II

Prereq: 8.04 or 8.041 U (Fall) 5-0-7 units Credit cannot also be received for 8.051

Vector spaces, linear operators, and matrix representations.  Inner products and adjoint operators. Commutator identities. Dirac's Bra-kets. Uncertainty principle and energy-time version. Spectral theorem and complete set of commuting observables. Schrodinger and Heisenberg pictures.  Axioms of quantum mechanics. Coherent states and nuclear magnetic resonance. Multiparticle states and tensor products. Quantum teleportation, EPR and Bell inequalities. Angular momentum and central potentials. Addition of angular momentum. Density matrices, pure and mixed states, decoherence.

B. Zwiebach

8.051 Quantum Physics II

Prereq: 8.04 and permission of instructor U (Spring) 2-0-10 units Credit cannot also be received for 8.05

Blended version of 8.05 using a combination of online and in-person instruction. Together with 8.06 covers quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wave functions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen. Limited to 20.

Fall: Staff Spring: W. Detmold

8.06 Quantum Physics III

Prereq: 8.05 U (Spring) 5-0-7 units

Continuation of 8.05 . Units: natural units, scales of microscopic phenomena, applications. Time-independent approximation methods: degenerate and nondegenerate perturbation theory, variational method, Born-Oppenheimer approximation, applications to atomic and molecular systems. The structure of one- and two-electron atoms: overview, spin-orbit and relativistic corrections, fine structure, variational approximation, screening, Zeeman and Stark effects. Charged particles in a magnetic field: Landau levels and integer quantum hall effect. Scattering: general principles, partial waves, review of one-dimension, low-energy approximations, resonance, Born approximation. Time-dependent perturbation theory. Students research and write a paper on a topic related to the content of 8.05 and 8.06 .

8.07 Electromagnetism II

Prereq: 8.03 and 18.03 U (Fall) 4-0-8 units

Survey of basic electromagnetic phenomena: electrostatics, magnetostatics; electromagnetic properties of matter. Time-dependent electromagnetic fields and Maxwell's equations. Electromagnetic waves, emission, absorption, and scattering of radiation. Relativistic electrodynamics and mechanics.

8.08 Statistical Physics II

Prereq: 8.044 and 8.05 U (IAP) 4-0-8 units

Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations.

Staff, L. Fu

8.09 Classical Mechanics III

Subject meets with 8.309 Prereq: 8.223 U (Spring) 4-0-8 units

Covers Lagrangian and Hamiltonian mechanics, systems with constraints, rigid body dynamics, vibrations, central forces, Hamilton-Jacobi theory, action-angle variables, perturbation theory, and continuous systems. Provides an introduction to ideal and viscous fluid mechanics, including turbulence, as well as an introduction to nonlinear dynamics, including chaos. Students taking graduate version complete different assignments.

Undergraduate Laboratory and Special Project Subjects

8.10 exploring and communicating physics (and other) frontiers.

Prereq: None U (Fall) Not offered regularly; consult department 2-0-0 units

Features a series of 12 interactive sessions that span a wide variety of topics at the frontiers of science - e.g., quantum computing, dark matter, the nature of time - and encourage independent thinking. Discussions draw from the professor's published pieces in periodicals as well as short excerpts from his books.  Also discusses, through case studies, the process of writing and re-writing. Subject can count toward the 6-unit discovery-focused credit limit for first year students.

8.13 Experimental Physics I

Prereq: 8.04 U (Fall, Spring) 0-6-12 units. Institute LAB

First in a two-term advanced laboratory sequence in modern physics focusing on the professional and personal development of the student as a scientist through the medium of experimental physics. Experimental options cover special relativity, experimental foundations of quantum mechanics, atomic structure and optics, statistical mechanics, and nuclear and particle physics. Uses modern physics experiments to develop laboratory technique, systematic troubleshooting, professional scientific attitude, data analysis skills and reasoning about uncertainty. Provides extensive training in oral and written communication methods. Limited to 12 students per section.

J. Conrad, N. Fakhri, C. Paus, G. Roland

8.14 Experimental Physics II

Prereq: 8.05 and 8.13 U (Spring) 0-6-12 units

Second in a two-term advanced laboratory sequence in modern physics focusing on the professional and personal development of the student as a scientist through the medium of experimental physics. Experimental options cover special relativity, experimental foundations of quantum mechanics, atomic structure and optics, statistical mechanics, and nuclear and particle physics. Uses modern physics experiments to develop laboratory technique, systematic troubleshooting, professional scientific attitude, data analysis skills, and reasoning about uncertainty; provides extensive training in oral and written communication methods. Continues 8.13 practice in these skills using more advanced experiments and adds an exploratory project element in which students develop an experiment from the proposal and design stage to a final presentation of results in a poster session. Limited to 12 students per section.

8.16 Data Science in Physics

Subject meets with 8.316 Prereq: 8.04 and ( 6.100A , 6.100B , or permission of instructor) U (Spring) 3-0-9 units

Aims to present modern computational methods by providing realistic, contemporary examples of how these computational methods apply to physics research. Designed around research modules in which each module provides experience with a specific scientific challenge. Modules include: analyzing LIGO open data; measuring electroweak boson to quark decays; understanding the cosmic microwave background; and lattice QCD/Ising model. Experience in Python helpful but not required. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Students taking graduate version complete additional assignments.

8.18 Research Problems in Undergraduate Physics

Prereq: Permission of instructor U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

Opportunity for undergraduates to engage in experimental or theoretical research under the supervision of a staff member. Specific approval required in each case.

Consult N. Mavalvala

8.19 Readings in Physics

Prereq: None U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

Supervised reading and library work. Choice of material and allotment of time according to individual needs. For students who want to do work not provided for in the regular subjects. Specific approval required in each case.

Undergraduate Elective Subjects

8.20 introduction to special relativity.

Prereq: Calculus I (GIR) and Physics I (GIR) U (IAP) 2-0-7 units. REST

Introduces the basic ideas and equations of Einstein's special theory of relativity. Topics include Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of general relativity. Intended for freshmen and sophomores. Not usable as a restricted elective by Physics majors. Credit cannot be received for 8.20 if credit for 8.033 is or has been received in the same or prior terms.

8.21 Physics of Energy

Prereq: Calculus II (GIR) , Chemistry (GIR) , and Physics II (GIR) U (Spring) 5-0-7 units. REST

A comprehensive introduction to the fundamental physics of energy systems that emphasizes quantitative analysis. Focuses on the fundamental physical principles underlying energy processes and on the application of these principles to practical calculations. Applies mechanics and electromagnetism to energy systems; introduces and applies basic ideas from thermodynamics, quantum mechanics, and nuclear physics. Examines energy sources, conversion, transport, losses, storage, conservation, and end uses. Analyzes the physics of side effects, such as global warming and radiation hazards. Provides students with technical tools and perspective to evaluate energy choices quantitatively at both national policy and personal levels.

8.223 Classical Mechanics II

Prereq: Calculus II (GIR) and Physics I (GIR) U (IAP) 2-0-4 units

A broad, theoretical treatment of classical mechanics, useful in its own right for treating complex dynamical problems, but essential to understanding the foundations of quantum mechanics and statistical physics. Generalized coordinates, Lagrangian and Hamiltonian formulations, canonical transformations, and Poisson brackets. Applications to continuous media. The relativistic Lagrangian and Maxwell's equations.

8.224 Exploring Black Holes: General Relativity and Astrophysics

Prereq: 8.033 or 8.20 Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Fall) 3-0-9 units

Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat space-time; the metric; curvature of space-time near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the term is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advanced models of the cosmos. Subject has online components that are open to selected MIT alumni. Alumni wishing to participate should contact Professor Bertschinger at [email protected]. Limited to 40.

E. Bertschinger

8.225[J] Einstein, Oppenheimer, Feynman: Physics in the 20th Century

Same subject as STS.042[J] Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 3-0-9 units. HASS-H

See description under subject STS.042[J] . Enrollment limited.

D. I. Kaiser

8.226 Forty-three Orders of Magnitude

Prereq: ( 8.04 and 8.044 ) or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 3-0-9 units

Examines the widespread societal implications of current scientific discoveries in physics across forty-three orders of magnitude in length scale. Addresses topics ranging from climate change to nuclear nonproliferation. Students develop their ability to express concepts at a level accessible to the public and to present a well-reasoned argument on a topic that is a part of the national debate. Requires diverse writing assignments, including substantial papers. Enrollment limited.

8.228 Relativity II

Prereq: 8.033 or permission of instructor U (IAP) 2-0-4 units

A fast-paced and intensive introduction to general relativity, covering advanced topics beyond the 8.033 curriculum. Provides students with a foundation for research relying on knowledge of general relativity, including gravitational waves and cosmology. Additional topics in curvature, weak gravity, and cosmology.

8.231 Physics of Solids I

Prereq: 8.044 ; Coreq: 8.05 U (Fall) 4-0-8 units

Introduction to the basic concepts of the quantum theory of solids. Topics: periodic structure and symmetry of crystals; diffraction; reciprocal lattice; chemical bonding; lattice dynamics, phonons, thermal properties; free electron gas; model of metals; Bloch theorem and band structure, nearly free electron approximation; tight binding method; Fermi surface; semiconductors, electrons, holes, impurities; optical properties, excitons; and magnetism.

8.241 Introduction to Biological Physics

Prereq: Physics II (GIR) and ( 8.044 or ( 5.601 and 5.602 )) Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 4-0-8 units Credit cannot also be received for 20.315 , 20.415

Introduces the main concepts of biological physics, with a focus on biophysical phenomena at the molecular and cellular scales. Presents the role of entropy and diffusive transport in living matter; challenges to life resulting from the highly viscous environment present at microscopic scales, including constraints on force, motion and transport within cells, tissues, and fluids; principles of how cellular machinery (e.g., molecular motors) can convert electro-chemical energy sources to mechanical forces and motion. Also covers polymer physics relevant to DNA and other biological polymers, including the study of configurations, fluctuations, rigidity, and entropic elasticity. Meets with 20.315 and 20.415 when offered concurrently.

8.245[J] Viruses, Pandemics, and Immunity

Same subject as 5.003[J] , 10.382[J] , HST.439[J] Subject meets with 5.002[J] , 10.380[J] , HST.438[J] Prereq: None U (Spring) Not offered regularly; consult department 2-0-1 units

See description under subject HST.439[J] . HST.438[J] intended for first-year students; all others should take HST.439[J] .

A. Chakraborty

8.251 String Theory for Undergraduates

Prereq: 8.033 , 8.044 , and 8.05 Acad Year 2024-2025: U (Spring) Acad Year 2025-2026: Not offered 4-0-8 units Credit cannot also be received for 8.821

Introduction to the main concepts of string theory, i.e., quantum mechanics of a relativistic string. Develops aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics, including the study of D-branes and string thermodynamics. Meets with 8.821 when offered concurrently.

8.276 Nuclear and Particle Physics

Prereq: 8.033 and 8.04 U (Spring) Not offered regularly; consult department 4-0-8 units

Presents a modern view of the fundamental structure of matter. Starting from the Standard Model, which views leptons and quarks as basic building blocks of matter, establishes the properties and interactions of these particles. Explores applications of this phenomenology to both particle and nuclear physics. Emphasizes current topics in nuclear and particle physics research at MIT. Intended for students with a basic knowledge of relativity and quantum physics concepts.

M. Williams

8.277 Introduction to Particle Accelerators

Prereq: ( 6.2300 or 8.07 ) and permission of instructor U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

Principles of acceleration: beam properties; linear accelerators, synchrotrons, and storage rings. Accelerator technologies: radio frequency cavities, bending and focusing magnets, beam diagnostics. Particle beam optics and dynamics. Special topics: measures of accelerators performance in science, medicine and industry; synchrotron radiation sources; free electron lasers; high-energy colliders; and accelerators for radiation therapy. May be repeated for credit for a maximum of 12 units.

W. Barletta

8.282[J] Introduction to Astronomy

Same subject as 12.402[J] Prereq: Physics I (GIR) U (Spring) 3-0-6 units. REST

Quantitative introduction to the physics of planets, stars, galaxies and our universe, from origin to ultimate fate, with emphasis on the physics tools and observational techniques that enable our understanding. Topics include our solar system, extrasolar planets; our Sun and other "normal" stars, star formation, evolution and death, supernovae, compact objects (white dwarfs, neutron stars, pulsars, stellar-mass black holes); galactic structure, star clusters, interstellar medium, dark matter; other galaxies, quasars, supermassive black holes, gravitational waves; cosmic large-scale structure, origin, evolution and fate of our universe, inflation, dark energy, cosmic microwave background radiation, gravitational lensing, 21cm tomography. Not usable as a restricted elective by Physics majors.

8.284 Modern Astrophysics

Prereq: 8.04 U (Fall) 3-0-9 units

Application of physics (Newtonian, statistical, and quantum mechanics; special and general relativity) to fundamental processes that occur in celestial objects. Includes main-sequence stars, collapsed stars (white dwarfs, neutron stars, and black holes), pulsars, galaxies, active galaxies, quasars, and cosmology. Electromagnetic and gravitational radiation signatures of astrophysical phenomena explored through examination of observational data. No prior knowledge of astronomy required.

8.286 The Early Universe

Prereq: Physics II (GIR) and 18.03 Acad Year 2024-2025: U (Fall) Acad Year 2025-2026: Not offered 3-0-9 units. REST

Introduction to modern cosmology. First half deals with the development of the big bang theory from 1915 to 1980, and latter half with recent impact of particle theory. Topics: special relativity and the Doppler effect, Newtonian cosmological models, introduction to non-Euclidean spaces, thermal radiation and early history of the universe, big bang nucleosynthesis, introduction to grand unified theories and other recent developments in particle theory, baryogenesis, the inflationary universe model, and the evolution of galactic structure.

8.287[J] Observational Techniques of Optical Astronomy

Same subject as 12.410[J] Prereq: 8.282[J] , 12.409 , or other introductory astronomy course U (Fall) 3-4-8 units. Institute LAB

See description under subject 12.410[J] . Limited to 18; preference to Course 8 and Course 12 majors and minors.

M. Person, R. Teague

8.290[J] Extrasolar Planets: Physics and Detection Techniques

Same subject as 12.425[J] Subject meets with 12.625 Prereq: 8.03 and 18.03 U (Fall) 3-0-9 units. REST

See description under subject 12.425[J] .

8.292[J] Fluid Physics

Same subject as 1.066[J] , 12.330[J] Prereq: 5.60, 8.044 , or permission of instructor U (Spring) 3-0-9 units

A physics-based introduction to the properties of fluids and fluid systems, with examples drawn from a broad range of sciences, including atmospheric physics and astrophysics. Definitions of fluids and the notion of continuum. Equations of state and continuity, hydrostatics and conservation of momentum; ideal fluids and Euler's equation; viscosity and the Navier-Stokes equation. Energy considerations, fluid thermodynamics, and isentropic flow. Compressible versus incompressible and rotational versus irrotational flow; Bernoulli's theorem; steady flow, streamlines and potential flow. Circulation and vorticity. Kelvin's theorem. Boundary layers. Fluid waves and instabilities. Quantum fluids.

L. Bourouiba

8.295 Practical Experience in Physics

Prereq: None U (Fall, IAP, Spring, Summer) 0-1-0 units Can be repeated for credit.

For Course 8 students participating in off-campus experiences in physics. Before registering for this subject, students must have an internship offer from a company or organization and must identify a Physics advisor. Upon completion of the project, student must submit a letter from the company or organization describing the work accomplished, along with a substantive final report from the student approved by the MIT advisor. Subject to departmental approval. Consult departmental academic office.

8.298 Selected Topics in Physics

Prereq: Permission of instructor U (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Presentation of topics of current interest, with content varying from year to year.

Consult I. Stewart

8.299 Physics Teaching

Prereq: None U (Fall, Spring) Units arranged [P/D/F] Can be repeated for credit.

For qualified undergraduate students interested in gaining some experience in teaching. Laboratory, tutorial, or classroom teaching under the supervision of a faculty member. Students selected by interview.

8.EPE UPOP Engineering Practice Experience

Engineering School-Wide Elective Subject. Offered under: 1.EPE , 2.EPE , 3.EPE , 6.EPE , 8.EPE , 10.EPE , 15.EPE , 16.EPE , 20.EPE , 22.EPE Prereq: None U (Fall, Spring) 0-0-1 units Can be repeated for credit.

See description under subject 2.EPE . Application required; consult UPOP website for more information.

K. Tan-Tiongco, D. Fordell

8.S014 Special Subject: Physics (New)

Prereq: None U (IAP) 2-0-4 units

Opportunity for group study of subjects in physics not otherwise included in the curriculum.

K. Rajagopal

8.S02 Special Subject: Physics

Prereq: None U (Spring) Not offered regularly; consult department 1-0-2 units

P. Dourmashkin

8.S198 Special Subject: Physics (New)

Prereq: None U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

8.S199 Special Subject: Physics (New)

Prereq: None U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged [P/D/F]

8.S227 Special Subject: Physics

Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units

8.S271 Special Subject: Physics

Prereq: None Acad Year 2024-2025: U (Spring) Acad Year 2025-2026: Not offered 2-0-4 units

8.S30 Special Subject: Physics

Prereq: None Acad Year 2024-2025: U (Fall, Spring) Acad Year 2025-2026: Not offered Units arranged

A. Bernstein, J. Walsh

8.S50 Special Subject: Physics

Prereq: None U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit.

8.UR Undergraduate Research

Research opportunities in physics. For further information, contact the departmental UROP coordinator.

N. Mavalvala

8.THU Undergraduate Physics Thesis

Prereq: None U (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Program of research leading to the writing of an S.B. thesis; to be arranged by the student under approved supervision.

Information: N. Mavalvala

Graduate Subjects

8.309 classical mechanics iii.

Subject meets with 8.09 Prereq: None G (Spring) 4-0-8 units

8.311 Electromagnetic Theory I

Prereq: 8.07 G (Spring) 4-0-8 units

Basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional emf and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. Subject uses appropriate mathematics but emphasizes physical phenomena and principles.

8.315[J] Mathematical Methods in Nanophotonics

Same subject as 18.369[J] Prereq: 8.07 , 18.303 , or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

See description under subject 18.369[J] .

S. G. Johnson

8.316 Data Science in Physics

Subject meets with 8.16 Prereq: 8.04 and ( 6.100A , 6.100B , or permission of instructor) Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

8.321 Quantum Theory I

Prereq: 8.05 G (Fall) 4-0-8 units

A two-term subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron.

8.322 Quantum Theory II

Prereq: 8.07 and 8.321 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 4-0-8 units

8.323 Relativistic Quantum Field Theory I

Prereq: 8.321 G (Spring) 4-0-8 units

A one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics. Topics: classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields, spin fields, and Gauge bosons. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization.

8.324 Relativistic Quantum Field Theory II

Prereq: 8.322 and 8.323 G (Fall) 4-0-8 units

The second term of the quantum field theory sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: perturbation theory and Feynman diagrams, scattering theory, Quantum Electrodynamics, one loop renormalization, quantization of non-abelian gauge theories, the Standard Model of particle physics, other topics.

8.325 Relativistic Quantum Field Theory III

Prereq: 8.324 G (Spring) 4-0-8 units

The third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics: quantum chromodynamics; Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry.

8.333 Statistical Mechanics I

Prereq: 8.044 and 8.05 G (Fall) 4-0-8 units

First part of a two-subject sequence on statistical mechanics. Examines the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.

8.334 Statistical Mechanics II

Prereq: 8.333 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 4-0-8 units

Second part of a two-subject sequence on statistical mechanics. Explores topics from modern statistical mechanics: the hydrodynamic limit and classical field theories. Phase transitions and broken symmetries: universality, correlation functions, and scaling theory. The renormalization approach to collective phenomena. Dynamic critical behavior. Random systems.

8.351[J] Classical Mechanics: A Computational Approach

Same subject as 6.5160[J] , 12.620[J] Prereq: Physics I (GIR) , 18.03 , and permission of instructor G (Fall) 3-3-6 units

See description under subject 12.620[J] .

J. Wisdom, G. J. Sussman

8.370[J] Quantum Computation

Same subject as 2.111[J] , 6.6410[J] , 18.435[J] Prereq: 8.05 , 18.06 , 18.700 , 18.701 , or 18.C06[J] G (Fall) 3-0-9 units

See description under subject 18.435[J] .

I. Chuang, A. Harrow, P. Shor

8.371[J] Quantum Information Science

Same subject as 6.6420[J] , 18.436[J] Prereq: 18.435[J] G (Spring) 3-0-9 units

Examines quantum computation and quantum information. Topics include quantum circuits, the quantum Fourier transform and search algorithms, the quantum operations formalism, quantum error correction, Calderbank-Shor-Steane and stabilizer codes, fault tolerant quantum computation, quantum data compression, quantum entanglement, capacity of quantum channels, and quantum cryptography and the proof of its security. Prior knowledge of quantum mechanics required.

I. Chuang, A. Harrow

8.372 Quantum Information Science III

Prereq: 8.371[J] Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

Third subject in the Quantum Information Science (QIS) sequence, building on 8.370[J] and 8.371[J] . Further explores core topics in quantum information science, such as quantum information theory, error-correction, physical implementations, algorithms, cryptography, and complexity. Draws connections between QIS and related fields, such as many-body physics, and applications such as sensing.

8.381, 8.382 Selected Topics in Theoretical Physics

Prereq: Permission of instructor G (Fall, Spring) Not offered regularly; consult department 3-0-9 units

Topics of current interest in theoretical physics, varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.391 Pre-Thesis Research

Prereq: Permission of instructor G (Fall) Units arranged [P/D/F] Can be repeated for credit.

Advanced problems in any area of experimental or theoretical physics, with assigned reading and consultations.

8.392 Pre-Thesis Research

Prereq: Permission of instructor G (Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

8.395[J] Teaching College-Level Science and Engineering

Same subject as 1.95[J] , 5.95[J] , 7.59[J] , 18.094[J] Subject meets with 2.978 Prereq: None G (Fall) 2-0-2 units

See description under subject 5.95[J] .

8.396[J] Leadership and Professional Strategies & Skills Training (LEAPS), Part I: Advancing Your Professional Strategies and Skills

Same subject as 5.961[J] , 9.980[J] , 12.396[J] , 18.896[J] Prereq: None G (Spring; second half of term) 2-0-1 units

Part I (of two parts) of the LEAPS graduate career development and training series. Topics include: navigating and charting an academic career with confidence; convincing an audience with clear writing and arguments; mastering public speaking and communications; networking at conferences and building a brand; identifying transferable skills; preparing for a successful job application package and job interviews; understanding group dynamics and different leadership styles; leading a group or team with purpose and confidence. Postdocs encouraged to attend as non-registered participants. Limited to 80.

8.397[J] Leadership and Professional Strategies & Skills Training (LEAPS), Part II: Developing Your Leadership Competencies

Same subject as 5.962[J] , 9.981[J] , 12.397[J] , 18.897[J] Prereq: None G (Spring; first half of term) 2-0-1 units

Part II (of two parts) of the LEAPS graduate career development and training series. Topics covered include gaining self awareness and awareness of others, and communicating with different personality types; learning about team building practices; strategies for recognizing and resolving conflict and bias; advocating for diversity and inclusion; becoming organizationally savvy; having the courage to be an ethical leader; coaching, mentoring, and developing others; championing, accepting, and implementing change. Postdocs encouraged to attend as non-registered participants. Limited to 80.

8.398 Doctoral Seminar in Physics

Prereq: None G (Fall, Spring) 1-0-2 units Can be repeated for credit.

A seminar for first-year PhD students presenting topics of current interest, with content varying from year to year. Open only to first-year graduate students in Physics.

Consult J. Thaler

8.399 Physics Teaching

Prereq: Permission of instructor G (Fall, Spring) Units arranged [P/D/F] Can be repeated for credit.

For qualified graduate students interested in gaining some experience in teaching. Laboratory, tutorial, or classroom teaching under the supervision of a faculty member. Students selected by interview.

Consult C. Paus

Physics of Atoms, Radiation, Solids, Fluids, and Plasmas

8.421 atomic and optical physics i.

Prereq: 8.05 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

The first of a two-term subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical phsyics. The interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

M. Zwierlein

8.422 Atomic and Optical Physics II

Prereq: 8.05 Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

The second of a two-term subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical physics. Non-classical states of light- squeezed states; multi-photon processes, Raman scattering; coherence- level crossings, quantum beats, double resonance, superradiance; trapping and cooling- light forces, laser cooling, atom optics, spectroscopy of trapped atoms and ions; atomic interactions- classical collisions, quantum scattering theory, ultracold collisions; and experimental methods.

8.431[J] Nonlinear Optics

Same subject as 6.6340[J] Prereq: 6.2300 or 8.03 G (Spring) 3-0-9 units

See description under subject 6.6340[J] .

J. G. Fujimoto

8.481, 8.482 Selected Topics in Physics of Atoms and Radiation

Prereq: 8.321 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units

Presentation of topics of current interest, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.511 Theory of Solids I

Prereq: 8.231 G (Fall) 3-0-9 units

First term of a theoretical treatment of the physics of solids. Concept of elementary excitations. Symmetry- translational, rotational, and time-reversal invariances- theory of representations. Energy bands- electrons and phonons. Topological band theory. Survey of electronic structure of metals, semimetals, semiconductors, and insulators, excitons, critical points, response functions, and interactions in the electron gas. Theory of superconductivity.

8.512 Theory of Solids II

Prereq: 8.511 G (Spring) 3-0-9 units

Second term of a theoretical treatment of the physics of solids. Interacting electron gas: many-body formulation, Feynman diagrams, random phase approximation and beyond. General theory of linear response: dielectric function; sum rules; plasmons; optical properties; applications to semiconductors, metals, and insulators. Transport properties: non-interacting electron gas with impurities, diffusons. Quantum Hall effect: integral and fractional. Electron-phonon interaction: general theory, applications to metals, semiconductors and insulators, polarons, and field-theory description. Superconductivity: experimental observations, phenomenological theories, and BCS theory.

8.513 Many-Body Theory for Condensed Matter Systems

Prereq: 8.033 , 8.05 , 8.08 , and 8.231 Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

Concepts and physical pictures behind various phenomena that appear in interacting many-body systems. Visualization occurs through concentration on path integral, mean-field theories and semiclassical picture of fluctuations around mean-field state. Topics covered: interacting boson/fermion systems, Fermi liquid theory and bosonization, symmetry breaking and nonlinear sigma-model, quantum gauge theory, quantum Hall theory, mean-field theory of spin liquids and quantum order, string-net condensation and emergence of light and fermions.

8.514 Strongly Correlated Systems in Condensed Matter Physics

Prereq: 8.322 and 8.333 Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

Study of condensed matter systems where interactions between electrons play an important role. Topics vary depending on lecturer but may include low-dimension magnetic and electronic systems, disorder and quantum transport, magnetic impurities (the Kondo problem), quantum spin systems, the Hubbard model and high-temperature superconductors. Topics are chosen to illustrate the application of diagrammatic techniques, field-theory approaches, and renormalization group methods in condensed matter physics.

8.581, 8.582 Selected Topics in Condensed Matter Physics

Prereq: Permission of instructor Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units Can be repeated for credit.

Presentation of topics of current interest, with contents varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.590[J] Topics in Biophysics and Physical Biology

Same subject as 7.74[J] , 20.416[J] Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 2-0-4 units

Provides broad exposure to research in biophysics and physical biology, with emphasis on the critical evaluation of scientific literature. Weekly meetings include in-depth discussion of scientific literature led by distinct faculty on active research topics. Each session also includes brief discussion of non-research topics including effective presentation skills, writing papers and fellowship proposals, choosing scientific and technical research topics, time management, and scientific ethics.

J. Gore, N. Fakhri

8.591[J] Systems Biology

Same subject as 7.81[J] Subject meets with 7.32 Prereq: ( 18.03 and 18.05 ) or permission of instructor G (Fall) 3-0-9 units

Introduction to cellular and population-level systems biology with an emphasis on synthetic biology, modeling of genetic networks, cell-cell interactions, and evolutionary dynamics. Cellular systems include genetic switches and oscillators, network motifs, genetic network evolution, and cellular decision-making. Population-level systems include models of pattern formation, cell-cell communication, and evolutionary systems biology. Students taking graduate version explore the subject in more depth.

8.592[J] Statistical Physics in Biology

Same subject as HST.452[J] Prereq: 8.333 or permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

A survey of problems at the interface of statistical physics and modern biology: bioinformatic methods for extracting information content of DNA; gene finding, sequence comparison, phylogenetic trees. Physical interactions responsible for structure of biopolymers; DNA double helix, secondary structure of RNA, elements of protein folding. Considerations of force, motion, and packaging; protein motors, membranes. Collective behavior of biological elements; cellular networks, neural networks, and evolution.

M. Kardar, L. Mirny

8.593[J] Biological Physics

Same subject as HST.450[J] Prereq: 8.044 recommended but not necessary G (Spring) Not offered regularly; consult department 4-0-8 units

Designed to provide seniors and first-year graduate students with a quantitative, analytical understanding of selected biological phenomena. Topics include experimental and theoretical basis for the phase boundaries and equation of state of concentrated protein solutions, with application to diseases such as sickle cell anemia and cataract. Protein-ligand binding and linkage and the theory of allosteric regulation of protein function, with application to proteins as stores as transporters in respiration, enzymes in metabolic pathways, membrane receptors, regulators of gene expression, and self-assembling scaffolds. The physics of locomotion and chemoreception in bacteria and the biophysics of vision, including the theory of transparency of the eye, molecular basis of photo reception, and the detection of light as a signal-to-noise discrimination.

8.613[J] Introduction to Plasma Physics I

Same subject as 22.611[J] Prereq: ( 6.2300 or 8.07 ) and ( 18.04 or Coreq: 18.075 ) G (Fall) 3-0-9 units

See description under subject 22.611[J] .

N. Loureiro, I. Hutchinson

8.614[J] Introduction to Plasma Physics II

Same subject as 22.612[J] Prereq: 22.611[J] Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

See description under subject 22.612[J] .

N. Loureiro

8.624 Plasma Waves

Prereq: 22.611[J] Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

Comprehensive theory of electromagnetic waves in a magnetized plasma. Wave propagation in cold and hot plasmas. Energy flow. Absorption by Landau and cyclotron damping and by transit time magnetic pumping (TTMP). Wave propagation in inhomogeneous plasma: accessibility, WKB theory, mode conversion, connection formulae, and Budden tunneling. Applications to RF plasma heating, wave propagation in the ionosphere and laser-plasma interactions. Wave propagation in toroidal plasmas, and applications to ion cyclotron (ICRF), electron cyclotron (ECRH), and lower hybrid (LHH) wave heating. Quasi-linear theory and applications to RF current drive in tokamaks. Extensive discussion of relevant experimental observations.

M. Porkolab

8.641 Physics of High-Energy Plasmas I

Prereq: 22.611[J] G (Fall) Not offered regularly; consult department 3-0-9 units

Physics of High-Energy Plasmas I and II address basic concepts of plasmas, with temperatures of thermonuclear interest, relevant to fusion research and astrophysics. Microscopic transport processes due to interparticle collisions and collective modes (e.g., microinstabilities). Relevant macroscopic transport coefficients (electrical resistivity, thermal conductivities, particle "diffusion"). Runaway and slide-away regimes. Magnetic reconnection processes and their relevance to experimental observations. Radiation emission from inhomogeneous plasmas. Conditions for thermonuclear burning and ignition (D-T and "advanced" fusion reactions, plasmas with polarized nuclei). Role of "impurity" nuclei. "Finite-β" (pressure) regimes and ballooning modes. Convective modes in configuration and velocity space. Trapped particle regimes. Nonlinear and explosive instabilities. Interaction of positive and negative energy modes. Each subject can be taken independently.

8.642 Physics of High-Energy Plasmas II

8.670[j] principles of plasma diagnostics.

Same subject as 22.67[J] Prereq: 22.611[J] Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 4-4-4 units

See description under subject 22.67[J] .

J. Hare, A. White

8.681, 8.682 Selected Topics in Fluid and Plasma Physics

Prereq: 22.611[J] G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Presentation of topics of current interest, with content varying from year to year. Subject not routinely offered; given when interest is indicated.

Consult M. Porkolab

Nuclear and Particle Physics

8.701 introduction to nuclear and particle physics.

Prereq: None. Coreq: 8.321 G (Fall) 3-0-9 units

The phenomenology and experimental foundations of particle and nuclear physics; the fundamental forces and particles, composites. Interactions of particles with matter, and detectors. SU(2), SU(3), models of mesons and baryons. QED, weak interactions, parity violation, lepton-nucleon scattering, and structure functions. QCD, gluon field and color. W and Z fields, electro-weak unification, the CKM matrix. Nucleon-nucleon interactions, properties of nuclei, single- and collective- particle models. Electron and hadron interactions with nuclei. Relativistic heavy ion collisions, and transition to quark-gluon plasma.

8.711 Nuclear Physics

Prereq: 8.321 and 8.701 G (Spring) 4-0-8 units

Modern, advanced study in the experimental foundations and theoretical understanding of the structure of nuclei, beginning with the two- and three-nucleon problems. Basic nuclear properties, collective and single-particle motion, giant resonances, mean field models, interacting boson model. Nuclei far from stability, nuclear astrophysics, big-bang and stellar nucleosynthesis. Electron scattering: nucleon momentum distributions, scaling, olarization observables. Parity-violating electron scattering. Neutrino physics. Current results in relativistic heavy ion physics and hadronic physics. Frontiers and future facilities.

8.712 Advanced Topics in Nuclear Physics

Prereq: 8.711 or permission of instructor G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Subject for experimentalists and theorists with rotation of the following topics: (1) Nuclear chromodynamics-- introduction to QCD, structure of nucleons, lattice QCD, phases of hadronic matter; and relativistic heavy ion collisions. (2) Medium-energy physics-- nuclear and nucleon structure and dynamics studied with medium- and high-energy probes (neutrinos, photons, electrons, nucleons, pions, and kaons). Studies of weak and strong interactions.

8.751[J] Quantum Technology and Devices

Same subject as 22.51[J] Subject meets with 22.022 Prereq: 22.11 G (Spring) 3-0-9 units

See description under subject 22.51[J] .

P. Cappellaro

8.781, 8.782 Selected Topics in Nuclear Theory

Prereq: 8.323 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units

Presents topics of current interest in nuclear structure and reaction theory, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

Consult E. Farhi

8.811 Particle Physics

Prereq: 8.701 G (Fall) 3-0-9 units

Modern review of particles, interactions, and recent experiments. Experimental and analytical methods. QED, electroweak theory, and the Standard Model as tested in recent key experiments at ee and pp colliders. Mass generation, W, Z, and Higgs physics. Weak decays of mesons, including heavy flavors with QCD corrections. Mixing phenomena for K, D, B mesons and neutrinos. CP violation with results from B-factories. Future physics expectations: Higgs, SUSY, sub-structure as addressed by new experiments at the LHC collider.

8.812 Graduate Experimental Physics

Prereq: 8.701 G (IAP) Not offered regularly; consult department 1-8-3 units

Provides practical experience in particle detection with verification by (Feynman) calculations. Students perform three experiments; at least one requires actual construction following design. Topics include Compton effect, Fermi constant in muon decay, particle identification by time-of-flight, Cerenkov light, calorimeter response, tunnel effect in radioactive decays, angular distribution of cosmic rays, scattering, gamma-gamma nuclear correlations, and modern particle localization.

8.821 String Theory

Prereq: 8.324 Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units Credit cannot also be received for 8.251

An introduction to string theory. Basics of conformal field theory; light-cone and covariant quantization of the relativistic bosonic string; quantization and spectrum of supersymmetric 10-dimensional string theories; T-duality and D-branes; toroidal compactification and orbifolds; 11-dimensional supergravity and M-theory. Meets with 8.251 when offered concurrently.

8.831 Supersymmetric Quantum Field Theories

Prereq: Permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units Can be repeated for credit.

Topics selected from the following: SUSY algebras and their particle representations; Weyl and Majorana spinors; Lagrangians of basic four-dimensional SUSY theories, both rigid SUSY and supergravity; supermultiplets of fields and superspace methods; renormalization properties, and the non-renormalization theorem; spontaneous breakdown of SUSY; and phenomenological SUSY theories. Some prior knowledge of Noether's theorem, derivation and use of Feynman rules, l-loop renormalization, and gauge theories is essential.

8.851 Effective Field Theory

Prereq: 8.324 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units Credit cannot also be received for 8.S851

Covers the framework and tools of effective field theory, including: identifying degrees of freedom and symmetries; power counting expansions (dimensional and otherwise); field redefinitions, bottom-up and top-down effective theories; fine-tuned effective theories; matching and Wilson coefficients; reparameterization invariance; and advanced renormalization group techniques. Main examples are taken from particle and nuclear physics, including the Soft-Collinear Effective Theory.

8.871 Selected Topics in Theoretical Particle Physics

Prereq: 8.323 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units Can be repeated for credit.

Presents topics of current interest in theoretical particle physics, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.872 Selected Topics in Theoretical Particle Physics

8.881, 8.882 selected topics in experimental particle physics.

Prereq: 8.811 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Presents topics of current interest in experimental particle physics, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

Space Physics and Astrophysics

8.901 astrophysics i.

Prereq: Permission of instructor G (Spring) 3-0-9 units

Size and time scales. Historical astronomy. Astronomical instrumentation. Stars: spectra and classification. Stellar structure equations and survey of stellar evolution. Stellar oscillations. Degenerate and collapsed stars; radio pulsars. Interacting binary systems; accretion disks, x-ray sources. Gravitational lenses; dark matter. Interstellar medium: HII regions, supernova remnants, molecular clouds, dust; radiative transfer; Jeans' mass; star formation. High-energy astrophysics: Compton scattering, bremsstrahlung, synchrotron radiation, cosmic rays. Galactic stellar distributions and populations; Oort constants; Oort limit; and globular clusters.

8.902 Astrophysics II

Prereq: 8.901 G (Fall) 3-0-9 units

Galactic dynamics: potential theory, orbits, collisionless Boltzmann equation, etc. Galaxy interactions. Groups and clusters; dark matter. Intergalactic medium; x-ray clusters. Active galactic nuclei: unified models, black hole accretion, radio and optical jets, etc. Homogeneity and isotropy, redshift, galaxy distance ladder. Newtonian cosmology. Roberston-Walker models and cosmography. Early universe, primordial nucleosynthesis, recombination. Cosmic microwave background radiation. Large-scale structure, galaxy formation.

M. McDonald

8.913 Plasma Astrophysics I

Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units

For students interested in space physics, astrophysics, and plasma physics in general. Magnetospheres of rotating magnetized planets, ordinary stars, neutron stars, and black holes. Pulsar models: processes for slowing down, particle acceleration, and radiation emission; accreting plasmas and x-ray stars; stellar winds; heliosphere and solar wind- relevant magnetic field configuration, measured particle distribution in velocity space and induced collective modes; stability of the current sheet and collisionless processes for magnetic reconnection; theory of collisionless shocks; solitons; Ferroaro-Rosenbluth sheet; solar flare models; heating processes of the solar corona; Earth's magnetosphere (auroral phenomena and their interpretation, bowshock, magnetotail, trapped particle effects); relationship between gravitational (galactic) plasmas and electromagnetic plasmas. 8.913 deals with heliospheric, 8.914 with extra-heliospheric plasmas.

8.914 Plasma Astrophysics II

Prereq: Permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

8.921 Stellar Structure and Evolution

Observable stellar characteristics; overview of observational information. Principles underlying calculations of stellar structure. Physical processes in stellar interiors; properties of matter and radiation; radiative, conductive, and convective heat transport; nuclear energy generation; nucleosynthesis; and neutrino emission. Protostars; the main sequence, and the solar neutrino flux; advanced evolutionary stages; variable stars; planetary nebulae, supernovae, white dwarfs, and neutron stars; close binary systems; and abundance of chemical elements.

8.942 Cosmology

Prereq: Permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

Thermal backgrounds in space. Cosmological principle and its consequences: Newtonian cosmology and types of "universes"; survey of relativistic cosmology; horizons. Overview of evolution in cosmology; radiation and element synthesis; physical models of the "early stages." Formation of large-scale structure to variability of physical laws. First and last states. Some knowledge of relativity expected. 8.962 recommended though not required.

8.952 Particle Physics of the Early Universe

Prereq: 8.323 ; Coreq: 8.324 Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

Basics of general relativity, standard big bang cosmology, thermodynamics of the early universe, cosmic background radiation, primordial nucleosynthesis, basics of the standard model of particle physics, electroweak and QCD phase transition, basics of group theory, grand unified theories, baryon asymmetry, monopoles, cosmic strings, domain walls, axions, inflationary universe, and structure formation.

8.962 General Relativity

Prereq: 8.07 , 18.03 , and 18.06 G (Spring) 4-0-8 units

The basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.

8.971 Astrophysics Seminar

Prereq: Permission of instructor G (Fall, Spring) Not offered regularly; consult department 2-0-4 units Can be repeated for credit.

Advanced seminar on current topics, with a different focus each term. Typical topics: astronomical instrumentation, numerical and statistical methods in astrophysics, gravitational lenses, neutron stars and pulsars.

Consult D. Chakrabarty

8.972 Astrophysics Seminar

Advanced seminar on current topics, with a different focus each term. Typical topics: gravitational lenses, active galactic nuclei, neutron stars and pulsars, galaxy formation, supernovae and supernova remnants, brown dwarfs, and extrasolar planetary systems. The presenter at each session is selected by drawing names from a hat containing those of all attendees. Offered if sufficient interest is indicated.

8.981, 8.982 Selected Topics in Astrophysics

Prereq: Permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Topics of current interest, varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.995 Practical Experience in Physics

Prereq: None G (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

For Course 8 students participating in off-campus experiences in physics. Before registering for this subject, students must have an internship offer from a company or organization, must identify a Physics advisor, and must receive prior approval from the Physics Department. Upon completion of the project, student must submit a letter from the company or organization describing the work accomplished, along with a substantive final report from the student approved by the MIT advisor. Consult departmental academic office.

8.998 Teaching and Mentoring MIT Students

Prereq: None U (Fall, Spring) 2-0-1 units

Designed for first-time physics mentors and others interested in improving their knowledge and skills in teaching one-on-one and in small groups, particularly TEAL TAs and graduate student TAs. Topics include: cognition, metacognition, and the role of affect; communication skills (practice listening, questioning, and eliciting student ideas); the roles of motivation and mindset in learning; fostering belonging and self-efficacy through peer mentorship; facilitating small-group interactions to enhance peer instruction and learning; physics-specific learning strategies, such as how to teach/learn problem solving; research-based techniques for effective mentorship in STEM. Includes a one-hour class on pedagogy topics, a one-hour weekly Physics Mentoring Community of Practice meeting, and weekly assignments to read or watch material in preparation for class discussions, and written reflections before class.

8.S301 Special Subject: Physics

Prereq: Permission of instructor G (Spring) Units arranged

Covers topics in Physics that are not offered in the regular curriculum. Limited enrollment; preference to Physics graduate students.

A. Lightman

8.S308 Special Subject: Physics (New)

Prereq: None G (IAP) Units arranged

J. Tailleur

8.S372 Special Subject: Physics

Prereq: None G (Spring) Not offered regularly; consult department 3-0-9 units

Covers topics in Physics that are not offered in the regular curriculum.

8.S373 Special Subject: Physics

Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

8.S421 Special Subject: Physics

Prereq: Permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) Units arranged Can be repeated for credit.

W. Ketterle

8.S998 Special Subject: Physics

Prereq: None U (Fall, Spring) Not offered regularly; consult department Units arranged [P/D/F]

8.THG Graduate Physics Thesis

Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Program of research leading to the writing of an SM, PhD, or ScD thesis; to be arranged by the student and an appropriate MIT faculty member.

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Quantum Science and Engineering

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The MIT Quantum Science and Engineering collective is led by a steering committee and a broader advisory council .

Ike Chuang is a pioneer in the field of quantum information science. His experimental realization of two, three, five, and seven quantum bit quantum computers using nuclear spins in molecules provided the first laboratory demonstrations of many important quantum algorithms, including Shor's quantum factoring algorithm. The error correction, algorithmic cooling, and entanglement manipulation techniques he developed provide new ways to obtain complete quantum control over light and matter, and lay a foundation for possible large-scale quantum information processing systems.

Chuang came to MIT in 2000 from IBM, where he was a research staff member. He received his doctorate in electrical engineering from Stanford University, where he was a Hertz Foundation Fellow. Chuang holds two bachelors and one master's degrees in physics and electrical engineering from MIT, and was a postdoc fellow at Los Alamos National Laboratory and the University of California at Berkeley. He is the author, together with Michael Nielsen, of the textbook Quantum Computation and Quantum Information .

Wolfgang Ketterle's research is in atomic physics and laser spectroscopy, particularly in the area of laser cooling and trapping of neutral atoms with the goal of exploring new aspects of ultracold atomic matter. Ketterle conducts experimental research in atomic physics and laser spectroscopy and focuses currently on Bose-Einstein condensation in dilute atomic gases. He was among the first scientists to observe this phenomenon in 1995, and realized the first atom laser in 1997. 

Ketterle joined MIT’s Department of Physics in 1993 where he is the John D. MacArthur Professor of Physics. Ketterle holds a master’s degree from the Technical University of Munich and a PhD in physics from the University of Munich. He conducted postdoctoral research at the Max-Planck Institute for Quantum Optics, the University of Heidelberg, and at MIT. In 2001, the Nobel Prize in Physics was awarded jointly to Eric A. Cornell, Wolfgang Ketterle, and Carl E. Wieman "for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates."

Will Oliver provides programmatic and technical leadership targeting the development of quantum and classical high-performance computing technologies at MIT and MIT’s Lincoln Laboratory. Oliver’s research interests include the materials growth, fabrication, design, and measurement of superconducting qubits, as well as the development of cryogenic packaging and control electronics involving cryogenic CMOS and single-flux quantum digital logic. 

Oliver is a principal investigator in MIT’s Engineering Quantum Systems group and associate director in MIT’s Research Laboratory of Electronics. He is also a principal investigator in the Quantum Information and Integrated Nanosystems group at MIT Lincoln Laboratory. He received his PhD in electrical engineering from Stanford University, master’s degrees in electrical engineering and computer science from MIT. Oliver is a Fellow of the American Physical Society; serves on the US Committee for Superconducting Electronics; is an IEEE Applied Superconductivity Conference (ASC) Board Member; and is a member of IEEE, APS, Sigma Xi, Phi Beta Kappa, and Tau Beta Pi.

Peter Shor consolidated the field of quantum computation by designing the quantum algorithm for factoring large numbers. He proved that a quantum computer could solve a hard computational problem exponentially faster than any classical computer. He also introduced quantum error correcting codes and fault tolerant quantum computation. The theory of error correcting codes is now a well-established branch of this science, substantiating the possibility for error-free quantum computation.

Shor joined the Department of Mathematics in 2003 from his research staff position at AT&T. He received his PhD in applied mathematics from MIT and completed postdoctoral fellowship at the Mathematical Science Research Institute. He is a member of the National Academy of Science and is a fellow of the American Academy of Arts and Sciences. In 2017, Shor received the Dirac Medal of the International Centre for Theoretical Physics.

Advisory Council

The MIT Quantum Science and Engineering executive committee helps guide the QSE leadership to establish strategic academic and research priorities. 

Members for 2019-2020

Browse Course Material

Course info, instructors.

• Prof. Isaac Chuang
• Prof. Peter Shor

Departments

As taught in.

• Algorithms and Data Structures
• Cryptography
• Theory of Computation
• Computation
• Discrete Mathematics
• Quantum Mechanics

Quantum Information Science I

Course description.

This course is a three-course series that provides an introduction to the theory and practice of quantum computation. The three-course series comprises:

8.370.1x : Foundations of Quantum and Classical computing—quantum mechanics, reversible computation, and quantum measurement 8.370.2x : Simple Quantum Protocols and …

8.370.1x : Foundations of Quantum and Classical computing—quantum mechanics, reversible computation, and quantum measurement 8.370.2x : Simple Quantum Protocols and Algorithms—teleportation and superdense coding, the Deutsch-Jozsa and Simon’s algorithm, Grover’s quantum search algorithm, and Shor’s quantum factoring algorithm 8.370.3x : Foundations of Quantum communication—noise and quantum channels, and quantum key distribution

Prior knowledge of quantum mechanics is helpful but not required. It is best if you know some linear algebra.

This course was organized as a three-part series on MITx by MIT’s Department of Physics and is now archived on the Open Learning Library , which is free to use. You have the option to sign up and enroll in each module if you want to track your progress, or you can view and use all the materials without enrolling.

You are leaving MIT OpenCourseWare

Doctoral Degrees

A doctoral degree requires the satisfactory completion of an approved program of advanced study and original research of high quality..

Please note that the Doctor of Philosophy (PhD) and Doctor of Science (ScD) degrees are awarded interchangeably by all departments in the School of Engineering and the School of Science, except in the fields of biology, cognitive science, neuroscience, medical engineering, and medical physics. This means that, excepting the departments outlined above, the coursework and expectations to earn a Doctor of Philosophy and for a Doctor of Science degree from these schools are generally the same. Doctoral students may choose which degree they wish to complete.

Applicants interested in graduate education should apply to the department or graduate program conducting research in the area of interest. Some departments require a doctoral candidate to take a “minor” program outside of the student’s principal field of study; if you wish to apply to one of these departments, please consider additional fields you may like to pursue.

Below is a list of programs and departments that offer doctoral-level degrees.

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Physics Graduate Student Council

Core course tips

Pictured: Killian Court in springtime

If you’re a new student, you may be wondering a lot about the written diagnostic exams for the core courses. (These exams are sometimes referred to as the written exam, Part 2, the written qualifier, quals, etc. by various people. They’re all the same thing.) You have come to the right place!

At MIT, all graduate students are required to take four core courses, two or three courses in their area of research, and two breadth courses. The four core courses are:

Classical mechanics

Electricity and magnetism

Quantum mechanics

Statistical mechanics

There are two ways to meet the core requirement: either by passing the relevant course with a grade of B+ or by testing out via a corresponding exam. It’s not a qualifying exam. It’s just a way to see where you’re at and potentially test out of courses.

PGSC strongly urges all first-year students to make an attempt at all four written exams in their first August, no matter how you think you’re going to do. There are three reasons for this: (1) it’ll serve as a good diagnostic to help you see where you’re at, (2) no matter how you think you’ll do, you might get lucky and get a question you know how to do, and (3) it’s good practice for the next time around, when you’ll have to take the exam. There is absolutely zero penalty for taking the exam, no matter how you do, and the exams are anonymous so the graders won’t know who you are.

Students come to our program from a wide variety of academic backgrounds and life experiences, and every year there are diagnostic exam results ranging across the entire spectrum. Yes, it is not uncommon at all that a student won’t pass any on their first try — and there are even some who don’t pass until the last try! – and there is nothing wrong with that!  The exam helps serve as a diagnostic to help you and your advisor figure out what material you need to learn or review, and to help you devise a coursework plan for your first few semesters at MIT. Written Exam scores are not indicative of academic potential or future performance; students beginning from all starting points in their first August go on to complete the Ph.D. program, do groundbreaking research, and have successful career.

Let’s say you want to brush up on basic physics, though, or maybe even prepare for one or more of these exams. Perhaps you’re super rusty and haven’t taken any physics courses in a long, long time; whether you’ve been out in the workforce, taking a gap year, or doing a research master’s on string theory, classical mechanics now looks like a foreign language. Or maybe you made some coursework choices your first year at MIT that you might not have made with 20/20 hindsight, and your deadlines for finishing these requirements are coming up. Perchance you don’t have (m)any friends or family members who have gone to grad school in the sciences before, and you’re realizing that you have no idea what you’ve signed yourself up for. Don’t worry. You’re not alone.

But where do you begin?

There are a few different approaches you can take to learning the material, depending on what suits your learning style best:

• Watching videos and working through a formal course
• Reading notes or textbooks,
• Reviewing and memorizing relevant formulas
• Working through old problems alongside their solutions,

or some combination of the above. Here are some tips!

Online Coursework

One of the great things about MIT is they put a lot online through OpenCourseWare . You can find class notes, videos, homework, exams, and sometimes solutions to all of the above without every having to show up to a class. Here are all the relevant core courses and their numbers, from intro undergrad all the way up through the hardest grad classes. (One small note about the grad courses: usually they cover some topics beyond what could be tested on the written exam.)

Sometimes you can also find archives of old classes on MIT’s old class site Stellar , or you can ask senior graduate students in your division or UROP friends to send you lecture notes or old problem sets from classes they took. Do not underestimate your professors’ willingness to find you course materials as well.

Don’t be embarrassed about going all the way back to the beginning, if that’s what you need. It’s perfectly fine.

• 8.01 – introductory mechanics
• 8.223 – intermediate mechanics
• 8.09/8.309 – classical mechanics III (graduate)
• 8.02 – introductory E&M
• 8.07 – intermediate E&M
• 8.311 – graduate E&M
• 8.04 – quantum physics I
• 8.05 – quantum physics II
• 8.321 – graduate quantum mechanics
• MIT also offers additional quantum courses like 8.06 and 8.322 , but the ones we’ve listed above are the traditional sequence to prepare for the exam
• 8.044 – statistical mechanics I
• 8.08 – statistical mechanics II
• 8.333 – graduate statistical mechanics
• MIT also offers another statistical mechanics course, 8.334 , that is the sequel to the core course

Textbook recommendations

If you’re coming straight from college, generally whichever textbook you used in your core classes there probably will suffice for preparing for MIT’s exams and coursework. If you don’t remember what you used, the Physics Department offers a set of textbook recommendations .

Back to square 1? 

If it’s been a long while since you’ve taken any undergrad-level physics courses — whether you’ve taken a gap between undergrad and grad school, or you’ve been focused on a master’s project and settled into a rhythm of just looking up the basics when you need them —  and you find yourself needing to go all the way back to the beginning on a lot of topics, we find that a good place to start is the  Feynman Lectures on Physics . You can usually find a cheap copy on the internet, or if you’re already enrolled at MIT, there are plenty of copies in the library. The Feynman Lectures are notoriously difficult to learn from as a new physics student, but if you’re going back to review, they might very well be perfect for you. They’re entertaining, and unlike a standard textbook, you won’t have to spend too much time trying to dig up the pertinent facts from a mess of examples and instruction on how to do math; the lectures are pretty streamlined. Landau and Lifshitz also have a very thin and very good book on classical mechanics.

Many thanks to Bob Jaffe for making these recommendations initially.

Formula sheets

Maybe you’re at the point now where you have the concepts down pat, or you only have a couple days to go before the exam, and you want to brush up on all the relevant equations and make yourself a formula sheet. Here are some ideas.

These sheets don’t necessarily have everything you need, but they are at least a good place to start!

• CM:  AP Physics formula sheet ; equations from Iain Stewart’s review notes  about Lagrangian and Hamiltonian mechanics
• E&M: AP Physics  formula sheet , Alan Guth’s long  formula sheet for 8.07
• QM: Barton Zwiebach’s formula sheet for 8.05
• SM: formula sheets embedded in the final exams for 8.044. It’s not enough, but it will get you started.

Old problems

As you’ll hear from many an MIT professor, there is absolutely no difference between a student who “knows physics” and a student who learns how to do the few dozen or so problem types that can come up on an exam of a certain subject area. So one way to tackle an exam is just to make sure that (1) you’ve seen a good smattering of problem types, (2) you have a general idea about how to tackle each one, and (3) you’ve worked through as many as you can (either alongside the solutions or not, depending on how much you’ve had time to review).

You’ll notice as you start working through problems that they get reused a lot , both within our own department and across different institutions! So where do you find these problems?

Old MIT qualifying exams

• The department posts a number of recent exams and solutions online
• The PhysREFS have even more exam scans on their webpage
• There are more old problems (and sometimes solutions) in the Physics Reading Room from the 80’s and 90’s
• Senior graduate students often have scans of old qualifying exams (and course exams!) as well (or remember what questions they got on their exams) — just ask! If nobody you know knows things, hit PGSC or PhysREFS up and we can try to connect you with resources.
• There are even books online with sets of old problems from MIT (and other institutions) — particularly the Problems and Solutions in Physics Series of books. These were originally published in the 90’s, so they have lots of older problems as well

Qualifying exams from elsewhere

You can find lots of old problems online from other places. Many of these same problem types may appear on MIT exams. (Though be aware that difficulty level and material covered may vary between institutions.)

• Princeton preliminary exams  (solutions can be found here )
• Yale quals and solutions
• Columbia  quals and solutions
• Problem bank from Texas A&M’s physics department  (conveniently grouped by topic all in one document)
• University of Maryland quals 
• Brown quals
• U of I quals
• UC Irvine quals

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The plasma research effort at MIT is concerned with a wide variety of problems, ranging from astrophysical plasmas to laboratory and fusion-grade plasmas, as well as with using plasmas for environmental remediation. This work combines theory and experiment and involves faculty members from physics and other departments. The program has the goals of understanding the physics of plasmas and charged-particle beams and of designing plasma containment devices, with the ultimate aim of achieving the conditions in which a plasma can ignite by fusion reactions. Research is carried out not only on-site, but also at other major national and international laboratories.

Most of the volume of the universe is in the electrodynamic plasma state. Moreover, the dynamics of the universe on a grand scale is described as a gravitational plasma. The theory of galaxies as gravitational plasmas is well-developed and its results, for example, spiral arm structures, are relatively well-correlated with the experimental observations. While many aspects of laboratory plasmas are understood and correlate with experiments in relatively simple magnetic geometries, the physics of high-temperature plasmas on a microscopic scale continues to be an area of intensive investigation.

The dynamics of laboratory plasmas, charged-particle beams, and space and astrophysical plasmas are often strongly influenced by the excitation of collective modes with similar characteristics and common theoretical descriptions. The interaction of collective modes, both with each other and with charged particles, results in a variety of highly nonlinear phenomena of great importance for fusion, astrophysical and nonneutral plasmas, as well as for accelerators and coherent radiation sources.

Affiliated Labs & Centers

• Plasma Science and Fusion Center

Fourteen MIT School of Science professors receive tenure for 2022 and 2023

In 2022, nine MIT faculty were granted tenure in the School of Science:

Gloria Choi examines the interaction of the immune system with the brain and the effects of that interaction on neurodevelopment, behavior, and mood. She also studies how social behaviors are regulated according to sensory stimuli, context, internal state, and physiological status, and how these factors modulate neural circuit function via a combinatorial code of classic neuromodulators and immune-derived cytokines. Choi joined the Department of Brain and Cognitive Sciences after a postdoc at Columbia University. She received her bachelor’s degree from the University of California at Berkeley, and her PhD from Caltech. Choi is also an investigator in The Picower Institute for Learning and Memory.

Nikta Fakhri develops experimental tools and conceptual frameworks to uncover laws governing fluctuations, order, and self-organization in active systems. Such frameworks provide powerful insight into dynamics of nonequilibrium living systems across scales, from the emergence of thermodynamic arrow of time to spatiotemporal organization of signaling protein patterns and discovery of odd elasticity. Fakhri joined the Department of Physics in 2015 following a postdoc at University of Göttingen. She completed her undergraduate degree at Sharif University of Technology and her PhD at Rice University.

Geobiologist Greg Fournier uses a combination of molecular phylogeny insights and geologic records to study major events in planetary history, with the hope of furthering our understanding of the co-evolution of life and environment. Recently, his team developed a new technique to analyze multiple gene evolutionary histories and estimated that photosynthesis evolved between 3.4 and 2.9 billion years ago. Fournier joined the Department of Earth, Atmospheric and Planetary Sciences in 2014 after working as a postdoc at the University of Connecticut and as a NASA Postdoctoral Program Fellow in MIT’s Department of Civil and Environmental Engineering. He earned his BA from Dartmouth College in 2001 and his PhD in genetics and genomics from the University of Connecticut in 2009.

Daniel Harlow researches black holes and cosmology, viewed through the lens of quantum gravity and quantum field theory. His work generates new insights into quantum information, quantum field theory, and gravity. Harlow joined the Department of Physics in 2017 following postdocs at Princeton University and Harvard University. He obtained a BA in physics and mathematics from Columbia University in 2006 and a PhD in physics from Stanford University in 2012. He is also a researcher in the Laboratory for Nuclear Science’s Center for Theoretical Physics.

A biophysicist, Gene-Wei Li studies how bacteria optimize the levels of proteins they produce at both mechanistic and systems levels. His lab focuses on design principles of transcription, translation, and RNA maturation. Li joined the Department of Biology in 2015 after completing a postdoc at the University of California at San Francisco. He earned an BS in physics from National Tsinghua University in 2004 and a PhD in physics from Harvard University in 2010.

Michael McDonald focuses on the evolution of galaxies and clusters of galaxies, and the role that environment plays in dictating this evolution. This research involves the discovery and study of the most distant assemblies of galaxies alongside analyses of the complex interplay between gas, galaxies, and black holes in the closest, most massive systems. McDonald joined the Department of Physics and the Kavli Institute for Astrophysics and Space Research in 2015 after three years as a Hubble Fellow, also at MIT. He obtained his BS and MS degrees in physics at Queen’s University, and his PhD in astronomy at the University of Maryland in College Park.

Gabriela Schlau-Cohen combines tools from chemistry, optics, biology, and microscopy to develop new approaches to probe dynamics. Her group focuses on dynamics in membrane proteins, particularly photosynthetic light-harvesting systems that are of interest for sustainable energy applications. Following a postdoc at Stanford University, Schlau-Cohen joined the Department of Chemistry faculty in 2015. She earned a bachelor’s degree in chemical physics from Brown University in 2003 followed by a PhD in chemistry at the University of California at Berkeley.

Phiala Shanahan’s research interests are focused around theoretical nuclear and particle physics. In particular, she works to understand the structure and interactions of hadrons and nuclei from the fundamental degrees of freedom encoded in the Standard Model of particle physics. After a postdoc at MIT and a joint position as an assistant professor at the College of William and Mary and senior staff scientist at the Thomas Jefferson National Accelerator Facility, Shanahan returned to the Department of Physics as faculty in 2018. She obtained her BS from the University of Adelaide in 2012 and her PhD, also from the University of Adelaide, in 2015.

Omer Yilmaz explores the impact of dietary interventions on stem cells, the immune system, and cancer within the intestine. By better understanding how intestinal stem cells adapt to diverse diets, his group hopes to identify and develop new strategies that prevent and reduce the growth of cancers involving the intestinal tract. Yilmaz joined the Department of Biology in 2014 and is now also a member of Koch Institute for Integrative Cancer Research. After receiving his BS from the University of Michigan in 1999 and his PhD and MD from University of Michigan Medical School in 2008, he was a resident in anatomic pathology at Massachusetts General Hospital and Harvard Medical School until 2013.

In 2023, five MIT faculty were granted tenure in the School of Science:

Physicist Riccardo Comin explores the novel phases of matter that can be found in electronic solids with strong interactions, also known as quantum materials. His group employs a combination of synthesis, scattering, and spectroscopy to obtain a comprehensive picture of these emergent phenomena, including superconductivity, (anti)ferromagnetism, spin-density-waves, charge order, ferroelectricity, and orbital order. Comin joined the Department of Physics in 2016 after postdoctoral work at the University of Toronto. He completed his undergraduate studies at the Universita’ degli Studi di Trieste in Italy, where he also obtained a MS in physics in 2009. Later, he pursued doctoral studies at the University of British Columbia, Canada, earning a PhD in 2013.

Netta Engelhardt researches the dynamics of black holes in quantum gravity and uses holography to study the interplay between gravity and quantum information. Her primary focus is on the black hole information paradox, that black holes seem to be destroying information that, according to quantum physics, cannot be destroyed. Engelhardt was a postdoc at Princeton University and a member of the Princeton Gravity Initiative prior to joining the Department of Physics in 2019. She received her BS in physics and mathematics from Brandeis University and her PhD in physics from the University of California at Santa Barbara. Engelhardt is a researcher in the Laboratory for Nuclear Science’s Center for Theoretical Physics and the Black Hole Initiative at Harvard University.

Mark Harnett studies how the biophysical features of individual neurons endow neural circuits with the ability to process information and perform the complex computations that underlie behavior. As part of this work, his lab was the first to describe the physiological properties of human dendrites. He joined the Department of Brain and Cognitive Sciences and the McGovern Institute for Brain Research in 2015. Prior, he was a postdoc at the Howard Hughes Medical Institute’s Janelia Research Campus. He received his BA in biology from Reed College in Portland, Oregon and his PhD in neuroscience from the University of Texas at Austin.

Or Hen investigates quantum chromodynamic effects in the nuclear medium and the interplay between partonic and nucleonic degrees of freedom in nuclei. Specifically, Hen utilizes high-energy scattering of electron, neutrino, photon, proton and ion off atomic nuclei to study short-range correlations: temporal fluctuations of high-density, high-momentum, nucleon clusters in nuclei with important implications for nuclear, particle, atomic, and astrophysics. Hen was an MIT Pappalardo Fellow in the Department of Physics from 2015 to 2017 before joining the faculty in 2017. He received his undergraduate degree in physics and computer engineering from the Hebrew University and earned his PhD in experimental physics at Tel Aviv University.

Sebastian Lourido is interested in learning about the vulnerabilities of parasites in order to develop treatments for infectious diseases and expand our understanding of eukaryotic diversity. His lab studies many important human pathogens, including Toxoplasma gondii , to model features conserved throughout the phylum. Lourido was a Whitehead Fellow at the Whitehead Institute for Biomedical Research until 2017, when he joined the Department of Biology and became a Whitehead Member. He earned his BS from Tulane University in 2004 and his PhD from Washington University in St. Louis in 2012.

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Atoms on the edge

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Typically, electrons are free agents that can move through most metals in any direction. When they encounter an obstacle, the charged particles experience friction and scatter randomly like colliding billiard balls.

But in certain exotic materials, electrons can appear to flow with single-minded purpose. In these materials, electrons may become locked to the material’s edge and flow in one direction, like ants marching single-file along a blanket’s boundary. In this rare “edge state,” electrons can flow without friction, gliding effortlessly around obstacles as they stick to their perimeter-focused flow. Unlike in a superconductor, where all electrons in a material flow without resistance, the current carried by edge modes occurs only at a material’s boundary.

Now MIT physicists have directly observed edge states in a cloud of ultracold atoms. For the first time, the team has captured images of atoms flowing along a boundary without resistance, even as obstacles are placed in their path. The results, which appear today in Nature Physics , could help physicists manipulate electrons to flow without friction in materials that could enable super-efficient, lossless transmission of energy and data.

“You could imagine making little pieces of a suitable material and putting it inside future devices, so electrons could shuttle along the edges and between different parts of your circuit without any loss,” says study co-author Richard Fletcher, assistant professor of physics at MIT. “I would stress though that, for us, the beauty is seeing with your own eyes physics which is absolutely incredible but usually hidden away in materials and unable to be viewed directly.”

The study’s co-authors at MIT include graduate students Ruixiao Yao and Sungjae Chi, former graduate students Biswaroop Mukherjee PhD ’20 and Airlia Shaffer PhD ’23, along with Martin Zwierlein, the Thomas A. Frank Professor of Physics. The co-authors are all members of MIT’s Research Laboratory of Electronics and the MIT-Harvard Center for Ultracold Atoms.

Forever on the edge

Physicists first invoked the idea of edge states to explain a curious phenomenon, known today as the Quantum Hall effect, which scientists first observed in 1980, in experiments with layered materials, where electrons were confined to two dimensions. These experiments were performed in ultracold conditions, and under a magnetic field. When scientists tried to send a current through these materials, they observed that electrons did not flow straight through the material, but instead accumulated on one side, in precise quantum portions.

To try and explain this strange phenomenon, physicists came up with the idea that these Hall currents are carried by edge states. They proposed that, under a magnetic field, electrons in an applied current could be deflected to the edges of a material, where they would flow and accumulate in a way that might explain the initial observations. “The way charge flows under a magnetic field suggests there must be edge modes,” Fletcher says. “But to actually see them is quite a special thing because these states occur over femtoseconds, and across fractions of a nanometer, which is incredibly difficult to capture.”

Rather than try and catch electrons in an edge state, Fletcher and his colleagues realized they might be able to recreate the same physics in a larger and more observable system. The team has been studying the behavior of ultracold atoms in a carefully designed setup that mimics the physics of electrons under a magnetic field.

“In our setup, the same physics occurs in atoms, but over milliseconds and microns,” Zwierlein explains. “That means that we can take images and watch the atoms crawl essentially forever along the edge of the system.”

A spinning world

In their new study, the team worked with a cloud of about 1 million sodium atoms, which they corralled in a laser-controlled trap, and cooled to nanokelvin temperatures. They then manipulated the trap to spin the atoms around, much like riders on an amusement park Gravitron.

“The trap is trying to pull the atoms inward, but there’s centrifugal force that tries to pull them outward,” Fletcher explains. “The two forces balance each other, so if you’re an atom, you think you’re living in a flat space, even though your world is spinning. There’s also a third force, the Coriolis effect, such that if they try to move in a line, they get deflected. So these massive atoms now behave as if they were electrons living in a magnetic field.”

Into this manufactured reality, the researchers then introduced an “edge,” in the form of a ring of laser light, which formed a circular wall around the spinning atoms. As the team took images of the system, they observed that when the atoms encountered the ring of light, they flowed along its edge, in just one direction.

“You can imagine these are like marbles that you’ve spun up really fast in a bowl, and they just keep going around and around the rim of the bowl,” Zwierlein offers. “There is no friction. There is no slowing down, and no atoms leaking or scattering into the rest of the system. There is just beautiful, coherent flow.”

“These atoms are flowing, free of friction, for hundreds of microns,” Fletcher adds. “To flow that long, without any scattering, is a type of physics you don’t normally see in ultracold atom systems.”

This effortless flow held up even when the researchers placed an obstacle in the atoms’ path, like a speed bump, in the form of a point of light, which they shone along the edge of the original laser ring. Even as they came upon this new obstacle, the atoms didn’t slow their flow or scatter away, but instead glided right past without feeling friction as they normally would.

“We intentionally send in this big, repulsive green blob, and the atoms should bounce off it,” Fletcher says. “But instead what you see is that they magically find their way around it, go back to the wall, and continue on their merry way.”

The team’s observations in atoms document the same behavior that has been predicted to occur in electrons. Their results show that the setup of atoms is a reliable stand-in for studying how electrons would behave in edge states.

“It’s a very clean realization of a very beautiful piece of physics, and we can directly demonstrate the importance and reality of this edge,” Fletcher says. “A natural direction is to now introduce more obstacles and interactions into the system, where things become more unclear as to what to expect.”

This research was supported, in part, by the National Science Foundation.

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• Richard Fletcher
• Martin Zwierlein
• Research Laboratory of Electronics
• MIT-Harvard Center for Ultracold Atoms
• Department of Physics

Related Topics

• Superconductivity
• Materials science and engineering
• National Science Foundation (NSF)

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