transition signal in essay

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Transition signals In addition... However... Likewise...

Transition signals are useful in achieving good cohesion and coherence in your writing. This page gives information on what transition signals are , the grammar of transition signals, and different types of transition signals. There is also an example essay at the end in which you can highlight the different types of transition signal, as well as some exercises to help you practice this area.

What are transition signals?

For another look at the same content, check out YouTube or Youku , or the infographic .

Transition signals, along with repeated words and reference words, are one of the main ways to achieve good cohesion and coherence in your writing. They are therefore a way to help ensure that your ideas and sentences cohere or 'stick together'. Transition signals are used to signal relationships between ideas in your writing. For example, the transition signal 'for example' is used to give examples, while the word 'while' is used to show a contrast. In addition, there are phrases like 'in addition' for adding new ideas. Likewise there are words such as 'likewise' to connect similar ideas.

Grammar of transition signals

Check out the transition signals infographic »

Broadly speaking, transition signals can be divided into three types:

• sentence connectors
• clause connectors
• other connectors

Sentence connectors are used to connect two sentences together. They are joined by a full-stop (period) or semi-colon, and are followed by a comma. The following are examples of sentence connectors.

• Transition signals are very useful. However , they should not be used to begin every sentence.
• Transition signals are very useful; however , they should not be used to begin every sentence.
• Contrast signals are one type of transition signals. In addition , there are others such as compare signals and addition signals.
• There are three main ways to improve cohesion in your writing. First , you can use transition signals.

Clause connectors are used to connect two clauses together to form one sentence. They are joined by a comma. The following are examples of clause connectors.

• Transition signals are very useful, but they should not be used to begin every sentence.
• Although transition signals are very useful, they should not be used to begin every sentence.
• Contrast signals are one type of transition signal, and there are others such as compare signals and addition signals.

Other connectors follow different grammar patterns. Many are followed by noun phrases. Some are verbs and should therefore be used as verbs in a sentence. The following are examples of other connectors.

• Despite their importance in achieving cohesion, transition signals should not be used to begin every sentence.
• Good cohesion is the result of using repeated words, reference words, and transition signals.
• It is clear that careful use of transition signals will improve the cohesion in your writing.
• Contrast signals are one type of transition signal. Another type is comparison signals.

Types of transition signals

For another look at the same content, check out the video on YouTube (also available on Youku ).

Below are examples of different types of transition signals. They are divided by type, and sub-divided according to grammar. More information on some of these is given in relevant essay sections. You can also check out the second YouTube video on the EAP Foundation YouTube channel , which looks at types in more detail, with example sentences.

To introduce an additional idea

Sentence connectors

• furthermore
• in addition
• additionally

Clause connectors

• another (+ noun)
• an additional (+ noun)

For more on comparison signals, see the compare and contrast essays section.

• in the same way
• both... and
• not only... but also
• neither... nor
• to be similar to
• to be alike
• to be similar

To contrast

For more on contrast signals, see the compare and contrast essays section.

• in contrast
• in/by comparison
• on the other hand
• compared to/with
• to be different (from)
• to be dissimilar
• to be unlike
• to differ (from)

To show concession

Concession transitions show an unexpected result. They are similar to but not the same as contrast transitions. E.g. Although the sun was shining, he took an umbrella to work. [The sun shining means taking an umbrella is unexpected.]

• nevertheless
• nonetheless
• even though
• despite (+ noun)
• in spite of (+ noun)

To introduce a cause/reason

For more on cause signals, see the cause and effect essays section.

• for this reason
• to result from
• to be the result of
• to be the effect of
• to be the consequence of
• as a result of
• as a consequence of

To introduce an effect/result

For more on effect signals, see the cause and effect essays section.

• as a result
• as a consequence
• consequently
• to result in
• to have an effect on
• the cause of
• the reason for

To give an example

• for example
• for instance
• in this case
• such as (+ noun)
• an example of (+ noun)
• to demonstrate

To show chronological order

• first, second, etc.
• first of all
• the first, the second
• the next, the last, the final
• before (lunch etc.)
• after (the war etc.)
• since (1970 etc.)
• in the year (2000 etc.)

To show order of importance

• first and foremost
• more/most importantly
• a more important
• the most important
• the second most significant
• the primary

To show an alternative

• alternatively

To identify or clarify

• in other words
• specifically

To reinforce

To conclude.

• in conclusion
• to summarise
• to conclude
• It is clear that...
• We can see that...
• The evidence suggests...
• These examples show...

Example essay

Below is an example essay. It is the one used in the persuasion essay section. Click on the different areas (in the shaded boxes to the right) to highlight the different types of transition signal in this essay.

Title: Consider whether human activity has made the world a better place.

History shows that human beings have come a long way from where they started. They have developed new technologies which means that everybody can enjoy luxuries they never previously imagined. However , the technologies that are temporarily making this world a better place to live could well prove to be an ultimate disaster due to , among other things, the creation of nuclear weapons, increasing pollution, and loss of animal species. The biggest threat to the earth caused by modern human activity comes from the creation of nuclear weapons. Although it cannot be denied that countries have to defend themselves, the kind of weapons that some of them currently possess are far in excess of what is needed for defence. If these weapons were used, they could lead to the destruction of the entire planet. Another harm caused by human activity to this earth is pollution. People have become reliant on modern technology, which can have adverse effects on the environment. For example , reliance on cars causes air and noise pollution. Even seemingly innocent devices, such as computers and mobile phones, use electricity, most of which is produced from coal-burning power stations, which further adds to environmental pollution. If we do not curb our direct and indirect use of fossil fuels, the harm to the environment may be catastrophic. Animals are an important feature of this earth and the past decades have witnessed the extinction of a considerable number of animal species. This is the consequence of human encroachment on wildlife habitats, for example deforestation to expand human cities. Some may argue that such loss of species is natural and has occurred throughout earth's history. However , the current rate of species loss far exceeds normal levels, and is threatening to become a mass extinction event. In summary , there is no doubt that current human activities such as the creation of nuclear weapons, pollution, and destruction of wildlife, are harmful to the earth. It is important for us to see not only the short-term effects of our actions, but their long-term effects as well. Otherwise , human activities will be just another step towards destruction.

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Author: Sheldon Smith    ‖    Last modified: 03 February 2022.

Sheldon Smith is the founder and editor of EAPFoundation.com. He has been teaching English for Academic Purposes since 2004. Find out more about him in the about section and connect with him on Twitter , Facebook and LinkedIn .

Compare & contrast essays examine the similarities of two or more objects, and the differences.

Cause & effect essays consider the reasons (or causes) for something, then discuss the results (or effects).

Discussion essays require you to examine both sides of a situation and to conclude by saying which side you favour.

Problem-solution essays are a sub-type of SPSE essays (Situation, Problem, Solution, Evaluation).

Transition signals are useful in achieving good cohesion and coherence in your writing.

Reporting verbs are used to link your in-text citations to the information cited.

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Transition Signals in Writing

What are transition signals.

Transition signals are connecting words or phrases that strengthen the internal cohesion of your writing. Transition signals act like bridges between parts of your writing. They link your sentences and paragraphs together smoothly so that they flow and there are no abrupt jumps or breaks between ideas.

Transition signals also act like signposts making it easier for the reader to follow your ideas. They help carry over a thought from one sentence to another, from one paragraph to another, or between separate sentences, paragraphs or topics.

There are several types of transition signals. Some lead your reader forward and imply the building of an idea or thought, while others make your reader compare ideas or draw conclusions from the preceding thoughts.

Sample text

The following words and phrases can be used to indicate transitions and to cue your reader about how ideas are logically connected in your writing. This list is also helpful for providing alternative options if you find yourself constantly using the same linking word or phrase.

To indicate sequence or to logically order ideas

first, second, third etc.

followed by

before, after

next, finally

previously, subsequently

initially, followed by

concurrently

at that time

To refer to a specific incident or example

for example

to illustrate

for instance

in the case of case

specifically

in this case

on this occasion

To provide emphasis or indicate importance

particularly

To indicate time

at that/this point

immediately

simultaneously

then, later

at that/ this time

To compare and/ or contrast

To compare:

• on the one hand
• correspondingly

in the same way

To contrast:

in contrast

on the other hand

• a different view is

on the contrary

• differing from
• balanced against
• by/ in comparison

To indicate result or cause and effect

as a result (of this)

consequently

as a consequence

accordingly

for this reason

because (of this)

so much (so) that

To introduce a similar idea

To add another idea or more information.

in addition

furthermore

it could also be said

additionally

To introduce an opposite idea, to show exception or concession

alternatively

it could also be said that

nevertheless

despite/in spite of (this)

even though

nonetheless

notwithstanding (this)

regardless (of this)

To give an example

take the case of

to demonstrate

To identify or clarify

that is (to say)

in other words

To summarise or conclude

on the whole

in conclusion

as a result

to summarise

• Transition signals in writing
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• Paraphrasing, summarising, quoting
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• Knowledge Base
• Transition sentences | Tips & examples for clear writing

Transition Sentences | Tips & Examples for Clear Writing

Published on June 9, 2020 by Jack Caulfield . Revised on July 23, 2023.

Clear transitions are crucial to clear writing: They show the reader how different parts of your essay, paper, or thesis are connected. Transition sentences can be used to structure your text and link together paragraphs or sections.

… In this case, the researchers concluded that the method was unreliable.

However , evidence from a more recent study points to a different conclusion . …

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Table of contents

Transitioning between paragraphs, transitioning to a new section, transitions within a paragraph, other interesting articles.

When you start a new paragraph , the first sentence should clearly express:

• What this paragraph will discuss
• How it relates to the previous paragraph

The examples below show some examples of transition sentences between paragraphs and what they express.

Placement of transition sentences

The beginning of a new paragraph is generally the right place for a transition sentence. Each paragraph should focus on one topic, so avoid spending time at the end of a paragraph explaining the theme of the next one.

The first dissenter to consider is …

However, several scholars dissent from this consensus. The first one to consider is …

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While transitions between paragraphs are generally a single sentence, when you start a new section in a longer text, you may need an entire transition paragraph. Transitioning to a new section involves summarizing the content of the previous section and expressing how the new one will build upon or depart from it.

For example, the following sentences might be an effective transition for a new section in a literary analysis essay.

Having established that the subjective experience of time is one of Mann’s key concerns in The Magic Mountain , it is now possible to explore how this theme facilitates the novel’s connection with World War I. The war itself is not narrated in the book, but rather hinted at as something awaiting Castorp beyond the final pages. In this way, Mann links his protagonist’s subjective experience of time to more than just his illness; it is also used to explore the period leading up to the outbreak of war.

As in academic writing generally, aim to be as concise as you can while maintaining clarity: If you can transition to a new section clearly with a single sentence, do so, but use more when necessary.

It’s also important to use effective transitions within each paragraph you write, leading the reader through your arguments efficiently and avoiding ambiguity.

The known-new contract

The order of information within each of your sentences is important to the cohesion of your text. The known-new contract , a useful writing concept, states that a new sentence should generally begin with some reference to information from the previous sentence, and then go on to connect it to new information.

In the following example, the second sentence doesn’t follow very clearly from the first. The connection only becomes clear when we reach the end.

By reordering the information in the second sentence so that it begins with a reference to the first, we can help the reader follow our argument more smoothly.

Note that the known-new contract is just a general guideline. Not every sentence needs to be structured this way, but it’s a useful technique if you’re struggling to make your sentences cohere.

Transition words and phrases

Using appropriate transition words helps show your reader connections within and between sentences. Transition words and phrases come in four main types:

• Additive transitions, which introduce new information or examples
• Adversative transitions, which signal a contrast or departure from the previous text
• Causal transitions, which are used to describe cause and effect
• Sequential transitions, which indicate a sequence

The table below gives a few examples for each type:

Grouping similar information

While transition words and phrases are essential, and every essay will contain at least some of them, it’s also important to avoid overusing them. One way to do this is by grouping similar information together so that fewer transitions are needed.

For example, the following text uses three transition words and jumps back and forth between ideas. This makes it repetitive and difficult to follow.

Rewriting it to group similar information allows us to use just one transition, making the text more concise and readable.

If you want to know more about AI tools , college essays , or fallacies make sure to check out some of our other articles with explanations and examples or go directly to our tools!

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Transitional Words and Phrases

One of your primary goals as a writer is to present ideas in a clear and understandable way. To help readers move through your complex ideas, you want to be intentional about how you structure your paper as a whole as well as how you form the individual paragraphs that comprise it. In order to think through the challenges of presenting your ideas articulately, logically, and in ways that seem natural to your readers, check out some of these resources: Developing a Thesis Statement , Paragraphing , and Developing Strategic Transitions: Writing that Establishes Relationships and Connections Between Ideas.

While clear writing is mostly achieved through the deliberate sequencing of your ideas across your entire paper, you can guide readers through the connections you’re making by using transitional words in individual sentences. Transitional words and phrases can create powerful links between your ideas and can help your reader understand your paper’s logic.

In what follows, we’ve included a list of frequently used transitional words and phrases that can help you establish how your various ideas relate to each other. We’ve divided these words and phrases into categories based on the common kinds of relationships writers establish between ideas.

Two recommendations: Use these transitions strategically by making sure that the word or phrase you’re choosing matches the logic of the relationship you’re emphasizing or the connection you’re making. All of these words and phrases have different meanings, nuances, and connotations, so before using a particular transitional word in your paper, be sure you understand its meaning and usage completely, and be sure that it’s the right match for your paper’s logic. Use these transitional words and phrases sparingly because if you use too many of them, your readers might feel like you are overexplaining connections that are already clear.

Categories of Transition Words and Phrases

Causation Chronology Combinations Contrast Example

Importance Location Similarity Clarification Concession

Conclusion Intensification Purpose Summary

Transitions to help establish some of the most common kinds of relationships

Causation– Connecting instigator(s) to consequence(s).

accordingly as a result and so because

consequently for that reason hence on account of

since therefore thus

Chronology– Connecting what issues in regard to when they occur.

after afterwards always at length during earlier following immediately in the meantime

later never next now once simultaneously so far sometimes

soon subsequently then this time until now when whenever while

Combinations Lists– Connecting numerous events. Part/Whole– Connecting numerous elements that make up something bigger.

additionally again also and, or, not as a result besides even more

finally first, firstly further furthermore in addition in the first place in the second place

last, lastly moreover next second, secondly, etc. too

Contrast– Connecting two things by focusing on their differences.

after all although and yet at the same time but

despite however in contrast nevertheless nonetheless notwithstanding

on the contrary on the other hand otherwise though yet

Example– Connecting a general idea to a particular instance of this idea.

as an illustration e.g., (from a Latin abbreviation for “for example”)

for example for instance specifically that is

to demonstrate to illustrate

Importance– Connecting what is critical to what is more inconsequential.

chiefly critically

foundationally most importantly

of less importance primarily

Location– Connecting elements according to where they are placed in relationship to each other.

above adjacent to below beyond

centrally here nearby neighboring on

opposite to peripherally there wherever

Similarity– Connecting to things by suggesting that they are in some way alike.

by the same token in like manner

in similar fashion here in the same way

likewise wherever

Other kinds of transitional words and phrases Clarification

i.e., (from a Latin abbreviation for “that is”) in other words

that is that is to say to clarify to explain

to put it another way to rephrase it

granted it is true

naturally of course

finally lastly

in conclusion in the end

to conclude

Intensification

in fact indeed no

of course surely to repeat

undoubtedly without doubt yes

for this purpose in order that

so that to that end

to this end

in brief in sum

in summary in short

to sum up to summarize

Improving Your Writing Style

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Clear, Concise Sentences

Use the active voice

Put the action in the verb

Tidy up wordy phrases

Reduce wordy verbs

Reduce prepositional phrases

Reduce expletive constructions

Avoid using vague nouns

Avoid unneccessarily inflated words

Avoid noun strings

Connecting Ideas Through Transitions

Using Transitional Words and Phrases

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Transition signals

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What are transition signals?

Transition signals are linking words or phrases that connect your ideas and add cohesion to your writing. They signpost or indicate to the reader the relationships between sentences and between paragraphs, making it easier for the reader to understand your ideas. We use a variety of transition signals to fulfil a number of functions. Some of these functions include: to show the order or sequence of events; to indicate that a new idea or an example will follow; to show that a contrasting idea will be presented, or to signal a summary or a conclusion.

How are transition signals useful?

Transition signals will:

•     make it easier for the reader to follow your ideas.

•     create powerful links between sentences and paragraphs to improve the flow of information across the whole text. The result is that the writing is smoother.

•     help to carry over a thought from one sentence to another, from one idea to another or from one paragraph to another.

How are transition signals used?

•     Transition signals are usually placed at the start of sentences; however, they may also appear in the middle or end of sentences.

•     A transition signal, or the clause introduced by a transition signal, is usually separated from the rest of the sentence by commas.

•     You DO NOT need to use transition signals in every sentence in a paragraph; however, good use of transition words will help to make the relationship between the ideas in your writing clear and logical.

Which transition signals can I use?

Before choosing a particular transition signal to use, be sure you understand its meaning and usage completely and be sure that it's the right match for the logic in your paper. Transition signals all have different meanings, nuances, and connotations.

•     To introduce an example:

•     To introduce an opposite idea or show exception:

•     To show agreement:

•     To introduce an additional idea:

•     To indicate sequence or order, or logically divide an idea:

•     To indicate time:

•     To compare:

•     To contrast:

•     To show cause and effect:

•     To summarise or conclude:

The example below illustrates how transition signals can be used to improve the quality of a piece of writing. Note how the ideas flow more smoothly and the logical relationships between the ideas are expressed clearly.

At HELPS, we endeavour to support UTS students in a number of ways. First , we offer 15-minute ‘drop in’ sessions with a HELPS Advisor. Making an appointment for these sessions is not necessary. Here , students can gain assistance with their academic writing and presentation skills. Specifically , students may ask for assistance with: understanding an assignment question; understanding assessment criteria; clarifying an assignment type (e.g. what’s a literature review?); planning for an assignment; strategies for effective reading/note-taking skills; and obtaining information from self-study resources. During this time , the HELPS Advisor may refer students for a longer, 40-minute consultation. Students cannot, however , book one-to-one advice sessions online; only a HELPS Advisor can do that.

Getting one-to-one advice is an opportunity for an in-depth discussion with a HELPS Advisor in relation to your specific needs on an assessment. For example , you may require assistance preparing for an oral presentation. Alternatively , you may ask a HELPS Advisor to discuss a draft of an assignment to ensure that you have addressed the assessment criteria. While HELPS Advisors cannot edit your work, they can point out persistent errors in your text and show you how to correct these. In other words , they can help you to edit your own work. 

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The Learning Centre 2013, Transition signals in writing , UNSW, viewed 20 September 2013, < https://student.unsw.edu.au/transition-signals-writing >.

Unilearning 2000, Transition signals , UOW, viewed 20 September 2013, <The UniLearning website is no longer available>.

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Writing Studio

Common transition words and phrases.

In an effort to make our handouts more accessible, we have begun converting our PDF handouts to web pages. Download this page as a PDF: Transitions Return to Writing Studio Handouts

Transitions clarify the logic of your argument by orienting your reader as you develop ideas between sentences and paragraphs. These tools should alert readers to shifts in your argument while and also maintain the smoothness and clarity of your prose. Below, you’ll find some of the most commonly used transition categories and examples of each. Depending on the example, these suggestions may be within sentences or at the beginning of sentences.

Transitions by Category

1. addition.

Use when presenting multiple ideas that flow in the same direction, under the same heading/ idea also, another, finally, first, first of all, for one thing, furthermore, in addition, last of all, likewise, moreover, next, and, second, the third reason

2. Sequence/ Order

Use to suggest a temporal relationship between ideas; places evidence in sequence first, second (etc.), next, last, finally, first of all, concurrently, immediately, prior to, then, at that time, at this point, previously, subsequently, and then, at this time, thereafter, previously, soon, before, after, followed by, after that, next, before, after, meanwhile, formerly, finally, during

3. Contrast

Use to demonstrate differences between ideas or change in argument direction but, however, in contrast, on the other hand, on the contrary, yet, differ, difference, balanced against, differing from, variation, still, on the contrary, unlike, conversely, otherwise, on the other hand, however

4. Exception

Use to introduce an opposing idea however, whereas, on the other hand, while, instead, in spite of, yet, despite, still, nevertheless, even though, in contrast, but, but one could also say…

5. Comparison

Use to demonstrate similarities between ideas that may not be under the same subject heading or within the same paragraph like, likewise, just, in a different way / sense, whereas, like, equally, in like manner, by comparison, similar to, in the same way, alike, similarity, similarly, just as, as in a similar fashion, conversely

6. Illustration

Use to develop or clarify an idea, to introduce examples, or to show that the second idea is subordinate to the first for example, to illustrate, on this occasion, this can be seen, in this case, specifically, once, to illustrate, when/where, for instance, such as, to demonstrate, take the case of, in this case

7. Location

Use to show spatial relations next to, above, below, beneath, left, right, behind, in front, on top, within

8. Cause and Effect

Use to show that one idea causes, or results from, the idea that follows or precedes it because, therefore, so that, cause, reason, effect, thus, consequently, since, as a result, if…then, result in

9. Emphasis

Use to suggest that an idea is particularly important to your argument important to note, most of all, a significant factor, a primary concern, a key feature, remember that, pay particular attention to, a central issue, the most substantial issue, the main value, a major event, the chief factor, a distinctive quality, especially valuable, the chief outcome, a vital force, especially relevant, most noteworthy, the principal item, above all, should be noted

10. Summary or Conclusion

Use to signal that what follows is summarizing or concluding the previous ideas; in humanities papers, use these phrases sparingly. to summarize, in short, in brief, in sum, in summary, to sum up, in conclusion, to conclude, finally

Some material adapted from Cal Poly Pomona College Reading Skills Program and “ Power Tools for Technical Communication .” 

Writing Effective Sentence Transitions (Advanced)

Transitions are the rhetorical tools that clarify the logic of your argument by orienting your reader as you develop ideas between sentences and paragraphs. The ability to integrate sentence transitions into your prose, rather than simply throwing in overt transition signals like “in addition,” indicates your mastery of the material. (Note: The visibility of transitions may vary by discipline; consult with your professor to get a better sense of discipline or assignment specific expectations.)

Transition Signals

Transition signals are words or phrases that indicate the logic connecting sets of information or ideas. Signals like therefore, on the other hand, for example, because, then, and afterwards can be good transition tools at the sentence and paragraph level. When using these signals, be conscious of the real meaning of these terms; they should reflect the actual relationship between ideas.

Review Words

Review words are transition tools that link groups of sentences or whole paragraphs. They condense preceding discussion into a brief word or phrase. For example: You’ve just completed a detailed discussion about the greenhouse effect. To transition to the next topic, you could use review words like “this heat-trapping process” to refer back to the green house effect discussion. The relative ability to determine a cogent set of review words might signal your own understanding of your work; think of review words as super-short summaries of key ideas.

Preview words

Preview words condense an upcoming discussion into a brief word or phrase. For example: You’ve just explained how heat is trapped in the earth’s atmosphere. Transitioning to the theory that humans are adding to that effect, you could use preview words like “sources of additional CO2 in the atmosphere include” to point forward to that discussion.

Transition Sentences

The strongest and most sophisticated tools, transition sentences indicate the connection between the preceding and upcoming pieces of your argument. They often contain one or more of the above transition tools. For example: You’ve just discussed how much CO2 humans have added to the atmosphere. You need to transition to a discussion of the effects. A strong set of transition sentences between the two sections might sound like this:

“These large amounts of CO2 added to the atmosphere may lead to a number of disastrous consequences for residents of planet earth. The rise in global temperature that accompanies the extra CO2 can yield effects as varied as glacial melting and species extinction.”

In the first sentence, the review words are “These large amounts of CO2 added to the atmosphere”; the preview words are “number of disastrous consequences”; the transition signals are “may lead to.” The topic sentence of the next paragraph indicates the specific “disastrous consequences” you will discuss.

If you don’t see a way to write a logical, effective transition between sentences, ideas or paragraphs, this might indicate organizational problems in your essay; you might consider revising your work.

Some material adapted from Cal Poly Pomona College Reading Skills Program  and “ Power Tools for Technical Communication .”

Last revised: 07/2008 | Adapted for web delivery: 05/2021

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Unit 8: Academic Writing Resources

52 Transition Words for Cohesion and Coherence

Transition words and phrases.

Transition words and phrases are used to connect ideas together. They are used within paragraphs and between paragraphs to enhance the flow of ideas.

Below are some common expressions. Some are useful for connecting paragraphs while others are more appropriate for joining ideas within a sentence. The best way to learn which transition words can be used for which purposes is to pay attention to the way they are used in the texts you read.

Transition words in any given category are NOT synonyms, and often require different grammatical structures. Choose exactly the best word for your purposes (don’t just substitute). Use the Skell Corpus to check how these expressions are used in example sentences.

Additive Transitions

Function: to connect two ideas together by adding additional information

furthermore, moreover, in addition, also

admittedly, certainly, typically

in fact, indeed

first, second, third

Order of Importance Transitions

Function: to signal the importance of events

above all, first and foremost, more/most

importantly, significantly, primarily

a more important, the most important, the primary / main, the second most significant

Contrastive Transitions

Function: to signal a contradiction or difference

however, nevertheless, in contrast, on the other hand

although, even though, whereas, while

despite, in spite of, compared to/with

Comparative Transitions

Function: to emphasize similarity

likewise, similarly, at the same time

by comparison, in much the same way, once again

Cause and Effect Transitions

Function: to signal that one event happens as a result of another

as a result / consequence, consequently, therefore / thus, for this reason

because, since

due to, be the result of, given that

Giving Examples

Function: to introduce an illustration or example

for example, for instance, to illustrate

specifically, in particular, that is

such as, an example of

Conclusion Transitions

Function: to signal a final summary of ideas

to summarize, in summary, in short, in sum

in conclusion, to conclude

accordingly, ultimately

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Transition words for essays

The right transition words can transform a mediocre essay into a great paper. In this post, we discuss why effective transitions can substantially improve the quality and readability of your essay and provide examples of commonly used transition words.

What are transitions?

Transitions are the places in your paper where you move on to a new idea or paragraph. They may also be points at which you want to add to, expand upon, or conclude a previous statement.

The best transitions are signaled clearly by keywords and phrases that let the reader know that you’re moving on. Transition words typically occur at the beginning of a sentence.

How do transition words improve your essay?

Quality transitions are often the difference between a decent essay and a strong one. Transition words give clear signals to the reader that you are moving on to a new idea and this enables them to more easily follow your argument.

When a reader can efficiently follow the main threads of your paper, then they are more likely to be persuaded by your argument, which is the point of papers like argumentative essays .

Types of transition words

The transition words that you use in your paper will naturally depend on what kind of transition you’re making. In this section, we break down the main types of transitions that you might use in your essay and provide examples of common transition words.

Adding a point

There may be multiple times throughout a paper where you want to add to a point that you made or that came from one of your sources. To signal this, you might use one of the following phrases:

• additionally
• furthermore
• in addition

Elaborating on a point

At other times, you may need to expand, or elaborate upon, a previously stated idea. In that case, you may utilize one of these keywords:

• by extension
• in other words
• put differently

Introducing examples

Sometimes you may want to introduce an example that illustrates a previous point. To introduce examples, you can use one of the following phrases:

• for example
• for instance
• specifically
• to take a case in point

Indicating comparisons and contrasts

Some types of essays, like position papers, require you to introduce contrasting points of view. In order to transition from one perspective to another, you may want to use a transition word or phrase that signals a comparison or contrast:

Comparison :

• along the same lines
• in the same way
• in the same vein
• by contrast
• even though
• in contrast
• nevertheless
• nonetheless
• on the contrary
• on the other hand

Showing cause and effect

If you’re building an argument and you want to indicate that one point is dependent on another, you might want to employ one of these phrases to signal that transition:

• accordingly
• as a result
• consequently

When you are ready to conclude a point or prepare your reader for your paper’s conclusion, it’s important to signal that you’re at that stage. Consider using one of these transition words to do so:

• in conclusion
• to summarize

If you are transitioning between your own words and borrowed material from secondary sources, be sure to properly cite any ideas that aren’t your own. You can use the BibGuru citation generator to create instant, accurate citations for a range of source types, including books , articles , and websites .

Frequently Asked Questions about transition words for essays

Commonly used transition words include: additionally, although, as a result, for example, for instance, however, moreover, therefore, thus, and ultimately.

To link two points together, or to add to a previous point, you might use transition words like:

The most popular types of transitions are those that introduce examples or that add to, elaborate upon, compare or contrast, or conclude a previous point.

To signal a transition in an essay, use a transition word or phrase. Choose a phrase based on the kind of transition that you’re making.

Transition words give clear signals to the reader that you are moving on to a new idea and or that you want to add to, expand, or conclude a previous point. Transition words can also be used to introduce examples and to indicate a comparison or contrast.

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For students and teachers.

Transition Words

As a "part of speech" transition words are used to link words, phrases or sentences. They help the reader to progress from one idea (expressed by the author) to the next idea. Thus, they help to build up coherent relationships within the text.

Transitional Words

This structured list of commonly used English transition words — approximately 200, can be considered as quasi complete. It can be used (by students and teachers alike) to find the right expression. English transition words are essential, since they not only connect ideas, but also can introduce a certain shift, contrast or opposition, emphasis or agreement, purpose, result or conclusion, etc. in the line of argument. The transition words and phrases have been assigned only once to somewhat artificial categories, although some words belong to more than one category.

There is some overlapping with prepositions and postpositions, but for the purpose of usage and completeness of this concise guide, I did not differentiate.

Linking & Connecting Words — Part 1/2

Agreement / Addition / Similarity

Opposition / limitation / contradiction, examples / support / emphasis, cause / condition / purpose, effect / consequence / result, conclusion / summary / restatement, time / chronology / sequence, space / location / place.

The transition words like also, in addition, and, likewise , add information , reinforce ideas , and express agreement with preceding material.

in the first place

not only ... but also

as a matter of fact

in like manner

in addition

coupled with

in the same fashion / way

first, second, third

in the light of

not to mention

to say nothing of

equally important

by the same token

identically

together with

comparatively

correspondingly

furthermore

additionally

Transition phrases like but , rather and or , express that there is evidence to the contrary or point out alternatives , and thus introduce a change the line of reasoning ( contrast ).

although this may be true

in contrast

different from

of course ..., but

on the other hand

on the contrary

at the same time

in spite of

even so / though

be that as it may

(and) still

even though

nevertheless

nonetheless

notwithstanding

These transitional phrases present specific conditions or intentions .

in the event that

granted (that)

as / so long as

on (the) condition (that)

for the purpose of

with this intention

with this in mind

in the hope that

to the end that

for fear that

in order to

seeing / being that

provided that

only / even if

inasmuch as

These transitional devices (like especially ) are used to introduce examples as support , to indicate importance or as an illustration so that an idea is cued to the reader.

in other words

to put it differently

for one thing

as an illustration

in this case

for this reason

to put it another way

that is to say

with attention to

by all means

important to realize

another key point

first thing to remember

most compelling evidence

must be remembered

point often overlooked

to point out

on the positive side

on the negative side

specifically

surprisingly

significantly

particularly

in particular

for example

for instance

to demonstrate

to emphasize

to enumerate

Some of these transition words ( thus, then, accordingly, consequently, therefore, henceforth ) are time words that are used to show that after a particular time there was a consequence or an effect .

Note that for and because are placed before the cause/reason. The other devices are placed before the consequences or effects.

as a result

under those circumstances

in that case

because the

consequently

accordingly

These transition words and phrases conclude , summarize and / or restate ideas, or indicate a final general statement . Also some words (like therefore ) from the Effect / Consequence category can be used to summarize.

as can be seen

generally speaking

in the final analysis

all things considered

as shown above

in the long run

given these points

as has been noted

for the most part

in conclusion

to summarize

by and large

on the whole

in any event

in either case

These transitional words (like finally ) have the function of limiting, restricting, and defining time . They can be used either alone or as part of adverbial expressions .

at the present time

from time to time

sooner or later

up to the present time

to begin with

in due time

in the meantime

in a moment

without delay

all of a sudden

at this instant

first, second

immediately

straightaway

by the time

occasionally

Many transition words in the time category ( consequently; first, second, third; further; hence; henceforth; since; then, when; and whenever ) have other uses.

Except for the numbers ( first, second, third ) and further they add a meaning of time in expressing conditions, qualifications, or reasons. The numbers are also used to add information or list examples . Further is also used to indicate added space as well as added time.

These transition words are often used as part of adverbial expressions and have the function to restrict, limit or qualify space . Quite a few of these are also found in the Time category and can be used to describe spatial order or spatial reference.

in the middle

to the left/right

in front of

on this side

in the distance

here and there

in the foreground

in the background

in the center of

adjacent to

opposite to 

List of Transition Words

Transition Words are also sometimes called (or put in the category of) Connecting Words. Please feel free to download them via this link to the category page: Linking Words & Connecting Words as a PDF. It contains all the transition words listed on this site. The image to the left gives you an impression how it looks like.

Usage of Transition Words in Essays

Transition words and phrases are vital devices for essays , papers or other literary compositions. They improve the connections and transitions between sentences and paragraphs. They thus give the text a logical organization and structure (see also: a List of Synonyms ).

All English transition words and phrases (sometimes also called 'conjunctive adverbs') do the same work as coordinating conjunctions : they connect two words, phrases or clauses together and thus the text is easier to read and the coherence is improved.

Usage: transition words are used with a special rule for punctuation : a semicolon or a period is used after the first 'sentence', and a comma is almost always used to set off the transition word from the second 'sentence'.

Example 1: People use 43 muscles when they frown; however, they use only 28 muscles when they smile.

Example 2: however, transition words can also be placed at the beginning of a new paragraph or sentence - not only to indicate a step forward in the reasoning, but also to relate the new material to the preceding thoughts..

Use a semicolon to connect sentences, only if the group of words on either side of the semicolon is a complete sentence each (both must have a subject and a verb, and could thus stand alone as a complete thought).

Further helpful readings about expressions, writing and grammar: Compilation of Writing Tips How to write good   ¦   Correct Spelling Study by an English University

Are you using WORD for writing professional texts and essays? There are many easy Windows Shortcuts available which work (almost) system-wide (e.g. in every programm you use).

Complete List of Transition Words

100 Words and Phrases to Use Between Paragraphs

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Transition words and phrases can help your paper move along, smoothly gliding from one topic to the next. As a result, they come in very handy as you're writing.

Transitions, which connect one idea to the next, may seem challenging at first, but they get easier once you consider the many possible methods for linking paragraphs together—even if they seem to be unrelated.

If you have trouble thinking of a way to connect your paragraphs, consider a few of these 100 top transitions as inspiration. The type of transition words or phrases you use depends on the category of transition you need, as explained below.

Additive Transitions

Probably the most common type, additive transitions are those you use when you want to show that the current point is an addition to the previous one, according to Edusson, a website that provides students with essay-writing tips and advice . Put another way, additive transitions signal to the reader that you are adding to an idea or that your ideas are similar. Follow each transition word or phrase with a comma:

• In the first place
• Furthermore
• Alternatively
• As well (as this)
• What is more
• In addition (to this)
• On the other hand
• Either (neither)
• As a matter of fact
• Besides (this)
• To say nothing of
• Additionally
• Not to mention (this)
• Not only (this) but also (that) as well
• In all honesty
• To tell the truth

Example Additive Transition

An example of additive transitions used in a sentence would be:

" In the first place , no 'burning' in the sense of combustion, as in the burning of wood, occurs in a volcano;  moreover , volcanoes are not necessarily mountains;  furthermore , the activity takes place not always at the summit but more commonly on the sides or flanks..." – Fred Bullard, "Volcanoes in History, in Theory, in Eruption"

In this example and others in this piece, the transition words or phrases are printed in italics to make them easier to find as you peruse the passages.

Adversative Transitions

Adversative transitions are used to signal conflict, contradiction, concession, and dismissal, according to Michigan State University. Examples include:

• In contrast
• But even so
• Nevertheless
• Nonetheless
• (And) still
• In either case
• (Or) at least
• Whichever happens
• Whatever happens
• In either event

Example Adversative Transition

An example of an adversative transition phrase used in a sentence would be:

" On the other hand, professor Smith completely disagreed with the author's argument."

Causal Transitions

Causal transitions—also called cause-and-effect transitions—show how certain circumstances or events were caused by other factors. Using them helps readers follow the logic of arguments and clauses in your paper. Examples include:

• Accordingly
• As a result
• Consequently
• For this reason
• Granting (that)
• On the condition (that)
• In the event that
• As a result (of this)
• Because (of this)
• As a consequence
• In consequence
• So much (so) that
• For the purpose of
• With this intention
• With this in mind
• Under those circumstances
• That being the case

Example Causal Transition

An example of a causal transition used in a sentence would be:

"The study of human chromosomes is in its infancy,  and so  it has only recently become possible to study the effect of environmental factors upon them." –Rachel Carson, "Silent Spring"

Sequential Transitions

Sequential transitions express a numerical sequence, continuation, conclusion , digression , resumption, or summation. Here are some examples:

• In the (first, second, third, etc.) place
• To begin with
• To start with
• Subsequently
• To conclude with
• As a final point
• Last but not least
• To change the topic
• Incidentally
• To get back to the point
• As was previously stated

Example Sequential Transition

An example of a sequential transition would be:

"We should teach that words are not the things to which they refer. We should teach that words are best understood as convenient tools for handling reality... Finally , we should teach widely that new words can and should be invented if the need arises." –Karol Janicki, "Language Misconceived"

How to Practice Using Transition Words

In sum , use transition words and phrases judiciously to keep your paper moving, hold your readers' attention, and retain your audience until the final word. In practice, it's a good idea to rewrite some of the introductory sentences at the beginning and the transition statements at the end of every paragraph once you have completed the first draft of your paper. Practice with some of the words on this list and decide which flows best.

Edusson. " Common Transitions to Use in Cause and Effect Essay ."

Academic Help. " Common Transitions Words and Phrases ."

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Conclusion transition words: Phrases for summarizing and ending

Transition words help us structure our thoughts and guide the reader or listener through what we are saying. When it’s time to summarize your message or end a paragraph, conclusion transition words let you signal this closing.

It’s good to know some synonyms for ‘in conclusion’ and ‘to conclude’, because although these are good examples of concluding words, they can get repetitive.

Our comprehensive list of transition words for conclusion and summary should give you all the inspiration you need, whether you are writing an essay or speech, or just want to become more confident forming an argument. These signal words can also be helpful for restating ideas, drawing attention to key points as you conclude.

We have included plenty of examples of how you can use these transition words for concluding paragraphs or sentences, so by the end of this article, you should be clear on how to use them properly.

Conclusion transition words with examples

We have grouped these summarizing and concluding transition words according to how and where they can be used. For example, some should only be used when forming a final conclusion, whereas others can be used to summarize sections mid-way through your speech or writing.

First, let’s be clear about the difference between a summary and a conclusion .

Summary vs conclusion

A conclusion comes at the end of a speech, chapter, or piece of text, and it brings together all of the points mentioned. A summary, however, can be placed anywhere (even at the beginning). A summary gives a brief outline of the main points but is not as in-depth as a conclusion.

If you are giving a presentation or writing a blog, you may wish to summarize the main points in your introduction so that people know what you are going to cover. You could also summarize a section part-way through before moving on to another angle or topic.

In contrast, the conclusion always comes at the end, and you should only use specific conclusion transition words as you are drawing to a close.

Transition words for conclusion paragraphs

Let’s begin with some discourse markers that signal you are moving to the concluding paragraph in your presentation, speech, essay, or paper. These can all be used to start a conclusion paragraph.

• In conclusion
• To conclude
• We can conclude that
• Given these points
• In the final analysis
• As can be seen
• In the long run
• When all is said and done
• I’ll end by
• As we draw to a close

The last three on this list, the ‘closing’ transition words, would generally only be used in spoken discourse.

Some transition words for order and sequencing should also help with structuring what you want to say, including the ending.

Example conclusion sentences

The following sentences show how to use conclusion words correctly:

• In conclusion , we can say that plan A will be of greater benefit to the company.
• When all is said and done , it’s clear that we should steer clear of this investment strategy.
• Given these points , I believe the trial was a great success.
• I’ll end by reminding you all that this experiment was just the beginning of a much larger project.
• To wrap up , let’s look at how this learning can be applied.
• In the long run , we will make more profit by investing heavily in new machinery.
• Having analyzed seven of our competitors in detail, we can conclude that our content marketing strategy should be updated.

Transition words for summary

The following summary transition words may be used as part of a conclusion paragraph, but they are especially helpful for concisely drawing together several points.

• To summarize
• On the whole
• Generally speaking
• All things considered
• In a nutshell (informal)
• In any case

Note that although you can insert summary transition words anywhere, the specific phrases ‘In summary’, ‘To summarize’ and ‘To sum up’ are generally only used at the end, similar to conclusion phrases.

Example summary sentences

• In brief , this presentation is going to cover the pros and cons of the device and how we can apply this to our own product development.
• This new technology is, in a word , revolutionary.
• All things considered , we found that Berlin was a great city for a weekend break.
• To summarize , we can say that Shakespeare’s writing continues to have a global influence.
• We can say that the combustion engine was, on the whole , a good invention.
• In any case , we should put the necessary precautions in place.
• Generally speaking , girls are more thoughtful than boys.

Transition words to end a paragraph

You may wish to add ending transition words in the final sentence of a paragraph to conclude the ideas in that section of text, before moving on to another point.

Here are some transition words to conclude a paragraph:

• This means that
• With this in mind
• By and large
• For the most part

Note that some of these could equally be used to begin a new paragraph, so long as that paragraph is summarizing the points previously mentioned.

Cause and effect transition words could also be helpful in this context.

Examples of transition words for the end of a paragraph

• Jamie is a vegan and Sheryl has a lot of allergies. This means that we should be careful which restaurant we choose.
• The weather forecast said it would rain this afternoon. With this in mind , should we postpone our hike?
• Each of the students has their own opinion about where to go for the field trip. Ultimately , though, it’s the teacher who will decide.

Restating points as you conclude

Conclusion transition words can also signal that you are restating a point you mentioned earlier. This is common practice in both writing and speaking as it draws the reader or listener’s attention back to something you want them to keep in mind. These are, therefore, also examples of transition words for emphasizing a point .

Here are some helpful transition words for concluding or summarizing by restating points:

• As mentioned previously
• As stated earlier
• As has been noted
• As shown above
• As I have said
• As I have mentioned
• As we have seen
• As has been demonstrated

You may switch most of these between the passive and active voice, depending on which is most appropriate. For example, ‘As has been demonstrated’ could become ‘As I have demonstrated’ and ‘As shown above’ could become ‘As I have shown’.

Example sentences to restate a point in conclusion or summary

• As I stated earlier , the only way we can get meaningful results from this survey is by including at least a thousand people.
• As has been demonstrated throughout this conference, there are exciting things happening in the world of neuroscience.
• As shown by this study, the trials have been promising.

If you were researching these transition words for concluding an essay, you might find it helpful to read this guide to strong essay conclusions . Of course, there are many ways to use summary transition words beyond essays. They may be a little formal for casual conversation, but they certainly can be used in speech as part of a presentation, debate, or argument.

Can you think of any other concluding words or phrases that should be on this list? Leave a comment below to share them!

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33 Transition Words and Phrases

Transitional terms give writers the opportunity to prepare readers for a new idea, connecting the previous sentence to the next one.

Many transitional words are nearly synonymous: words that broadly indicate that “this follows logically from the preceding” include accordingly, therefore, and consequently . Words that mean “in addition to” include moreover, besides, and further . Words that mean “contrary to what was just stated” include however, nevertheless , and nonetheless .

as a result : THEREFORE : CONSEQUENTLY

The executive’s flight was delayed and they accordingly arrived late.

in or by way of addition : FURTHERMORE

The mountain has many marked hiking trails; additionally, there are several unmarked trails that lead to the summit.

at a later or succeeding time : SUBSEQUENTLY, THEREAFTER

Afterward, she got a promotion.

even though : ALTHOUGH

She appeared as a guest star on the show, albeit briefly.

in spite of the fact that : even though —used when making a statement that differs from or contrasts with a statement you have just made

They are good friends, although they don't see each other very often.

in addition to what has been said : MOREOVER, FURTHERMORE

I can't go, and besides, I wouldn't go if I could.

as a result : in view of the foregoing : ACCORDINGLY

The words are often confused and are consequently misused.

in a contrasting or opposite way —used to introduce a statement that contrasts with a previous statement or presents a differing interpretation or possibility

Large objects appear to be closer. Conversely, small objects seem farther away.

used to introduce a statement that is somehow different from what has just been said

These problems are not as bad as they were. Even so, there is much more work to be done.

used as a stronger way to say "though" or "although"

I'm planning to go even though it may rain.

in addition : MOREOVER

I had some money to invest, and, further, I realized that the risk was small.

in addition to what precedes : BESIDES —used to introduce a statement that supports or adds to a previous statement

These findings seem plausible. Furthermore, several studies have confirmed them.

because of a preceding fact or premise : for this reason : THEREFORE

He was a newcomer and hence had no close friends here.

from this point on : starting now

She announced that henceforth she would be running the company.

in spite of that : on the other hand —used when you are saying something that is different from or contrasts with a previous statement

I'd like to go; however, I'd better not.

as something more : BESIDES —used for adding information to a statement

The city has the largest population in the country and in addition is a major shipping port.

all things considered : as a matter of fact —used when making a statement that adds to or strengthens a previous statement

He likes to have things his own way; indeed, he can be very stubborn.

for fear that —often used after an expression denoting fear or apprehension

He was concerned lest anyone think that he was guilty.

in addition : ALSO —often used to introduce a statement that adds to and is related to a previous statement

She is an acclaimed painter who is likewise a sculptor.

at or during the same time : in the meantime

You can set the table. Meanwhile, I'll start making dinner.

BESIDES, FURTHER : in addition to what has been said —used to introduce a statement that supports or adds to a previous statement

It probably wouldn't work. Moreover, it would be very expensive to try it.

in spite of that : HOWEVER

It was a predictable, but nevertheless funny, story.

in spite of what has just been said : NEVERTHELESS

The hike was difficult, but fun nonetheless.

without being prevented by (something) : despite—used to say that something happens or is true even though there is something that might prevent it from happening or being true

Notwithstanding their youth and inexperience, the team won the championship.

if not : or else

Finish your dinner. Otherwise, you won't get any dessert.

more correctly speaking —used to introduce a statement that corrects what you have just said

We can take the car, or rather, the van.

in spite of that —used to say that something happens or is true even though there is something that might prevent it from happening or being true

I tried again and still I failed.

by that : by that means

He signed the contract, thereby forfeiting his right to the property.

for that reason : because of that

This tablet is thin and light and therefore very convenient to carry around.

immediately after that

The committee reviewed the documents and thereupon decided to accept the proposal.

because of this or that : HENCE, CONSEQUENTLY

This detergent is highly concentrated and thus you will need to dilute it.

while on the contrary —used to make a statement that describes how two people, groups, etc., are different

Some of these species have flourished, whereas others have struggled.

NEVERTHELESS, HOWEVER —used to introduce a statement that adds something to a previous statement and usually contrasts with it in some way

It was pouring rain out, yet his clothes didn’t seem very wet.

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Home  / Blog  / Improve your Writing  / Master Transition Signals

Master transition signals - linking words

If there is anything guaranteed to put a smile on the face of essay assessors, including IELTS examiners, it’s a piece of writing that hits that “Coherence and Cohesion” sweet spot . Cohesion and Coherence enhance the readability of an essay by improving the logical flow of ideas. One excellent way to achieve Coherence and Cohesion is by using transition signals, which are linking words and phrases that “glue” your sentences and paragraphs together.

Transition signals fall into several broad categories. In this post, I’ll be analysing a few key types using texts about well-known figures. Let’s get started.

Michelle Obama’s passion for education

Michelle Obama

Can you figure out what these transition signals in bold have in common? Choose the correct answer:

a) They contrast ideas. b) They add information. c) They give an example.

Former First Lady Michelle Obama has always been very involved in humanitarian pursuits with youth. After graduating with a Law degree from Harvard, Michelle founded the Chicago chapter of Public Allies, which engages young adults in leadership programmes. Furthermore , her initiative, Let’s Move!, targets the prevalent issue of childhood obesity. In addition to these pursuits, Michelle joined forces with her husband in launching Let Girls Learn, which helps girls around the globe to complete high school. Moreover , Michelle’s Reach Higher project is aimed at giving young adults the tools to finish their higher education. Besides her involvement in education, Michelle also supports several other initiatives, including Joining Forces. The programme runs projects for American veterans related to employment and general wellness. Information sourced from Obama White House archives .

The transition signals above all add information linked to Michelle Obama’s humanitarian endeavours, so the correct answer is “b”. As you can see from the example, transition signals that show addition are primarily used at the beginning of a new sentence as sentence connectors .

Other addition transition signals include (but are not limited to): “additionally”, “in addition to”, and “apart from this”.

Now let’s look at how we can use more than one type of transition signal by reading a passage about a beloved South African icon…

Nelson Mandela

What is the function of the two types of transition signals in this text? Choose one answer below:

a) They show comparison & contrast as well as cause & effect. b) They reinforce ideas and show sequence. c) They offer conclusions and show alternatives.

Many of us know Mandela as the icon who championed equal rights for all South Africans. But there are also many facts about him that are less well-known. For instance, he was mad about sports and believed that football had the potential to inspire youth. Similarly , he was interested in the life lessons that could be acquired through boxing.  While Mandela was expelled from the University of Fort Hare in 1931 for joining a student protest, he didn’t give up. On the contrary , he eventually earned honorary degrees from over 50 universities. The king of Mandela’s village planned an arranged marriage for the young Nelson. For this reason , he fled to Johannesburg. Mandela was a self-professed master of disguises, dressing as a field worker, a chauffeur, and even a chef. Consequently , he was able to evade authorities. Mandela lived to the ripe old age of 95, whereas his own father sadly passed away when Mandela was just nine years’ old.

If you chose “a” as your answer, bravo. The transition words in red show comparison or contrast. The words in yellow show cause and effect.

Compare & contrast transition signals

Let’s look at compare & contrast transition signals in more detail, since the “compare and contrast essay” is a common type of academic essay, which examines the similarities and differences between two or more ideas.  As the EAP Foundation explains: “To compare is to examine how things are similar, while to contrast is to see how they differ.” For example:

Children can quite easily acquire a new language. Conversely , adults need to work harder to acquire a second language. Here we are examining the difference between the way children and adults acquire language, so a contrast transition signal is used.

Just as children can quite easily acquire a new language, so can they learn how to play musical instruments with less effort than adults. Here the sentence goes on to expand on the idea in a similar vein and so a comparison transition signal (just as… so) is used.

Let’s look at one more passage to examine two other types of transition signals…

Ellen DeGeneres and a famous fish

Ellen Degeneres

There are three transition signals below. Two types are used to emphasise an idea. One type is used to summarise ideas. Can you identify them?

The renowned comedienne and talk-show host, Ellen DeGeneres, once tore a ligament after reportedly leaning over to pick up her dog. But this didn’t stop her. In fact, Ellen continued to film her talk show from hospital. Ellen was the voice of the forgetful fish Dory in the Pixar film, Finding Nemo. Clearly, the star, who is rumoured to always change the topic mid-sentence, was a shoo-in for the role. But don’t let her quirkiness fool you. Ellen, whose net worth stands at around $370 million, is far from “blonde” , despite her hair colour. In fact, last year Forbes magazine named her the twelfth highest-paid celebrity in the world. In conclusion, Ellen has achieved great success. Information sourced from Fascinate.com .

Did you find them? The emphasis transition signals , used to emphasise a point, are “in fact” and “clearly”. A transition signal which is used to summarise information in this passage is “in conclusion.”

And on that note… In conclusion, you can master transition signals by reading articles, essays, and books. Here’s a bright idea – why not stock up on some biographies of well-known icons and get some inspiration while boosting your English language skills? Happy reading.

By Leigh-Anne Hunter

Read more about academic writing Writing Paragraphs , Stronger Topic Sentences , Mastering Topic Sentences , Paraphrasing like a Pro , Common Transition Signal Errors and How to Fix Them

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• Open access
• Published: 01 September 2024

A tunable transition metal dichalcogenide entangled photon-pair source

• Maximilian A. Weissflog   ORCID: orcid.org/0000-0002-3091-1441 1 , 2 ,
• Anna Fedotova   ORCID: orcid.org/0000-0002-4118-8789 1 , 3 ,
• Yilin Tang 4 ,
• Elkin A. Santos 1 ,
• Benjamin Laudert 1 ,
• Saniya Shinde   ORCID: orcid.org/0009-0001-9902-7945 1 ,
• Fatemeh Abtahi 1 ,
• Mina Afsharnia 1 ,
• Inmaculada Pérez Pérez   ORCID: orcid.org/0009-0004-7791-9813 1 ,
• Sebastian Ritter   ORCID: orcid.org/0000-0003-1491-6098 1 , 2 , 5 ,
• Hao Qin 4 ,
• Jiri Janousek 4 , 6 ,
• Sai Shradha 1 , 7 ,
• Isabelle Staude   ORCID: orcid.org/0000-0001-8021-572X 1 , 3 ,
• Sina Saravi   ORCID: orcid.org/0000-0003-4089-1189 1 ,
• Thomas Pertsch   ORCID: orcid.org/0000-0003-4889-0869 1 , 5 ,
• Frank Setzpfandt   ORCID: orcid.org/0000-0002-7919-8181 1 , 5 ,
• Yuerui Lu   ORCID: orcid.org/0000-0001-6131-3906 4 , 6 &
• Falk Eilenberger   ORCID: orcid.org/0000-0002-4646-2484 1 , 2 , 5  

Nature Communications volume  15 , Article number:  7600 ( 2024 ) Cite this article

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• Materials for optics
• Nanoscale materials
• Optical materials and structures
• Quantum optics
• Sub-wavelength optics

Entangled photon-pair sources are at the core of quantum applications like quantum key distribution, sensing, and imaging. Operation in space-limited and adverse environments such as in satellite-based and mobile communication requires robust entanglement sources with minimal size and weight requirements. Here, we meet this challenge by realizing a cubic micrometer scale entangled photon-pair source in a 3R-stacked transition metal dichalcogenide crystal. Its crystal symmetry enables the generation of polarization-entangled Bell states without additional components and provides tunability by simple control of the pump polarization. Remarkably, generation rate and state tuning are decoupled, leading to equal generation efficiency and no loss of entanglement. Combining transition metal dichalcogenides with monolithic cavities and integrated photonic circuitry or using quasi-phasematching opens the gate towards ultrasmall and scalable quantum devices.

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Introduction.

Entangled photon pairs are the key-enabler for real-world implementations of quantum technologies like secure quantum key distribution 1 , 2 , quantum sensing, and imaging 3 , as well as distributed quantum computing schemes 4 . Consequently, a large variety of entangled photon-pair sources (EPS) has been developed, often relying on spontaneous parametric down-conversion (SPDC) in second-order nonlinear crystals 5 . Setting out from the first EPS implementations based on single bulk crystals 6 , ever more complex source designs were developed to meet requirements for the degree of entanglement, quantum state fidelity, tunability, and brightness of the sources. Solutions to create entangled photon pairs are typically based on the interference of two distinct SPDC processes and range from using two crossed nonlinear crystals 7 via a combination of different down-conversion paths in Sagnac and linear interferometers 5 to integrated photonic systems 8 . Achieving a high degree of entanglement in such sources imposes very narrow tolerances on the properties of the different SPDC processes to allow the necessary coherent superposition. This technological challenge is further increased by the demand to operate these complex sources in adverse and space-limited environments, such as a satellite 9 , 10 , or in customer-level applications like mobile-phone quantum key distribution, which also need a simple and scalable approach. Tunability between different entangled states is desirable for active quantum networks 11 . In light of these demands, a requirement list for an ideal EPS design would be the generation of high-fidelity, maximally entangled (Bell) states, switching between different entangled states, wide frequency coverage, and high brightness, combined with a robust, scalable design and small footprint using as few optical components as possible. A very promising nonlinear material for such an EPS are 3R-phase transition metal dichalcogenide (3R-TMD) crystals, for instance, 3R-phase molybdenum disulfide (3R-MoS 2 ). Owing to its bulk-noncentrosymmetry, the signal yield of nonlinear conversion in multilayer 3R-MoS 2 12 , 13 , 14 , 15 is drastically increased compared to monolayer (ML) TMDs 16 , 17 , 18 , 19 , 20 . The high second-order nonlinearity of 3R-MoS 2 ( χ (2)  ≈ 100 pm/V  21 in transparency region and peak values χ (2)  > 800 pm/V 14 , 21 , 22 with excitonic enhancement in absorbing region) is at the same level or largely exceeds the nonlinearity of many established materials (beta barium borate (BBO) χ (2)  = 3.9 pm/V 23 , potassium titanyl phosphate (KTP) χ (2)  = 29.2 pm/V, lithium niobate (LiNbO 3 ) χ (2)  = 49.8 pm/V, gallium arsenide (GaAs) χ (2)  = 340 pm/V (absorbing) and gallium phosphide (GaP) χ (2)  = 141 pm/V all at fundamental wavelength 1064 nm ref. 24 ). Leveraging this, it was demonstrated with second-harmonic generation (SHG) that 3R-MoS 2 requires two orders of magnitude shorter propagation length to reach the same second-order nonlinear conversion efficiency in the telecom range as LiNbO 3 13 . While in this case, crystals of only one coherence length were compared, the conversion efficiency of 3R-MoS 2 -based nonlinear sources can be scaled to the required level, e.g. through quasi-phasematching. Similar to periodic poling in ferroelectric materials, the nonlinearity in stacks of several multilayer 3R-MoS 2 crystals can be periodically modulated by suitably rotating consecutive crystals 20 , which was experimentally demonstrated very recently 21 .

In this work, we show that 3R-TMDs can serve as the core component of a compact and highly tunable EPS by demonstrating the generation of maximally entangled photon pairs from submicron 3R-MoS 2 crystals. Our photon-pair source based on 3R-MoS 2 leverages the crystal symmetry of this van-der-Waals material to intrinsically create polarization entanglement. We demonstrate the broadband generation of maximally polarization entangled Bell states with a measured fidelity of up to 96%. The need for external optical elements to create entanglement is obliterated, allowing to keep the optical system as simple as possible. Remarkably, the output quantum state of the TMD crystal can be easily tuned to different Bell and other maximally entangled states, all with the same generation efficiency. This property fundamentally stems from the crystal symmetry and goes beyond other recent demonstrations of thin-film nonlinear sources 25 , 26 , 27 . The high photoluminescence present in monolayer (ML) TMDs 28 is suppressed in 3R-MoS 2 , which is a decisive advantage compared to previous, inconclusive attempts to photon-pair generation in ML-TMDs 29 , 30 . The focus of this work is the demonstration of fundamental properties of generating entangled quantum states in 3R-MoS 2 and not yet a highly efficient and integrated device design. For specific technological applications requiring a high brightness of photon pairs in defined spectral bands 10 , orders of magnitude enhancement of the pair rate in the desired range may be achieved by periodic poling or integrating the nonlinear TMD crystal into singly- or doubly resonant, monolithic cavities 31 , 32 , an available technological process 33 , 34 . Based on our work, these readily developed technologies can, in the future, be combined to realize highly compact, flexible, and robust entangled photon-pair sources based on TMDs.

Fundamentals of photon-pair generation and polarization entanglement in transition metal dichalcogenides

In the monolayer limit, TMDs with the structural form M X 2 ( M  = Mo , W; X  = S,Se) are non-centrosymmetric and have a crystal lattice with three-fold rotational symmetry around the z -axis, corresponding to the point group D 3 h . This leads to a \({\hat{{{{\boldsymbol{\chi }}}}}}^{(2)}\) nonlinear tensor with non-vanishing elements \({\chi }_{\alpha \beta \gamma }^{(2)}={\chi }_{yyy}^{(2)}=-{\chi }_{yxx}^{(2)}=-{\chi }_{xxy}^{(2)}=-{\chi }_{xyx}^{(2)}\) 35 . The x - and y -direction are defined based on the crystallographic zigzag (ZZ) and armchair (AC) directions, see Fig.  1 b. This nonlinear tensor couples electric fields with signal and idler frequencies ω s ,  ω i , and polarization indices α ,  β to a higher-frequency pump field with ω p  =  ω s  +  ω i and polarization index γ . This enables classical three-wave mixing processes like second-harmonic generation (SHG) and sum-frequency generation (SFG) in TMDs, which were extensively studied 16 , 17 , 18 . The same nonlinearity also enables SPDC, where, due to vacuum fluctuations, pump photons with frequency ω p spontaneously split into pairs of signal and idler photons with frequencies ω s and ω i .

a A multilayer 3R-stack of MoS 2 generates pairs of polarization-entangled signal and idler photons via spontaneous parametric down-conversion (SPDC). Depending on the orientation of the pump polarization, different maximally entangled Bell states are generated. Lower inset: a sketch of the ABC-stacking scheme in 3R-MoS 2 . b Top view of the crystalline structure of 3R-MoS 2 stack shown in ( a ). The unit cells of the crystal are highlighted with black, dashed lines. The x - and y -coordinates, as well as the \(\left\vert {{{\rm{H}}}}\right\rangle\) - and \(\left\vert {{{\rm{V}}}}\right\rangle\) -polarization directions, are aligned with the zigzag (ZZ)- and armchair (AC)-directions of the crystal, respectively. The definition of the pump polarization angle φ p is marked in blue. c Theoretical evolution of the fidelities F ( ψ , Φ − ) and F ( ψ , Ψ + ) of the polarization state \(\left\vert \psi \right\rangle\) with the Bell states \(\left\vert {\Phi }^{-}\right\rangle=1/\sqrt{2}\left(\left\vert {{{\rm{H}}}}{{{\rm{H}}}}\right\rangle -\left\vert {{{\rm{V}}}}{{{\rm{V}}}}\right\rangle \right)\) and \(\left\vert {\Psi }^{+}\right\rangle=1/\sqrt{2}\left(\left\vert {{{\rm{H}}}}{{{\rm{V}}}}\right\rangle+\left\vert {{{\rm{V}}}}{{{\rm{H}}}}\right\rangle \right)\) , respectively, as well as the concurrence C for a full rotation of the pump angle φ p . d Height-map of the investigated 3R-MoS 2 crystal obtained with a vertical scanning interferometer. The black circle marks the measurement region. e Map of second-harmonic generation (SHG) intensity for the 3R-MoS 2 crystal shown in ( d ), obtained for excitation at central wavelength 2 × 788 nm = 1576 nm.

So far SPDC, which is the reverse process of SFG, could not be observed in TMDs 29 , 30 . Using TMDs for SPDC would be particularly interesting since their nonlinear tensor ensures that the generated signal and idler photons are intrinsically polarization-entangled. To demonstrate this, let us first consider a y -polarized pump photon. In this case, two pathways for down-conversion exist simultaneously, namely \({\vert y\rangle }_{{{\rm{pump}}}}{\rightarrow}^{{\chi}_{yyy}^{(2)}}\vert yy\rangle \) and \({\vert y\rangle }_{{{\rm{pump}}}}{\rightarrow}^{{\chi}_{xxy}^{(2)}}\vert xx\rangle \) . Since both processes are coherently driven by the same pump photon, the ensuing quantum state is a coherent superposition of the two conversion possibilities with equal magnitudes as \({\chi }_{yyy}^{(2)}=-{\chi }_{xxy}^{(2)}\) . The resulting polarization quantum state is \(\vert {\Phi }^{-}\rangle=1/\sqrt{2}\left(\vert xx\rangle -\vert yy\rangle \right)\) . This is one of the Bell states, a maximally entangled quantum state with high importance in quantum information processing. Equivalently, an x -polarized excitation results in a coherent superposition of the two down-conversion paths \({\vert x\rangle }_{{{{\rm{pump}}}}}{\rightarrow}^{{\chi}_{xyx}^{(2)}}\vert xy\rangle\) and \({\vert x\rangle }_{{{{\rm{pump}}}}}{\rightarrow}^{{\chi }_{yxx}^{(2)}}\vert yx\rangle\) . This generates the Bell state \(\vert {\Psi }^{+}\rangle=1/\sqrt{2}\left(\vert xy\rangle+\vert yx\rangle \right)\) , again maximally entangled. For a pump polarization rotated by the angle φ p with respect to the x -axis, the generated state is a superposition of these two Bell states in the form

where we have used now the horizontal \(\left\vert {{{\rm{H}}}}\right\rangle\) and vertical \(\left\vert {{{\rm{V}}}}\right\rangle\) basis states in the far-field for the notation. These are co-aligned with the crystallographic x -axis (ZZ) and the y -axis (AC), respectively (see Fig.  1 b). Based on this general form of the quantum state, it is straightforward to characterize the entanglement of states that lie in between the Ψ + -state for x -polarized excitation ( φ p  = 0°, horizontal) and the Φ − -state for y -polarized excitation ( φ p  = 90°, vertical). As an entanglement measure, we employ the concurrence C , a quantity ranging between C  = 0 for separable and C  = 1 for fully entangled states 36 . In Fig.  1 c, we plot the fidelity of the general state Eq. ( 1 ) with the Bell states Ψ + - and Φ − as well as the concurrence C for a full rotation of the pump polarization angle φ p . For a full derivation and the used definitions of concurrence and fidelity, refer to Supplementary Note  1 . While the state fidelities for the two Bell states peak at φ p  = 0° and 90°, the concurrence is C  = 1 for all φ p . In fact, the output polarization state from the TMD for any pump angle is always maximally entangled. Furthermore, analogous to the case of classical frequency up-conversion 17 , due to their crystal symmetry, the spontaneous down-conversion rate in TMDs is independent of the pump polarization. Therefore, TMDs generate fully entangled polarization states that are tunable with constant efficiency by means of pump polarization change.

A drawback of ML-TMDs is the low absolute signal yield in nonlinear conversion due to the very small interaction length with the medium 13 . More promising for the practical implementation of nonlinear devices based on TMDs is the use of moderately thicker crystals, with a stacking scheme that still preserves non-centrosymmetry. One such material is the 3R-polytype of TMDs like MoS 2 12 , 13 , 14 , 15 , where the layer-stacks are arranged in an ABC-ABC scheme that has no inversion center (one stacking period consists of three layers, compare inset of Fig.  1 a) 12 .

Since 3R-MoS 2 maintains the 3-fold rotational crystal symmetry and the related in-plane nonlinear tensor elements, it belongs to the C 3 v point group, also the thicker 3R-crystal stacks are suited to generate polarization-entangled quantum states. The signal yield, however, is much higher than for a monolayer. The out-of-plane, z -polarized nonlinear tensor components of 3R-MoS 2 practically only contribute to the generated quantum state for very large collection numerical apertures, refer to Supplementary Note  2 for a detailed discussion.

Experimental photon-pair generation and polarization analysis

Experimentally, we aim for photon-pair generation in the technically relevant telecom band in the near infrared around λ s,i  ≈ 1550 nm. Using mechanical exfoliation, we fabricate a 3R-MoS 2 crystal with sub-wavelength thickness, see “Methods” section. In Fig.  1 d, we show a height map of the crystal used as a photon-pair source in this work. For the SPDC measurement, we choose an area far away from the crystal edges and all cracks, which is important to minimize distortions of the nonlinear tensor induced by imperfections or strain 12 , 37 . To further define the measurement area for the SPDC experiments, we first spatially map the SHG emitted by the crystal, as shown in Fig.  1 e. We choose the large area of 285 nm thickness, see the marking in Fig.  1 d, which shows a strong SHG signal in the center of the crystal. The signal yield from this crystal exceeds an ML-MoS 2 by more than three orders of magnitude. We, however, note that this crystal thickness does not correspond to the global maximum conversion efficiency. This would be reached for a thickness of t  ≈ 800 nm, close to the coherence length of L c  ≈ 840 nm for the SHG conversion process excited at 1576 nm. At this thickness, the SHG and, by correspondence, also SPDC efficiency would be further increased by a factor of  ≈33× (see Supplementary Fig.  5 and Supplementary Note  3 ). While we did not reach this optimum thickness with the limited control offered by mechanical exfoliation, nanofabrication techniques that allow precise thickness control and nanopatterning of (3R-)MoS 2 have already been demonstrated 22 , 38 and can be used for future sample fabrication. For the photon-pair measurements, we use an experimental setup with two fiber-coupled, time-correlated single-photon detectors, as shown in Fig.  2 a. A pump beam with wavelength λ p  = 788 nm is focused onto the air-exposed side of the 3R-MoS 2 sample, and photon pairs are collected through the quartz substrate.

a Hanbury Brown-Twiss interferometer for photon-pair correlation measurements: continuous wave diode laser at 788 nm, linear polarizer 1 (lin. pol.) and half-wave plate 1 (HWP) for setting pump polarization angle φ p , aspheric lenses for focusing onto and collecting from the sample, long-pass interference filters (cut-on wavelength λ  = 1100 nm) for pump suppression, optional HWP 2 and lin. pol. 2 as polarization analyzer with angle φ pol , single mode fiber (SMF) and 50:50 fiber beamsplitter, superconducting nanowire single-photon detector (SNSPD), and time-to-digital converter (TDC). b Photoluminescence (PL) spectrum from 3R-MoS 2 crystal and SiO 2 substrate excited at λ p  = 788 nm. The green shaded area marks the region where no photoluminescence signal distinguishable from the detector darkcounts can be detected. c Coincidence histogram obtained from 3R-MoS 2 for excitation with average power P  = 17.2 mW and integration time 3.5 h, measured with a long-pass filter with cut-on wavelength 1500 nm. The coincidence-to-accidental ratio (CAR) in this measurement is CAR = 5.5. Error bars mark the standard deviation based on the Poissonian statistics of SPDC coincidence detection. Inset: Measured SPDC coincidence rate (blue dots) for different pump powers and its linear fit (orange line). d Spectrum of SPDC photons measured using fiber spectroscopy. The dashed green line marks the degenerate SPDC wavelength λ deg  = 2 ×  λ p  = 1576 nm. The dark orange shaded areas mark the standard deviation based on the statistics of SPDC coincidence detection. The light blue lines show the level and standard deviation (std.) of the noise floor. The dashed, dark blue line is the transmission curve of the used long-pass filter that limits the SPDC spectrum.

In our correlation experiment, any other emission from the sample in the same wavelength region would potentially mask the entangled photon signal. In particular, strong photoluminescence, as observed from direct bandgap transitions in ML-TMDs 28 , could complicate the observation of photon pairs 30 . We measure photoluminescence from our sample under excitation at λ p  = 788 nm from the same pump laser as in the SPDC experiments. We observe no photoluminescence signal distinguishable from the detector darkcounts beyond λ  = 1300 nm (see green shaded area Fig.  2 b, pump intensity ≈ 1.67 MW cm −2 ). This demonstrates the 3R-TMD’s potential for low background photon-pair generation in the telecom wavelength band.

Consequently, we perform pair-correlation measurements and observe a pronounced coincidence peak, compare Fig.  2 c. After background subtraction, we measure 1563 ± 43 coincidence counts with a coincidence-to-accidental ratio (CAR) of CAR = 5.5 ± 0.4 for an integration time of 3.5 h and a pump power incident on the sample of 17.2 mW (pump intensity  ≈ 648 kW cm −2 ). A normalized second-order correlation function g (2) (0) > 2, related to CAR via CAR =  g (2) (0)−1 25 , together with the linear scaling of the coincidence rate with pump power shown in Fig.  2 c is clear evidence for the SPDC origin of the coincidence peak (see Supplementary Note  5A and raw data in Supplementary Fig.  8 ). The maximum CAR we observe is CAR = 8.9 ± 5.5 for a pump power of 5.6 mW (see Supplementary Fig.  9 ). Furthermore, we measure the SPDC spectrum using fiber spectroscopy 39 , where the photon pairs are first sent through a long, dispersive medium before coincidence detection. In our experiment we insert 1 km of SMF28 single-mode fiber before the beamsplitter for the spectral measurement. After propagation through this medium with known dispersion, the arrival time difference between both photons can be mapped to their wavelength difference (see “Methods” for more details). As expected for a non-phase matched, thin crystal, the SPDC spectrum is very broad 25 , 40 , compare Fig.  2 d. In the experiment, the spectrum is limited only by the long-pass filter with cut-on 1500 nm, which is used to limit the SPDC spectrum to the operating bandwidth of the fiber beamsplitter and for suppression of residual photoluminescence (filter curve shown as dashed, dark blue line in Fig.  2 d).

The specific form of the nonlinear tensor of 3R-MoS 2 leads to a characteristic dependence of the generated photon’s polarization on the pump polarization, which we characterize next. Here we first consider the two cases of either an unpolarized detection or a single polarizer for both SPDC photons. While this does not yet allow to measure the degree of polarization entanglement which we cover in the next section, the measurements with a single analyzer are particularly instructive to relate to the polarization dependence of SHG measurements in similar configurations 17 . As reference, we show in Fig.  3 a a classical polarization-resolved second-harmonic measurement from 3R-MoS 2 observed through an analyzer, that is rotated in parallel to the pump polarization (see the “Methods” section). The characteristic six-fold symmetric pattern is oriented along the AC crystal direction (dashed brown line in Fig.  3 a) 17 . For SPDC detection without a polarizer, we observe the expected constant coincidence rate, independent of the pump polarization (Fig.  3 b) 19 . We assign the small fluctuations in the measured rate mainly to the polarization sensitivity of our SNSPD detectors, which in the telecom range is significant 41 . For measurements through a common analyzer for both signal and idler, the symmetry of the nonlinear tensor leads to a dependence of the SPDC rate R SPDC on pump polarization angle φ p and analyzer angle φ pol as \({R}_{{{{\rm{SPDC}}}}}\propto {\sin }^{2}(2{\varphi }_{{{{\rm{pol}}}}}+{\varphi }_{{{{\rm{p}}}}})\) (see Supplementary Note  1 for the derivation). To experimentally verify this, we insert an analyzer in front of the fiber and simultaneously rotate the pump and analyzer either in a parallel configuration φ pol  =  φ p (orange squares in Fig.  3 c) or perpendicular configuration φ pol  =  φ p  +  π /2 (blue dots in Fig.  3 c). Both yield a characteristic six-fold, co-aligned pattern that matches the theoretically expected dependence of the form \({R}_{{{{\rm{SPDC}}}}}\propto {\sin }^{2}(3{\varphi }_{{{{\rm{p}}}}})\) when analyzed in terms of the SPDC pump angle φ p . Note that this is fully consistent with frequently reported SHG measurements that show a 30° shift between measurements with parallel or perpendicular polarizer angle 17 , see Supplementary Note  1 for a more detailed discussion. Furthermore, by varying the pump polarization for several constant analyzer positions, we obtain a two-lobed pattern (see Fig.  3 d–f), confirming the theoretically derived polarization dependence. In Supplementary Note  1 we also discuss the polarization dependence when keeping the pump polarization angle constant and only rotating the analyzer. The raw coincidence histograms for all results in Fig.  3 are found in Supplementary Figs.  10 and 11 .

a Polarization-resolved second-harmonic measurement (blue circles) for the rotation of the pump polarization angle φ p,SHG , and parallelly polarized, co-rotating analyzer. The black curve is a fit with the theoretically expected dependence \({I}_{{{{\rm{SHG}}}}}\propto {\sin }^{2}(3{\varphi }_{{{{\rm{p,SHG}}}}})\) . The armchair (AC), and zigzag (ZZ) directions are marked with dashed brown and cyan lines, respectively. b Measured photon-pair rate for rotation of the SPDC pump polarization angle φ p for unpolarized detection. The black curve marks a fit with the theoretically expected constant function. c Measured photon-pair rate for rotating pump polarization φ p and detection through a co-rotating, perpendicularly oriented (blue circles), and parallelly oriented (purple squares) analyzer. In both cases, the expected \({R}_{{{{\rm{SPDC}}}}}\propto {\sin }^{2}(3{\varphi }_{{{{\rm{p}}}}})\) dependence (black curve) is overlayed. d–f Measured photon-pair rates for the rotating pump polarization φ p and an analyzer fixed at d φ pol  = 110° (20° offset from AC-axis), e φ pol  = 55° (25° offset from AC-axis), and f φ pol  = 50° (20° offset from AC-axis). The dash-dotted black line marks the direction of the analyzer transmission axis, the solid dashed line is the theoretically expected dependence \({R}_{{{{\rm{SPDC}}}}}\propto {\sin }^{2}(2{\varphi }_{{{{\rm{pol}}}}}+{\varphi }_{{{{\rm{p}}}}})\) . Error bars mark the standard deviation based on the Poissonian statistics of SPDC coincidence detection.

Quantum-state tomography and Bell-state generation

To completely characterize the generated polarization quantum state and to prove entanglement between signal and idler photons, we perform a tomographic measurement in two mutually unbiased polarization bases 42 . To deterministically separate signal and idler photons, we insert a short-pass dichroic mirror with a cut-on wavelength of 1600 nm into the SPDC collection path, as depicted in Fig.  4 a. The previously used long-pass with a cut-on wavelength of 1500 nm is removed now since the operating bandwidth of the dichroic mirror is larger than for the fiber beamsplitter. The broadband signal and idler spectra and the beamsplitter reflection spectrum are shown in Fig.  4 b. Here, the width of the observed SPDC spectrum is mostly limited by the detection range of our experimental setup where the efficiency of the used SNSPDs slowly drops towards wavelengths much longer than their optimized operation wavelength at 1550 nm. Due to the correlation-based spectral measurement method, this simultaneously limits the short-wavelength side of the spectrum. Due to the collection in single-mode fibers and the use of an approximately non-polarizing dichroic mirror, the photon pairs remain indistinguishable in all degrees of freedom but their frequency. Using a combination of waveplates and a linear polarizer in both paths allows to set two arbitrary, independent polarization bases. By performing projections into 16 different basis states, the density matrix \(\hat{\rho }\) of the polarization quantum state is fully determined 42 (see the “Methods” section). We use an established maximum-likelihood estimation method to determine a physically correct density matrix from measurements that are subject to noise and experimental uncertainties 42 , 43 .

a Experimental setup for quantum polarization-state tomography. A short-pass dichroic mirror (DM) with cut-on wavelength at λ  = 1600 nm splits the signal (orange, upper arm) and idler (red, lower arm) frequency modes. Quantum-state tomography is performed with a set of quarter-wave plate (QWP), half-wave plate (HWP) and linear polarizer in each arm, then temporal correlations are measured as with the experiment described in Fig.  2 a. b Measured spectra of the signal (orange) and idler (red) frequency modes. The dip around the degenerate wavelength (dashed green line) is caused by the slight detuning of the cut-on wavelength of the dichroic mirror from the degenerate SPDC wavelength. The dark-shaded areas mark the statistical uncertainty. The light blue lines show the level and standard deviation of the noise floor. The dashed, dark blue line is the reflection curve of the dichroic mirror. c and d Experimentally measured polarization density matrices \(\hat{\rho }\) for ( c ) for y -, and ( d ) x -polarized pump. For both cases, the real and imaginary parts \({\rm {Re}}(\hat{\rho })\) and \({\rm {Im}}(\hat{\rho })\) , respectively, are shown. e and f Theoretically expected polarization density matrices obtained from fully vectorial Green’s function calculations for y - and x -polarized excitations of 3R-MoS 2 , respectively.

In Fig.  4 c, d, we show the real and imaginary parts of the experimentally obtained density matrices \(\hat{\rho }\) for a y - (c) and x -polarized (d) pump (raw data in Supplementary Note  5C and Supplementary Figs.  12 – 14 ). Additionally, we compute the theoretically expected state emitted from our 3R-MoS 2 with thickness t  = 285 nm based on fully vectorial Green’s function calculations, taking into account the realistic conditions in our experiment for pump focusing, collection NA, collected SPDC bandwidth, etc. (see the “Methods” section) 44 , 45 . Taking the ratio of in-plane and out-of-plane nonlinear tensor components measured in ref. 14 as a reference, these calculations predict the generation of ideal Bell states and compare the theoretical density matrices in Fig.  4 e, f. This is closely matched by the experiment. For the y -polarized excitation, the measured density matrix has a fidelity of F  = 0.96 with a \(\left\vert {\Phi }^{-}\right\rangle=1/\sqrt{2}\left(\left\vert {{{\rm{H}}}}{{{\rm{H}}}}\right\rangle -\left\vert {{{\rm{V}}}}{{{\rm{V}}}}\right\rangle \right)\) state and a concurrence of C  = 0.973 ± 0.002, while for the x -polarized excitation, the fidelity with a \(\left\vert {\Psi }^{+}\right\rangle=1/\sqrt{2}\left(\left\vert {{{\rm{H}}}}{{{\rm{V}}}}\right\rangle+\left\vert {{{\rm{V}}}}{{{\rm{H}}}}\right\rangle \right)\) state is F  = 0.84 and the concurrence C  = 0.82 ± 0.02.

In this work, we observe photon-pair generation via SPDC in a transition metal dichalcogenide. We chose 3R-MoS 2 for our demonstration because its strong nonlinearity is preserved in multi-layer stacks. Simultaneously, it is much less affected by photoluminescence than monolayer TMDs, which had prevented the observation of SPDC in prior experiments. We demonstrate that TMDs intrinsically generate maximally entangled polarization Bell states. Experimentally we show this for two different pump polarizations and then further theoretically derive that, in fact, for any linear pump polarization, a different maximally entangled state is generated while the generation efficiency is independent of the pump polarization. This decoupling of entangled state tuning from the generation efficiency results in a highly flexible and easy-to-operate, tunable entangled photon-pair source. Since all these properties are directly derived from the crystal symmetry, no external optical components like interferometers etc. are needed for generating entanglement. This is the simplest conceivable, tunable entangled photon-pair source, a prerequisite for active quantum networks, which enable, for instance, multi-user quantum secret sharing 11 . Furthermore, this direct link to the crystal symmetry allows us to generalize our results for tuneable entanglement generation to other nonlinear materials of the same or similar symmetry group, for instance, lithium niobate or beta barium borate (BBO).

While we demonstrate here a prototype based on a single, thin 3R-MoS 2 crystal, the generation rate can be scaled to the required level, e.g. through quasi-phasematching. Similar to the periodic poling of ferroelectric nonlinear materials 5 , the nonlinearity of 3R-MoS 2 can be periodically poled by stacking several multilayer crystals with appropriate rotation angles between consecutive crystals 20 , 21 . With this, quasi-phasematching between pump, signal, and idler waves is possible and the length of the 3R-TMD stack can be increased beyond one coherence length to match the photon-pair rate required in specific applications. Another way of scaling up the source brightness is cavity integration. A cavity resonance at the pump wavelength effectively extends the interaction length with the nonlinear crystal, drastically enhancing the total pair-generation rate while resonances at the signal and idler wavelength strongly increase the spectral brightness in the desired frequency bands 31 , 32 . The integration of TMDs into high- Q , monolithic cavities is a readily developed technology 33 with doubly-resonant cavities in reach 34 . Also, excitonic enhancement of the second-order nonlinear susceptibility is a promising avenue to further increase the source brightness 46 . Schemes like quasi-phasematching and cavity integration, which result in narrower spectral and spatial emission, would not only enhance the generation rate but also improve the photon-pair collection efficiency. Additionally, an enhanced SPDC efficiency, for instance, through longer interaction lengths, proportionally reduces the effect of photoluminescence 47 . This, together with the enhanced generation and collection efficiency, will improve the coincidence-to-accidental ratio in our source.

The demonstrated continuous tuning of the output state while maintaining maximal entanglement and a constant generation efficiency goes beyond what was shown with previously developed thin-film sources 26 , 27 , 40 . Combined with the avenues for scaling the generation rate, coincidence-to-accidental ratio, and pair collection efficiency, this gives TMDs a clear advantage as a nonlinear material platform for entangled photon-pair sources. Furthermore, the high refractive index of 3R-MoS 2 is well suited for strong field confinement when being nanostructured 22 , 38 , 48 , making it a perfect platform for hyper-entangled photon-pair generation in resonant nanostructures 45 , 49 , 50 . Given that TMDs also withstand harsh conditions like those found in space 51 and can be easily integrated on top 52 or end-facet 53 of optical fibers 52 , waveguides 54 , and also metasurfaces 55 , we expect to see their immediate use in microscale or integrated photonic circuits and entangled photon-pair sources. Combined with their extremely low requirements for size and weight with highly scalable fabrication routes, they will enable quantum communication and quantum sensing for medical applications, life sciences, the semiconductor industry, and consumer applications alike.

Sample fabrication

Bulk 3R-MoS 2 crystals were grown using the chemical-vapor transport technique 15 . Subsequently, 3R-MoS 2 flakes were prepared on polydimethylsiloxane (PDMS), which begins with mechanical exfoliation of the crystals. Afterward, the substrates were pre-treated by oxygen plasma in order to eliminate potential contamination and improve the adhesion, followed by a dry transfer method to transfer the 3R-MoS 2 flakes onto quartz substrates.

Thickness characterization

Sample thicknesses were characterized by a surface profiler and vertical scanning interferometry (VSI, Bruker Contour GT-K). The surface profiler and VSI are utilized to access the average thickness, surface roughness, and uniformity of the 3R-MoS 2 sample.

Polarization-resolved SHG measurements and SHG mapping

Polarization-resolved SHG measurements were carried out with the same setup as used for quantum measurements but working in reverse: the fundamental beam was incident from one of the collecting fibers and focused/collected with the same optics (see Fig.  2 a). As a laser source, a tunable femtosecond laser (Coherent Chameleon with optical parametric oscillator Angewandte Physik und Elektronik GmbH APE OPO-X) with pulse width 100 fs, repetition rate 80 MHz, at a central wavelength 1576 nm and with FWHM 10 nm was used. Note that the pulses were not sent through the normal detector fiber but through a shorter single-mode fiber (Thorlabs SMF-28-J9-CUSTOM) with a length of 0.5 m to avoid distortion of the pulses. The pump polarization was controlled with a half-wave plate (Thorlabs AHWP05M-1600), which rotated together with an analyzer placed in the collection path (Thorlabs WP25M-UB). Two short-pass filters (Thorlabs FELH850) installed in the collection path filtered out the fundamental beam, and SHG was detected with sCMOS camera (Excelitas pco.edge 4.2 bi), all not shown in Fig.  2 a. For a detailed schematic of the experimental setup including the imaging arm, please refer to Supplementary Fig.  6 . The detected polarization of the second-harmonic wave was kept parallel to the pump polarization creating a characteristic six-fold pattern. This measurement was used as a reference to identify the orientation of the AC and ZZ crystal directions in the 3R-MoS 2 sample.

SHG mapping was performed using a custom-built nonlinear microscopy setup. A fundamental beam from a tunable femtosecond laser (Spectra-Physics Mai Tai and optical parametric oscillator Inspire HF 100) with a pulse width of 100 fs, repetition rate 80 MHz, at a central wavelength of 1576 nm, and with FWHM 10 nm was focused onto the sample via a 20x NA = 0.4 objective (Mitutoyo). The polarization of the fundamental beam was fixed to be parallel to the AC-axis of 3R-MoS 2 . The beam diameter reached  <6  μm FWHM. The SHG signal was collected via a 100x NA = 0.85 objective (Zeiss) and passed through two short-pass filters to remove the fundamental beam. The sample was then scanned with 1 μm step-width on a motorized XYZ -stage (Newport M-VP-25XL-XYZR), while the second-harmonic signal was detected using an EMCCD camera (Andor, iXon3).

In both experiments, the excitation wavelength was chosen to correspond to the degenerate wavelength of SPDC pumped at λ p  = 788 nm.

Photon-pair correlation measurements

Photon-pair correlation measurements shown in Figs.  2 and 3 were performed using the home-built Hanbury Brown-Twiss interferometer outlined in Fig.  2 a. A more detailed schematic of the experimental setup is provided in Supplementary Fig.  6 . Excitation photons from a continuous-wave laser at λ p  = 788 nm (diode laser, Thorlabs FPL785P) were sent through a linear polarizer and a half-wave plate for pump polarization control and focused onto the sample by an aspheric lens with numerical aperture NA = 0.4 (Thorlabs C110TMD-B), leading to a diffraction-limited 1/ e 2 pump beam radius of  ≈1.3 μm. The measurement position is imaged in the experimental setup in a separate imaging arm via the same camera (Excelitas pco.edge 4.2 bi) as also used for SHG measurements. Compare Supplementary Fig.  6 for details. Subsequently, photon pairs were collected in transmission geometry using a similar lens with anti-reflection coating for the C-band (Thorlabs C110TMD-C). Pump photons were removed using three interference long-pass filters with cut-on wavelength 1100 nm (Thorlabs FELH1100). For measurements shown in Figs.  2 and 3 , we also used a long-pass filter with a cut-on wavelength of 1500 nm (Thorlabs FELH1500) to suppress any residual photoluminescence and to limit the photon-pair bandwidth to the operation range of the fiber beamsplitter. The photon pairs were then coupled to single-mode fibers (Corning SMF28), separated using a broadband fiber beamsplitter with central wavelength 1550 nm (Thorlabs TW1550R5F1), and directed to two superconducting single-photon detectors (SNSPD, Single Quantum Eos). Coincident detection events are registered with a time-correlator (qutools quTAG or ID Quantique ID800). For the polarization measurements with a common analyzer for both photons in Fig.  3 , we implement a rotating analyzer using an achromatic half-wave plate (Thorlabs AHWP05M-1600) followed by a fixed linear polarizer (Thorlabs WP25M-UB), such that the polarization state in the detector fiber is always the same. This rules out the polarization dependence of the detectors. The total photon-pair detection efficiency of the setup η tot follows from \({\eta }_{{{{\rm{tot}}}}}={T}_{{{{\rm{opt}}}}}^{2}\times {T}_{{{{\rm{coupl}}}}}^{2}\times {\eta }_{{{{\rm{BS}}}}}\times {\eta }_{{{{\rm{detec}}}}}^{2}\times {\eta }_{{{{\rm{LP}}}}}^{2}\, \approx \, 0.6\,\%\) . For our setup, we estimate the following values: single photon optical transmission, including lenses, filters, mirrors, etc. T opt  ≈ 0.78; single-mode fiber coupling efficiency η coupl  ≈ 0.35; fiber beamsplitter non-uniformity and probabilistic splitting η BS  ≈ 0.95 2  × 0.5 = 0.45; detection efficiency of SNSPDs at degenerate SPDC wavelength and averaged over different polarizations η detec  ≈ 0.6; spectral detection factor for measurement with long-pass filter 1500 nm, η LP  = 0.5. The spectral detection factor takes into account that effectively half of the SPDC spectrum is detected when the long-pass filter at 1500 nm is inserted (compared to the spectrum in Fig.  4 b).

Fiber spectroscopy

Fiber spectroscopy was carried out to measure the photon-pair spectrum by mapping the spectral information onto the temporal domain using a dispersive medium. In this work, the dispersive medium consisted of two spools of SMF28 fiber (Corning), each with a length of 1 km.

The fiber spectroscopy experiment was conducted in two distinct configurations. In the first scenario, as shown in Fig.  2 a, the photon pairs traveled through the same fiber spool. Following this, they were split using a 50:50 fiber beamsplitter before being detected by SNSPDs (Single Quantum Eos with timing jitter ≤25 ps). The arrival time differences were measured by a correlation electronics (qutools quTAG with timing jitter ≤10 ps). In the second configuration, as shown in Fig.  4 a, the photon pairs were initially separated via a dichroic mirror. Subsequently, a 1 km dispersive fiber spool was introduced into each of the photon pathways, before detection through the SNSPDs. The group-velocity dispersion of the fiber leads to a time delay between signal and idler photons, which can be mapped to their wavelength difference 39 . Note that in this correlation-based measurement, always both photons of a pair need to be detected. An edge-pass filter, therefore, determines via energy conservation the entire width of the detected photon-pair spectrum. For instance, the spectrum measured in Fig.  2 d using a long-pass filter with cut-on wavelength λ c  = 1500 nm and pump wavelength 788  n m fixes the long-wavelength edge of the spectrum to \({(1/{\lambda }_{{{{\rm{p}}}}}-1/{\lambda }_{{{{\rm{c}}}}})}^{-1}=1660\,{\rm {nm}}\) .

Quantum-state tomography

For the tomographic measurement of the two-photon polarization quantum state, both photons have to be projected into mutually unbiased bases. For this, we first separated signal and idler photons based on their frequency in our Hanbury Brown-Twiss interferometer (see Fig.  4 a). A more detailed schematic of the experimental setup is provided in Supplementary Fig.  7 . We implemented a dichroic mirror by using the reflection of a slightly tilted short-pass interference filter with cut-off wavelength 1600 nm (Edmund Optics #84-656). In each collection arm of the correlation setup, an arbitrary polarization basis could be set using a sequence of the achromatic quarter-wave plate (Thorlabs AQWP05M-1600), half-wave plate (Thorlabs AHWP05M-1600), and linear polarizer (Thorlabs WP25M-UB). During all changes in the polarization basis, the orientation of the linear polarizer was kept constant in order to avoid effects from the polarization sensitivity of the detectors. For a full reconstruction, the state has to be measured in 16 different basis configurations. Please refer to Supplementary Note  5C for details on the chosen projection bases. We evaluated the measurements using a maximum likelihood method 42 , 43 . The uncertainty of the state concurrence C , derived from the experimentally measured density matrix, was determined using a Monte Carlo approach 56 .

Green’s function method for pair-generation in layered materials

Our theoretical formalism is based on the Green’s function (GF) quantization approach for the description of pair generation 57 , where the coincidence detection probability at different spatial coordinates for a signal and idler photon generated by a nonlinear source through SPDC takes the form:

where α , β , and γ indices run over the x , y , and z directions. Here, d σ are the components of detection vector d , where σ  =  x ,  y ,  z . E p, γ ( r ) are the vector components of the complex-valued monochromatic pump with frequency ω p  =  ω s  +  ω i . \({G}_{ij}({{{\bf{r}}}},{{{\bf{r}}}}^{\prime},\omega )\) are the tensor components of the electric GF. Finally, \({\chi }_{\alpha \beta \gamma }^{(2)}({{{\bf{r}}}})\) are the components of the second-order nonlinear tensor.

Here, the GF describes all the linear properties of the system and is incorporated into the quantum formalism to include nonlinear processes that involve the generation of entangled photons, such as SPDC. Due to the generality of the GF method, this formalism can describe any thickness of the 3R-MoS 2 nonlinear crystal, ultra-thin or thick, and it can be used to describe near- and far-field radiation in the non-paraxial regime 44 , 58 . Remarkably, this formalism allows us to keep track of any polarization and directionality effects in the pair-generation process, which makes it useful in the reconstruction of polarization states of entangled photons 45 . For modeling the 3R-MoS 2 crystal, we use the refractive index data provided in ref. 13 and the relative magnitude of the nonlinear tensor elements d 16 and d 31 from ref. 14 . For a detailed discussion of the influence of the different tensor elements on the generated quantum states, refer to Supplementary Note  2 .

Data availability

Raw data that supports this study is available in the Supplementary Information and has also been deposited in the figshare database under accession code https://doi.org/10.6084/m9.figshare.26756398 .

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Acknowledgements

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the International Research Training Group (IRTG) 2675 “Meta-ACTIVE”, project number 437527638 (T.P., F.S., F.E., I.S.), the Collaborative Research Center (CRC) 1375 “NOA” (T.P., F.S., F.E., I.S.), through “MEGAPHONE” project number 505897284 (S.Sar.) and through the Emmy Noether Program, project number STA 1426/2-1 (I.S.). The authors further acknowledge funding from the Bundesministerium für Bildung und Forschung (BMBF, German Federal Ministry of Education and Research) under the project identifiers 13N14877 (F.S.), 13XP5053A (F.E.), 16KISQ89 (F.E.); and by the State of Thuringia (Quantum Hub Thüringen, 2021 FGI 0043, T.P., F.S., F.E., I.S.). Furthermore, the authors acknowledge funding support from ANU PhD student scholarship (Y.T., H.Q.), Australian Research Council grant no. DP220102219 (Y.L.), LE200100032 (Y.L.), and ARC Centre of Excellence in Quantum Computation and Communication Technology (project number CE170100012, Y.L.). Additionally, this project has received funding from the European Union’s Horizon 2020 research and innovation program under the H2020-FETOPEN-2018-2020 grant agreement no. [899673] (Metafast, T.P., I.S.).

Open Access funding enabled and organized by Projekt DEAL.

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Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University Jena, Albert-Einstein-Straße 15, Jena, 07745, Germany

Maximilian A. Weissflog, Anna Fedotova, Elkin A. Santos, Benjamin Laudert, Saniya Shinde, Fatemeh Abtahi, Mina Afsharnia, Inmaculada Pérez Pérez, Sebastian Ritter, Sai Shradha, Isabelle Staude, Sina Saravi, Thomas Pertsch, Frank Setzpfandt & Falk Eilenberger

Max Planck School of Photonics, Hans-Knöll-Straße 1, Jena, 07745, Germany

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Anna Fedotova & Isabelle Staude

School of Engineering, College of Science and Computer Science, The Australian National University, Canberra, ACT, Australia

Yilin Tang, Hao Qin, Jiri Janousek & Yuerui Lu

Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Albert-Einstein-Straße 7, Jena, 07745, Germany

Sebastian Ritter, Thomas Pertsch, Frank Setzpfandt & Falk Eilenberger

Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology, The Australian National University, Canberra, ACT, Australia

Jiri Janousek & Yuerui Lu

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Contributions

M.A.W. conceived the ideas, coordinated the measurements and theoretical modeling, designed the SPDC and tomography experiments, did the analytical calculations, analyzed the data, created the figures, and wrote the first draft of the manuscript under the supervision of F.E., Y.L., T.P, I.S., S.Sar. and F.S. Y.T. fabricated all samples. M.A.W., A.F., and S.Shi. did the polarization-resolved SPDC measurements. B.L., F.A., and A.F. did the polarized SHG experiment. M.A.W. did the tomography experiments. E.S. did the GF calculations under the supervision of S.Sar. A.F. measured the SHG map and S.R. measured the PL spectra. M.A., I.P.P, A.F., and M.A.W designed and calibrated the correlation fiber spectrometer. Y.T., H.Q., and J.J. designed and carried out the experiment for thickness-dependent SHG efficiency. B.L. did analytical calculations and contributed to writing the first manuscript draft. F.A. and S.Shr. did preliminary SHG and PL analysis for 3R-MoS 2 samples. F.E., Y.L., T.P, I.S., S.Sar., and F.S. acquired funding and provided experimental resources. F.E., F.S., S.Sar., Y.L., and A.F. provided major revisions to the manuscript. All authors discussed the results and contributed to the manuscript.

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Correspondence to Maximilian A. Weissflog , Yuerui Lu or Falk Eilenberger .

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Competing interests.

M.A.W., S.Sar., F.S., T.P., and F.E. are inventors on a patent application by the Fraunhofer Institute for Applied Optics and Precision Engineering IOF (63287DE) expanding on the results presented in this manuscript. The remaining authors declare no competing interests.

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Weissflog, M.A., Fedotova, A., Tang, Y. et al. A tunable transition metal dichalcogenide entangled photon-pair source. Nat Commun 15 , 7600 (2024). https://doi.org/10.1038/s41467-024-51843-3

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DOI : https://doi.org/10.1038/s41467-024-51843-3

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