Demonstration of Quantum Polarized Microscopy Using an Entangled-Photon Source

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Thank you for submitting the revised manuscript. After reviewing this version, it appears that not all the comments and suggestions provided in the previous iterations were thoroughly considered or addressed. While some revisions are evident, several key points remain unresolved.

I believe that implementing all the suggestions is crucial to enhancing the clarity and overall quality of the manuscript.

At this point, I can't recommend full acceptance but provided the revisions are properly conducted it should be eventually published.

Author Response

Comment :

Thank you for submitting the revised manuscript. After reviewing this version, it appears that not all the comments and suggestions provided in the previous iterations were thoroughly considered or addressed. While some revisions are evident, several key points remain unresolved.

I believe that implementing all the suggestions is crucial to enhancing the clarity and overall quality of the manuscript.

At this point, I can't recommend full acceptance but provided the revisions are properly conducted it should be eventually published.

Response : 

Thank you for taking the time to review the revised version of our manuscript. We greatly appreciate your insightful feedback and constructive comments. We have carefully reviewed and incorporated all the comments provided in the previous iterations to the best of our understanding. Some of the reviewer comments were addressed point by point in the template, and the others were included in the attached document. Unfortunately, since the reviewer did not point out where was necessary to revise or address in the manuscript concretely, at this time we are unclear on where further revisions are required. So we did not give any revision regarding this comment.

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

The manuscript presents a well-structured and comprehensive study on the experimental demonstration of quantum polarized microscopy using an entangled-photon source. The methodology, results, and implications of the proposed technique are clearly articulated and backed by experimental evidence. The paper provides significant insights into advancing quantum microscopy techniques, making it a valuable contribution to the field of photonics and quantum imaging. I recommend it for acceptance with minor editorial adjustments, as outlined in the suggestions as follows:

1. A deeper comparison with other quantum microscopy techniques, particularly regarding signal-to-noise ratio and practical limitations, would enhance the manuscript's context.

2. The discussion on focusing the entangled-photon beam to improve spatial resolution could benefit from additional details or future work directions.

Author Response

Comment 1:

The manuscript presents a well-structured and comprehensive study on the experimental demonstration of quantum polarized microscopy using an entangled-photon source. The methodology, results, and implications of the proposed technique are clearly articulated and backed by experimental evidence. The paper provides significant insights into advancing quantum microscopy techniques, making it a valuable contribution to the field of photonics and quantum imaging.

Response 1:

Thank you for your positive and encouraging feedback on our manuscript. We greatly appreciate your kind words acknowledging the structure, methodology, and contributions of our study. We are delighted that you find our work on quantum polarized microscopy using an entangled-photon source to be a valuable contribution to the field of photonics and quantum imaging. Your comments motivate us to continue advancing this research.

Comment 2:

I recommend it for acceptance with minor editorial adjustments, as outlined in the suggestions as follows:

1. A deeper comparison with other quantum microscopy techniques, particularly regarding signal-to-noise ratio and practical limitations, would enhance the manuscript's context.

Response 2 : 

In response to your suggestion to make a deeper comparison with other quantum microscopy techniques, we would like to highlight that our method is unique compared to other quantum microscopy techniques. While the signal-to-noise ratio (SNR) of our method is comparable to the other studies. According to Hugo et al. [5], the SNR values ranging between 19 and 21.

Moreover as noted by Ono et al. [17], the SNR of quantum entanglement is 17.7±1.22.

One of the practical limitations regarding quantum holography using polarization entanglement [5], it requires a few ten hours for image acquisition due to the low frame rate of EMCCD cameras. In contrast, our proposed method achieves image acquisition in much less time.

Comment 3:

The discussion on focusing the entangled-photon beam to improve spatial resolution could benefit from additional details or future work directions.

Response 3: 

Although the entangled-photon beam was not focused at present, it should be focused with the lens to improve the spatial resolution, S/N ratio, and so on, but the throughput of photon might be reduced because the spatial coherence of the entangled photon is not so high as that of laser light. As future work to improve the spatial resolution we will employee the objective lens.

Reviewer 3 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

The Abstract, Introduction and description are significantly improved and, clearly, extensive experimental work was done to obtain the results presented in their Fig. 5. This could be an important step toward their goal of application to insensitive imaging applications in biology that is superior to the classical method. I recommend publication.

Author Response

Comment: 

The Abstract, Introduction and description are significantly improved and, clearly, extensive experimental work was done to obtain the results presented in their Fig. 5. This could be an important step toward their goal of application to insensitive imaging applications in biology that is superior to the classical method. I recommend publication.
Response: 

We sincerely appreciate your encouraging comments on our manuscript. We are pleased that you found the Abstract, Introduction, and descriptions significantly improved, and that the extensive experimental work reflected in Fig. 5 was recognized. Your remarks on the potential impact of our method for biological imaging applications beyond classical techniques are highly motivating. Thank you for recommending our work for publication.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents an approach to quantum polarization microscopy using an entangled photon source, demonstrating the potential for advancements in high-contrast, low-power imaging. The experimental results are impressive, particularly in their demonstration of improved contrast using the autocorrelation function, which outperforms classical coincidence counting techniques. The use of quantum-entangled photons in microscopy shows promise for applications where traditional methods may cause photo-damage, making this research highly relevant for fields like biological imaging and light matter interactions.

Before recommendation for acceptance some matters need to be adressed:

1.     The authors should enhance the introduction by incorporating recent advancements in light-matter interactions such as:

- "Critical phenomena in light–matter systems with collective matter interactions." Entropy 24.9 (2022): 1198.
- "Dispersion of organic exciton polaritons—A novel undergraduate experiment." European Journal of Physics 43.3 (2022): 035301.
- "Hybrid entanglement between optical discrete polarizations and continuous quadrature variables." Photonics. Vol. 8. No. 12. MDPI, 2021.

2.     In Figure. 2, a full caption should be provided. A well-constructed caption should be self-explanatory, helping readers understand the optical setup.

3.     Is there a reference for Eq. 2?

4.     In the concludions section, the authors should address the fluctuation noise and long acquisition times more thoroughly by suggesting potential strategies or technological advancements that could mitigate these issues, such as the integration of advanced noise reduction algorithms or more efficient photon detectors. A comparison with previous works can also be benefitial.

5.     To improve the spatial resolution of the proposed method, can you emphasize the need for future experimental implementations involving optimized focusing techniques and lens configurations?
could enhance imaging performance for biological systems?

Comments on the Quality of English Language

Minor editing of English language required. The grammar could be improved in the last section.

Author Response

Comments and Suggestions for Authors

This paper presents an approach to quantum polarization microscopy using an entangled photon source, demonstrating the potential for advancements in high-contrast, low-power imaging. The experimental results are impressive, particularly in their demonstration of improved contrast using the autocorrelation function, which outperforms classical coincidence counting techniques. The use of quantum-entangled photons in microscopy shows promise for applications where traditional methods may cause photo-damage, making this research highly relevant for fields like biological imaging and light matter interactions.

Thanks for your kindly review. It is highly appreciated that the reviewer gave us positive comments.

Before recommendation for acceptance some matters need to be addressed:

1.     The authors should enhance the introduction by incorporating recent advancements in light-matter interactions such as:

- "Critical phenomena in light–matter systems with collective matter interactions." Entropy 24.9 (2022): 1198.

I have read the referenced literature but have determined that it does not contain any content related to this manuscript.

- "Dispersion of organic exciton polaritons—A novel undergraduate experiment." European Journal of Physics 43.3 (2022): 035301.

This paper is also not related to our manuscript.

- "Hybrid entanglement between optical discrete polarizations and continuous quadrature variables." Photonics. Vol. 8. No. 12. MDPI, 2021.

In this study, a novel scheme is proposed for remotely generating hybrid entanglement between discrete polarization states and continuous quadrature optical qubits, which is heralded by a two-photon Bell-state measurement. However, their aim of study is not imaging, so we did not regard a reference.

2. In Figure. 2, a full caption should be provided. A well-constructed caption should be self-explanatory, helping readers understand the optical setup.

Thank you for your comment. We gave full captions to the symbolic denotation in Figure 2.

3.  Is there a reference for Eq. 2?

Equation 2 represents a Gaussian function. This Gaussian function has been used because the sharp dips in the thermal state can be described based on the fluctuation and arbitrariness. That can be characterized by Gaussian statistics.

4. In the conclusions section, the authors should address the fluctuation noise and long acquisition times more thoroughly by suggesting potential strategies or technological advancements that could mitigate these issues, such as the integration of advanced noise reduction algorithms or more efficient photon detectors.

Thank you for your insightful comment. We believe that optimization algorithms based on Compressive Sensing (CS) techniques [r1] hold significant promise for alleviating the issues of fluctuation noise and prolonged acquisition times, which are common in single-photon technologies. Accordingly, we added some comments on CS technique as suggestion for the solution of these issues.

[r1] Quantum imaging and information. Rep. Prog. Phys., 2019, 82, 124401.

A comparison with previous works can also be beneficial.

To compare our research with existing works, we have referenced [17], which illustrates that entanglement is crucial for enhancing the signal-to-noise ratio (SNR) of phase measurements beyond the standard quantum limit (SQL). This scenario is essentially different from our method in terms that phase measurement is employed, which require several 10 micro-meters accuracy in optical path length. Because we avoid such a precise setup and desire a convenient and robust measurement, we employ not phase-sensing measurement but polarization-sensing measurement.

5. To improve the spatial resolution of the proposed method, can you emphasize the need for future experimental implementations involving optimized focusing techniques and lens configurations?

In this paper, since we focus on demonstration of our proposed methodology, the experimental setup has not been optimized for improving resolution or S/N ratio, etc. Next time, we would like to present more fine images by optimizing the setup and imaging procedure including introduction of objective lens for focusing.

Could enhance imaging performance for biological systems?

Our proposed method has following two advantages for biological systems:

       1. Illumination intensity for Sample can be dramatically reduced.

       2. Wet species such as organ tissues can be clearly observed because dispersive interference can                be avoided owing to the basis of quantum interference.

This time we have not shown any biological imaging, but we hope our method shows fine performances also for biological imaging.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript titled " Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Source," authored by Samad et al., introduced an imaging technique using a quantum-polarized photon source. The work is well presented and well organized, the results are well supported by the experimental details. I would recommend acceptance of this manuscript, with a few comments that might help with improving the manuscript more.

1. The second-order autocorrelation function should be written as  $g^{(2)}(0)$.

2. The abstract can be improved by summarizing this work in the last sentences.

3. Figure 1b the vertical axis label is misleading. figure 2 font looks weird. 

4. in formula, using "x" math symbol not "*";

Author Response

Comments and Suggestions for Authors

The manuscript titled " Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Source," authored by Samad et al., introduced an imaging technique using a quantum-polarized photon source. The work is well presented and well organized, the results are well supported by the experimental details. I would recommend acceptance of this manuscript, with a few comments that might help with improving the manuscript more.

Thanks for your kindly review. It is highly appreciated that the reviewer gave us positive comments.

1. The second-order autocorrelation function should be written as $g^{(2)}(0)$.

Thank you for your comment. In our academic field, applied physics, it is common that the second-order autocorrelation function is denoted as g²(0) (without parentheses). Accordingly, we have followed this convention and kept g²(0) in the manuscript.

2.  The abstract can be improved by summarizing this work in the last sentences.

One of the key achievements of our proposed method is ensuring low power of illumination (order of Pico-Watts) for constructing the image.

3. Figure 1b the vertical axis label is misleading.

Since Figure 1 is a schematic illustration, we considered that concrete values were unnecessary.

figure 2 font looks weird. 

Thank you for your feedback. We have modified the fonts in Figure 2 to improve its appearance.

4. In formula, using "x" math symbol not "*".

Thank you for pointing out. We have corrected the formula to use the "×" math symbol instead of "*".

Reviewer 3 Report

Comments and Suggestions for Authors

Summary

The authors demonstrate imaging with sensing the coincidence count and autocorrelation using polarization entangled photon pair as source created using type-II SPDC processes.

While the paper is aimed towards an important question of how diffraction limited resolution in imaging can be overcome using quantum entangled states, the methodology is very vaguely explained, and it fails to make a convincing case of the novelty of the work. There is no detailed quantum optical analysis backing up this claim of why autocorrelation microscopy in this case gives an advantage. The results are also presented in a way that it is difficult to judge. Most importantly, scientific novelty is not clear and no real comparison is made with other similar works.

Specific Comments:

1.      It is mentioned that the source envisioned and used here are type II SPDC photon pair that are polarization entangled. Thus, this state is neither a Fock state nor a thermal state as those states are very well-defined specific photon states. If n number of photons occupy a single mode, it is referred to a Fock state. Thermal state is the n-photon mixed state where the photon number n follows Boltzmann statistics. It is therefore incorrect to associate a Fock state or a thermal state with the photon pair produced by SPDC.

It is also not clear why the photon statistics change between Fock state and thermal state by changing the polarizer angle. Changing the polarizer angle cannot convert a Fock state into a thermal state.

2.      The authors make a distinction between coincidence count and g⁽²⁾(0)- referred to as the autocorrelation function, without clear explanation of what those quantities mean. In most cases, the g⁽²⁾(0) value is the coincidence count as it corresponds to the coincidence rate at zero delay between two detectors. If the authors wish to define a different quantity, it should be properly explained.

3.      It is not clear what is new message in this manuscript. If the autocorrelation based imaging is something that is demonstrated here for the first time, it needs to be mentioned clearly.

4.      In Fig. 5, it is claimed that the autocorrelation imaging provide better contrast. However, it is not apparent from Fig. 5 (d) and (e) and no discussion is provided.

5.      Fig. 1(a) and (b) do not contain the axis values- specifically for the y axis and the labelling is unclear. Further, the two panels in Fig. 1(b) are the same figure in absence of the y axis values.

6.    What determines the width of the coincidence and autocorrelation functions,  here?

7.      There is no scientific reasoning provided on why the autocorrelation function is expected to provide better contrast and by how much. Likewise, the results do not contain any analysis of signal to noise and is not a convincing case of any quantum advantage.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In this manuscript the authors present an experimental demonstration of a quantum polarization microscope that  shows promise for imaging of systems susceptible to photo damage. Their anisotropic sample is an optical spiral retarder. The initial Fock state consists of a vertically polarized signal photon that can be rotated and a horizontally polarized idler photon. The "thermal" state is prepared by blocking one of these channels. 

This is an interesting manuscript that should be published, but as a physicist interested in photons but not familiar with the microscopy literature I have few comments that the authors might choose to consider to make their work accessible to a more general audience. In the Introduction could it be said that the thermal state is "prepared" rather than "raised" by blocking one photon? (I don't understand the meaning of raised.) In what sense is their blocked state thermal and how does this relate to three times the classical sensitivity? Is an "entanglement source" equivalent to an "entangled source"? The coincidence image in Fig. 5(b) seems less noisy than the autocorrelation image in 5(c). Is switching important because this technique makes it easy to implement?

 These minor corrections/additions suggested are optional.

Comments on the Quality of English Language

English is understandable but would benefit from some editorial corrections. 

Author Response

In this manuscript the authors present an experimental demonstration of a quantum polarization microscope that shows promise for imaging of systems susceptible to photo damage. Their anisotropic sample is an optical spiral retarder. The initial Fock state consists of a vertically polarized signal photon that can be rotated and a horizontally polarized idler photon. The "thermal" state is prepared by blocking one of these channels. 

This is an interesting manuscript that should be published, but as a physicist interested in photons but not familiar with the microscopy literature, I have few comments that the authors might choose to consider to make their work accessible to a more general audience. In the Introduction could it be said that the thermal state is "prepared" rather than "raised" by blocking one photon? (I don't understand the meaning of raised.)

Thanks for your kindly review. It is highly appreciated that the reviewer gave us positive comments.

Yes, it would be more appropriate to say that "the thermal state is prepared by blocking one photon, either the signal or the idler photon, using an analyzer. We revised the manuscript as the reviewer comments.

In what sense is their blocked state thermal and how does this relate to three times the classical sensitivity?

Thanks for your good question. Switching between the Fock state and thermal state occurs when signal photon and idler photon can be “distinguished” by somewhat perturbation for either signal or idler photon. In our case, the perturbation is realized by blocking either signal or idler photon. In addition, such switching is rapidly and smoothly conducted even if the perturbation is slightly small, resulting a sharp dip in g²(0) curve. As a result, the gradient at the dip becomes around three times larger than that of coincidence curve (sinusoidal curve), resulting in three times higher sensitivity.

Is an "entanglement source" equivalent to an "entangled source"? The coincidence image in Fig. 5(b) seems less noisy than the autocorrelation image in 5(c). Is switching important because this technique makes it easy to implement?

Thank you for pointing out. Yes, an "entanglement source" is equivalent to an "entangled source", so we revised it. As pointed out by the reviewer, the autocorrelation image appears noisy entirely. The reason for this can be considered as following two:

      1. In this report, we focus on demonstration of our method and, hence, the optimization for                      experimental setup, measuring conditions, noise reduction scheme, and so on, were not                        sufficiently carried out. In future, we conduct these optimizations aiming to obtain a finer                      image   using our method.

      2. As mentioned above, since we focused on demonstration, the entangled photon beam was not            focused or apertured, i.e., without any lens or iris. It is considered that the collimated beam                  with  large spot also made the image noisy.

Concerning last question, which means “switching” that between Fock state and thermal state, or the coincident image and autocorrelation image? Assumed the latter case, we would like to answer the question. In this study, the spiral retarder sample that induces a large polarization retardation. Therefore, a high sensitivity for polarization measurement was not needed. However, high sensitivity is necessary when the polarization variation in sample is very small. In such a situation, we believe that our proposed method is very useful.

English is understandable but would benefit from some editorial corrections. 

Thank you for the comment. We have carefully edited our manuscript.

Reviewer 5 Report

Comments and Suggestions for Authors

The paper titled "Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Sources" introduces an experimental demonstration of quantum polarization microscopy using an entangled-photon source, presenting an approach to enhance image contrast in microscopy. The idea of the paper is generally well, but it needs major revision specially for Methodology section before accepting it.

The section "Methodology of Imaging" needs improvement. I did not understand how Figure 1 was plotted. Is there an analytical approach to plotting it? Additionally, why does the Fock state, which is an antibunching state, show a correlation function larger than the thermal state? Typically, g(2)g^{(2)} for the thermal state is greater than 1, while for a single-photon state it is less than 1. Why does Figure 2 not reflect this?

Author Response

The paper titled "Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Sources" introduces an experimental demonstration of quantum polarization microscopy using an entangled-photon source, presenting an approach to enhance image contrast in microscopy. The idea of the paper is generally well, but it needs major revision specially for Methodology section before accepting it.

Thanks for your careful review and valuable comments. We would like to attempt to respond to all the concerns raised by the reviewer.

The section "Methodology of Imaging" needs improvement. I did not understand how Figure 1 was plotted. Is there an analytical approach to plotting it?

Thanks for your feedback. Figure 1 was only a schematic illustration used for explanation of the proposed methodology. Besides, this figure was drawn based not on theory. For a better readability, we added some descriptions shown below to the revised version.

The transition between Fock state-like and thermal states occurs when the signal and idler photons become distinguishable due to a perturbation caused by polarization change at the sample. This transition happens rapidly and smoothly, even with minimal perturbation, resulting in a sharp dip in the g²(0) curve.

The width of the coincidence rate corresponds to approximately π/4 radians, as the rate varies sinusoidally with respect to the polarization angle. While, the width of the autocorrelation function is attributed to fluctuations in the SPDC process. In an entangled photon source based on SPDC, the time interval of entangled photon pair varies slightly due to inherent statistical fluctuations in the emission process. These fluctuations result in a spread in the photons arrival times at the detectors, corresponding the width of the dips in g²(0) plots.

Additionally, why does the Fock state, which is an antibunching state, show a correlation function larger than the thermal state?

Thanks for pointing out. In our research, we utilize an entangled photon source that shows bunching characteristics, differing from antibunching characteristics observed for single-photon source. In the Fock state observed in entangled photon source, the point that the photon number for each photon pulse is mostly determined is common, but the interval of photon pulse is not precisely periodical, its photon state is categorized to the thermal state. However, in the thermal state like as Planck's blackbody radiation, the photon number for each photon pulse is more dispersive than in the case of entangled photon source. Therefore, the Fock state exhibits a bunching with more intense amplitude compared with normal thermal state, as illustrated in Figure 1(b). For a better readability, we added the experimental results of g²(τ) for Fock state and thermal state to the revised version.

Typically, g(2)g^{(2)} for the thermal state is greater than 1, while for a single-photon state it is less than 1.

Please see our response just above.

Why does Figure 2 not reflect this?

Figure 2 illustrates the experimental setup of the imaging system. Is this comment Figure 1(b) or 4 by mistake? Anyway, please see our response above.

Round 2

Reviewer 5 Report

Comments and Suggestions for Authors

The paper titled "Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Sources" introduces an experimental demonstration of quantum polarization microscopy using an entangled-photon source, presenting an approach to enhance image contrast in microscopy. The idea of the paper is generally well, but it needs major revision. 

Thank you for the authors' response. However, I remain unconvinced, particularly regarding the claims made in the Metrology section. The authors state that "we utilize an entangled photon source that shows bunching characteristics,". Unfortunately, they did not mention that they are using this characteristic of the source. Additionally, they do not explain how this is possible. I request that the authors provide a clear explanation or reference relevant studies in the manuscript. Furthermore, I am unclear about the difference between the Fock states, which exhibit g2(taw) <1 compared to thermal radiation, and the specific Fock state mentioned in this paper.

 Author Response

The paper titled "Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Sources" introduces an experimental demonstration of quantum polarization microscopy using an entangled-photon source, presenting an approach to enhance image contrast in microscopy. The idea of the paper is generally well, but it needs major revision. 

Thank you for the authors' response. However, I remain unconvinced, particularly regarding the claims made in the Metrology section. The authors state that "we utilize an entangled photon source that shows bunching characteristics,". Unfortunately, they did not mention that they are using this characteristic of the source. Additionally, they do not explain how this is possible. I request that the authors provide a clear explanation or reference relevant studies in the manuscript.

Thanks for your thoughtful review and valuable comments. Our entangled photon pair source exhibits bunching characteristics due to the photon statistical properties of light. It usually indicates that the photons tend to arrive in pairs or "bunches" rather than independently, which is typical in spontaneous parametric down-conversion (SPDC) and also confirms the generation of photon pairs. In our experiment, the correlated photon-pair source (entangled photon source) demonstrates bunching behavior in the second-order correlation measurement, g²(τ), between signal and idler photons [r1].

[r1] Correlated photon-pair source. Available online https://www.thorlabs.com (29^th July, 2024).

Furthermore, I am unclear about the difference between the Fock states, which exhibit g²(taw) <1 compared to thermal radiation, and the specific Fock state mentioned in this paper.

Both Fock and thermal states exhibit bunching characteristics, as shown by g²(τ) >1. In the case of Fock state, g²(0) >1 indicates that the time interval between photons [Signal and Idler] is reduced relative to the Poisson case (g²(0)=1) [r2], while photon number for each photon pulse is mostly determined but the interval of photon pulse is not precisely periodical. That’s why it shows the bunching behavior instead of antibunching (g²(τ) <1).Similarly for Fock state, the time interval of thermal state photons [Signal and Idler]  tend to cluster together more than in a Poisson case [r2] and in the case of Planck's blackbody radiation, the photon number for each photon pulse is more dispersive than in the case of entangled photon source leading to photon bunching behavior as g²(τ) >1 with lower amplitude.

Thus, while both states exhibit bunching behavior, the Fock state exhibits bunching with a more intense amplitude than the typical thermal state, as illustrated in Figure 1(b). To enhance clarity, we have added experimental results for g²(τ) for both the Fock and thermal states in the revised manuscript.

[r2] DAVID, S., and JAEGER SIMON. Quantum Metrology, Imaging, and Communication. SPRINGER, 2018.

In addition, we added these descriptions to the text accordingly:

The entangled photon pair source used in this experiment exhibits bunching characteristics, a phenomenon associated with the photon statistical properties of light. This behavior, where photons arrive in pairs or "bunches" rather than independently, is typical in spontaneous parametric down-conversion (SPDC) and confirms the pho-ton-pair generation. In our experiment, the bunching effect is evident in the second-order correlation measurement, g²(τ), between signal and idler photons [23]. Both Fock and thermal states exhibit bunching characteristics, as shown by g²(0) >1. For a Fock state, g²(0) >1 indicates that the time interval between photons [Signal and Idler] is stretched compared to the Poisson case (g²(0)=1) [24]. Although the photon number for each photon pulse is mostly determined to be two, the interval of photon pulse is not precisely periodical, resulting in a bunching effect instead of antibunching (g²(0) <1). In the case of thermal state, the time interval tend to cluster together more than in a Poisson distribution [24], which induces the photon number for each photon pulse more dispersive than in the case of Fock state. As a result, the photon bunching behavior in thermal state shows a lower amplitude of bunching peak. Thus, it is expected that both Fock and thermal states indicate bunching behavior, but the amplitude in the Fock state is more intense than that in the thermal states. Here, the variations of g²(τ) with respect to the time delay (τ) between the signal and idler photon for the Fock state and thermal state are schematically illustrated in Figure 1(a). This will be experimentally confirmed by the results shown in the next section. It is noticed that the coincidence window for measurements should be similar value as the width of bunching peak (∆τ) to observe the bunching peak correctly.

Round 3

Reviewer 5 Report

Comments and Suggestions for Authors

The paper titled "Demonstration of Quantum Polarized Microscopy using an Entangled-Photon Sources" introduces an experimental demonstration of quantum polarization microscopy using an entangled-photon source, presenting an approach to enhance image contrast in microscopy. Based on my review and the authors answers, I recommend that the manuscript be rejected. In the following you can find the reasons:

1. The authors, referred to one of the Thorlabs product (https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=13675). If they used this source, it is clearly mentioned in the properties of the product that g2(0) = .004. Also, it is mentioned that in the case if a g2(taw) measurement is performed only on one of the channels, with the other one ignored, then such a source will produce thermal statistics (g2>1). According to the draft of the paper, authors used the coincidence measurement and so they are not in the thermal source condition.

2. In the literature, g2(0) for Fock state is given as g2(0) = 1-1/n. Therefor, I expect to see in the experimental results with g2 values less than 1. However, in Fig.5 g2 around 6 has been reported. It is not clear for me the difference between the usual Fock state and Fock state-like (the phrase which authors uses)?!

The authors wrote that "Fock state, g2(0) >1 indicates that the time interval between photons [Signal and Idler] is reduced relative to the Poisson case". Also, they referred to re.24 (in the draft). While I agree that g2>1 indicates photon bunching, but it does not imply that a Fock state can have a g2 larger than 1. Also, in the cited literature, it does not mention the possiblity of g2>1 for Fock states. If the authors know any reference for such a phenomenon (g2>1 for Fock state) I will be glad if they could cite them.  

Author Response

Please find the attachment.

Author Response File: Author Response.pdf