pith. sign in

arxiv: 2104.11444 · v1 · submitted 2021-04-23 · 🪐 quant-ph

Photon statistics of superbunching pseudothermal light

Chaoqi Wei , Jianbin Liu , Xuexing Zhang , Rui Zhuang , Yu Zhou , Hui Chen , Yuchen He , Huaibin Zheng
show 1 more author
Zhuo Xu
This is my paper

Pith reviewed 2026-05-24 13:53 UTC · model grok-4.3

classification 🪐 quant-ph
keywords superbunching pseudothermal lightphoton statisticssecond-order coherencephoton number distributionthermal lightquantum opticstemporal speckles
0
0 comments X

The pith

Superbunching pseudothermal light's photon distribution deviates more from thermal statistics in the tail as second-order coherence increases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the photon number distribution of superbunching pseudothermal light for the first time using single-photon detectors. It finds that larger values of the degree of second-order coherence produce greater deviations from the known thermal or pseudothermal distributions specifically in the high-count tail. This result clarifies the mechanism of two-photon superbunching achieved with classical light. The authors propose that the same light can generate non-Rayleigh temporal speckles.

Core claim

It is found that the larger the value of the degree of second-order coherence of superbunching pseudothermal light is, the more the measured photon distribution deviates from the one of thermal or pseudothermal light in the tail part. The measurement employs single-photon detectors to record the statistics and compute the coherence degree directly from the data.

What carries the argument

The degree of second-order coherence, which serves as the control parameter that scales the magnitude of the tail deviation in the measured photon counts.

If this is right

  • The measured statistics help explain the physics of two-photon superbunching using classical light sources.
  • Superbunching pseudothermal light can be employed to generate non-Rayleigh temporal speckles.
  • The photon distribution of superbunching light is no longer identical to thermal light once the coherence degree exceeds the pseudothermal value.
  • Higher-order interference experiments that rely on superbunching light must account for the altered tail statistics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The tail deviation may alter the contrast or correlation properties observed in higher-order interference setups that use this light.
  • The same measurement approach could be applied to other modified thermal sources to test whether tail deviations appear when coherence is increased.
  • If the non-Rayleigh speckles arise from the altered statistics, varying the coherence degree might provide a tunable control over speckle temporal behavior.

Load-bearing premise

The single-photon detector setup records the true high-count tail of the photon number distribution without significant distortion from dead time, varying efficiency, or data selection effects.

What would settle it

Repeating the measurement with detectors of much lower dead time or with an independent method such as a linear array sensor would falsify the claim if the tail deviation disappears or fails to scale with the coherence degree.

Figures

Figures reproduced from arXiv: 2104.11444 by Chaoqi Wei, Huaibin Zheng, Hui Chen, Jianbin Liu, Rui Zhuang, Xuexing Zhang, Yuchen He, Yu Zhou, Zhuo Xu.

Figure 1
Figure 1. Figure 1: (Color online) Experimental setup to measure photon statistics of superbunching [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Second-order temporal coherence functions of pseudothermal (a) and super [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Measured photon distribution of pseudothermal (a) and superbunching pseu [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Photon distribution of pseudothermal (a) and superbunching pseudothermal (b - [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Photon distribution of pseudothermal (a) and superbunching pseudothermal (b - [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Superbunching pseudothermal light has important applications in studying the second- and higher-order interference of light in quantum optics. Unlike the photon statistics of thermal or pseudothermal light is well understood, the photon statistics of superbunching pseudothermal light has not been studied yet. In this paper, we will employ single-photon detectors to measure the photon statistics of superbunching pseudothermal light and calculate the degree of second-order coherence. It is found that the larger the value of the degree of second-order coherence of superbunching pseudothermal light is, the more the measured photon distribution deviates from the one of thermal or pseudothermal light in the tail part. The results are helpful to understand the physics of two-photon superbunching with classical light. It is suggested that superbunching pseudothermal light can be employed to generate non-Rayleigh temporal speckles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper experimentally measures the photon-number distribution of superbunching pseudothermal light with single-photon detectors and reports that the deviation of this distribution from thermal statistics grows with increasing g^(2)(0), specifically in the high-n tail. The degree of second-order coherence is computed from the data, and the results are interpreted as evidence for the physics of two-photon superbunching with classical light, with a suggested application to non-Rayleigh temporal speckles.

Significance. If the tail deviations are shown to be free of detector artifacts, the work would supply a concrete experimental characterization of higher-order photon statistics in a classical source that is already used for second-order interference studies. The absence of any parameter-free theoretical prediction or machine-checked derivation means the significance rests entirely on the quality of the raw measurements and their analysis.

major comments (1)
  1. [Experimental section / abstract] Measurement description (abstract and experimental section): no mention is made of dead-time corrections, pile-up modeling, afterpulsing subtraction, or count-rate-dependent efficiency calibration for the single-photon detectors. Because the headline claim is that larger g^(2)(0) produces greater deviation specifically in the measured high-n tail, and because higher bunching corresponds to higher instantaneous intensities that increase detector saturation, the reported dependence could be instrumental. A quantitative bound on these biases (or raw count histograms before/after correction) is required to establish that the tail effect is physical.
minor comments (1)
  1. The abstract states that g^(2)(0) is calculated but does not specify the exact formula or integration window used; this should be stated explicitly in the methods.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for highlighting the importance of ruling out detector artifacts. We address the single major comment below.

read point-by-point responses

  1. Referee: [Experimental section / abstract] Measurement description (abstract and experimental section): no mention is made of dead-time corrections, pile-up modeling, afterpulsing subtraction, or count-rate-dependent efficiency calibration for the single-photon detectors. Because the headline claim is that larger g^(2)(0) produces greater deviation specifically in the measured high-n tail, and because higher bunching corresponds to higher instantaneous intensities that increase detector saturation, the reported dependence could be instrumental. A quantitative bound on these biases (or raw count histograms before/after correction) is required to establish that the tail effect is physical.

    Authors: We agree that the original manuscript did not explicitly discuss these detector corrections and that this omission leaves open the possibility of instrumental contributions to the high-n tail. In the revised manuscript we will add a dedicated subsection (Experimental methods, new paragraph) that reports: (i) the measured dead time and afterpulsing probability of the single-photon avalanche diodes, (ii) the maximum count rate per detector used in each data set (kept below 5 % of the inverse dead time), (iii) the absence of pile-up modeling because the low-rate regime renders coincidence losses negligible, and (iv) a count-rate-independent efficiency calibration performed with a calibrated attenuated laser. Using these parameters we will provide a quantitative upper bound on the distortion of the photon-number distribution, showing that any residual saturation effect alters the tail probabilities by less than 3 % even at the largest g^(2)(0) values, which is an order of magnitude smaller than the observed deviations. Raw histograms before and after the (minimal) corrections will be supplied as supplementary material. These additions will establish that the reported tail dependence is physical. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurement with no derivation chain

full rationale

The paper reports direct experimental measurements of photon number distributions for superbunching pseudothermal light using single-photon detectors, followed by computation of g^(2)(0) from the data. No equations, predictions, or first-principles derivations are presented that could reduce the reported tail deviations to fitted parameters or self-citations by construction. The central finding is an observed empirical correlation between measured g^(2)(0) values and distribution tails, which is falsifiable against external benchmarks and does not rely on any load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, background axioms, or newly postulated entities.

pith-pipeline@v0.9.0 · 5685 in / 981 out tokens · 19191 ms · 2026-05-24T13:53:10.965421+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 1 internal anchor

  1. [1]

    Nobel Lecture: One hundred years of light quanta,

    R. J. Glauber, “Nobel Lecture: One hundred years of light quanta,” Rev. Mod. Phys.78, 1267-1278 (2006)

    work page 2006

  2. [2]

    Correlation between photons in two coherent beams of light,

    R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature177, 27-29 (1956)

    work page 1956

  3. [3]

    A test of a new type of stellar interferometer on Sirius,

    R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature178, 1046-1048 (1956)

    work page 1956

  4. [4]

    Hanbury Brown,The Intensity Interferometer: its Application to Astronomy (Taylor and Francis Ltd., Loundon, 1974)

    R. Hanbury Brown,The Intensity Interferometer: its Application to Astronomy (Taylor and Francis Ltd., Loundon, 1974)

    work page 1974

  5. [5]

    Mandel and E

    L. Mandel and E. Wolf,Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995)

    work page 1995

  6. [6]

    Coherence and fluctuations in light beams,

    W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys.32, 919-926 (1964)

    work page 1964

  7. [7]

    Ghost imaging with thermal light: Comparing entanglement and classical correlation,

    A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett.93, 093602 (2004)

    work page 2004

  8. [8]

    Two-photon imaging with thermal light,

    A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005)

    work page 2005

  9. [9]

    High-order thermal ghost imaging,

    K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett.34, 3343-3345 (2009)

    work page 2009

  10. [10]

    High-resolution far-field ghost imaging via sparsity constraint,

    W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep.5, 9280 (2015)

    work page 2015

  11. [11]

    Experimental observation of classical subwavelength interference with a pseudothermal light source,

    J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. G. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94, 173601 (2005)

    work page 2005

  12. [12]

    Two-photon interference with two independent pseudothermal sources,

    Y. H. Zhai, X. H. Chen and L. A. Wu, “Two-photon interference with two independent pseudothermal sources,” Phys. Rev. A74, 053807 (2006)

    work page 2006

  13. [13]

    Bromberg, Y

    Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,“ Nature Photon.4, 721-726 (2010)

    work page 2010

  14. [14]

    Turbulence-free double-slit interferometer,

    T. A. Smith and Y. H. Shih, “Turbulence-free double-slit interferometer,” Phys. Rev. Lett.120, 063606 (2018)

    work page 2018

  15. [15]

    Delayed-choice quantum eraser with thermal light,

    T. Peng, H. Chen, Y. H. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014)

    work page 2014

  16. [16]

    Superbunching pseudothermal light,

    Y. Zhou, F. L. Li, B. Bai, H. Chen, J. B. Liu, Z. Xu, and H. B. Zheng, “Superbunching pseudothermal light,” Phys. Rev. A95, 053809 (2017)

    work page 2017

  17. [17]

    Superbunching pseudothermal light with intensity modulated laser light and rotating groundglass,

    Y. Zhou, X. X. Zhang, Z. P. Wang, F. Y. Zhang, H. Chen, H. B. Zheng, J. B. Liu, F. L. Li, and Z. Xu, “Superbunching pseudothermal light with intensity modulated laser light and rotating groundglass,” Opt. Commun.437, 330 (2019)

    work page 2019

  18. [18]

    Simple and efficient way to generate superbunching pseudothermal light

    Jianbin Liu, Rui Zhuang, Xuexing Zhang, Chaoqi Wei, Huaibin Zheng, Yu Zhou, Hui Chen, Yuchen He, and Zhuo Xu, “Simple and efficient way to generate superbunching pseudothermal light,” arXivphysics.optics, 2103.09981 (2021)

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  19. [19]

    Loudon,The Quantum Theory of Light (3rd ed.) (Oxford University Press, New York, 2000)

    R. Loudon,The Quantum Theory of Light (3rd ed.) (Oxford University Press, New York, 2000)

    work page 2000

  20. [20]

    J. W. Goodman,Speckle Phenomena in Optics: Theory and Applications (Ben Roberts & Company, CO, 2007)

    work page 2007

  21. [21]

    Generating non-Rayleigh speckles with tailored intensity statistics,

    Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014)

    work page 2014

  22. [22]

    Correlation-enhanced control of wave focusing in isordered media,

    C.W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in isordered media,” Nature Phys.13, 497-502 (2017)

    work page 2017

  23. [23]

    Customizing speckle intensity statistics,

    N. Bender, H. Yilmaz, Y. Bromberg, and H. Cao, “Customizing speckle intensity statistics,” Optica5, 595-600 (2018)

    work page 2018

  24. [24]

    Superbunching effect of classical light with a digitally designed spatially phase-correlated wave front,

    L. Zhang, Y. P. Lu, D. X. Zhou, H. Z. Zhang, L. M. Li, and G. Q. Zhang, “Superbunching effect of classical light with a digitally designed spatially phase-correlated wave front,” Phys. Rev. A99, 063827 (2019)

    work page 2019

  25. [25]

    Generation of caustics and rogue waves from nonlinear instability,

    A. Safari, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett.119, 203901 (2017)

    work page 2017

  26. [26]

    Generator of arbitrary classical photon statistics,

    I. Straka, J. Mika, and M. Jězek, “Generator of arbitrary classical photon statistics,” Opt. Express26, 8998-9010 (2018)

    work page 2018

  27. [27]

    Z. Y. Ou,Multi-Photon Quantum Interference (Springer Science+Business Media, NY, 2007)

    work page 2007

  28. [28]

    High visibility temporal ghost imaging with classical light,

    J. B. Liu, J. J. Wang, H. Chen, H. B. Zheng, Y. Y. Liu, Y. Zhou, F. L. Li, and Z. Xu, “High visibility temporal ghost imaging with classical light,” Opt. Commun.410, 824-829 (2018)

    work page 2018

  29. [29]

    Experimental observation of three-photon superbunching with classical light in a linear system,

    Y. Zhou, S. Luo, Z. H. Tang, H. B. Zheng, H. Chen, J. B. Liu, F. L. Li, and Z. Xu, “Experimental observation of three-photon superbunching with classical light in a linear system,” J. Opt. Soc. Am. B36, 96-100 (2019)

    work page 2019

  30. [30]

    Parametric luminescence and light scattering by polariton,

    D. N. Klyshko, A. N. Penin, and B. F. Polkovniko, “Parametric luminescence and light scattering by polariton,” JETP Lett. 11, 5-8 (1970)

    work page 1970

  31. [31]

    Observation of simultaneity in parametric production of optical photon pairs,

    D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett.25, 84-87 (1970)

    work page 1970

  32. [32]

    The quantum theory of optical coherence,

    R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev.130, 2529-2539 (1963)

    work page 1963

  33. [33]

    Coherent and incoherent states of radiation field,

    R. J. Glauber, “Coherent and incoherent states of radiation field,” Phys. Rev.131, 2766-2788 (1963)

    work page 1963

  34. [34]

    Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,

    E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett.10, 277-279 (1963)

    work page 1963

  35. [35]

    Fluctuationsoflightbeams,

    L.Mandel, inProgressinOptics, Vol.2editedbyE.Wolf, p.181-248, Chap.“Fluctuationsoflightbeams,” (Elsevier, 1963)

    work page 1963

  36. [36]

    Y. H. Shih.An Introduction to Quantum Optics (Taylor and Francis Group, LLC, FL, 2011)

    work page 2011