Pith. sign in

REVIEW 3 major objections 4 minor 56 references

Enhancing Measurement Precision of Non-Degenerate Two-Photon Absorption

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper argues that the raw intensity correlation G(1,1) with optimized double-seeded squeezed light gives the best two-photon absorption precision, scaling as 6/n_T^3.5, while normalized g(1,1) loses the quantum gain but keeps loss…

desk verdict A useful theory comparison for non-degenerate TPA with two-mode squeezed light, but the loss model treats both modes as identical and the key scaling laws sit in an inaccessible companion file. read the letter →

arxiv 2506.07384 v1 pith:E2CM4W3J submitted 2025-06-09 quant-ph

Gaurav Shukla , Shahram Panahiyan , Devendra Kumar Mishra , Frank Schlawin This is my paper
classification quant-ph
keywords non-degeneratetwo-photonabsorptiontwo-modesqueezedlightintensitycorrelationG(11)normalizednoisereductionfactorquantummetrologyphotonlosscoherentstates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper compares three ways of reading out a transmission measurement of non-degenerate two-photon absorption (a process in which one photon from each of two different frequency modes is absorbed together), using two-mode squeezed light as the probe. It claims that the unnormalized intensity correlation G(1,1), optimized over squeezing, seeding, and phase, gives the most precise estimate of the absorbance, with estimation error scaling as about 6/$n_T^{3}$.5 at large photon number. The normalized correlation g(1,1) and the noise reduction factor scale only as 1/$n_T^{2}$, and under linear photon loss g(1,1) keeps its precision but no longer exhibits any quantum advantage, whereas G(1,1) remains the best despite some degradation. If correct, this tells experimentalists which observable and which squeezed input state to use, and it exposes a trade-off between loss robustness and quantum enhancement.

What carries the argument

The calculation builds on a Markovian master equation for the two-photon absorption sample, whose Lindblad operator removes one photon from each mode only when the two frequencies add up to the resonance. The smallness of two-photon absorption cross sections justifies expanding the evolution operator to first order in the absorbance, and photon loss is inserted as a beam splitter of transmittivity η acting identically on both modes. Each observable's error is obtained from error propagation, Δε² = Var(O)/(∂⟨O⟩/∂ε)² at ε=0, with the variance computed through a covariance matrix of photon-number moments. Optimization over the squeezing parameter r, the coherent seeding amplitudes, and the relative phase between seeding and squeezing is what produces the different scaling exponents collected in Table I.

What would settle it

Measure the G(1,1) estimation error for the optimized double-seeded squeezed state at several total photon numbers in a lossless setup; if the log-log slope is not -3.5, the central scaling claim fails. Then insert unequal loss for the two modes to test whether g(1,1) remains loss-immune and whether G(1,1) stays the best readout.

Watch

Extended reading notes

Core claim

For non-degenerate two-photon absorption probed by two-mode squeezed light in a transmission geometry, the paper establishes that the raw intensity correlation G(1,1) is the best measurement. With a double-seeded two-mode squeezed state and optimal squeezing and phase, the error in estimating the absorbance scales as Δε²_G(1,1) ≈ 6/$n_T^{{3.5}}$ in the lossless large-photon-number limit, compared with Δε² ≈ 1/$n_T^{2}$ for both g(1,1) and the noise reduction factor, and with 4/$n_T^{3}$ for classical coherent-state G(1,1). Under single-photon loss modeled by a common transmittivity η on both modes, G(1,1) degrades but remains the most precise; g(1,1) is practically unchanged by loss but its precision no longer reflects a non-classical advantage; and the noise reduction factor becomes sensitive to the loss itself, which the paper uses to switch two-photon absorption detection on and off. The paper concludes that the optimal choice of observable is a trade-off between robustness to imperfection and the size of the quantum enhancement.

Load-bearing premise

The central claim assumes the two light colours involved in non-degenerate two-photon absorption lose the same fraction of photons in the optics, so the recommended measurement could change if one colour is attenuated more than the other.

Editorial extensions

If this is right

  • With optimized double-seeded two-mode squeezed light, G(1,1) transmission measurements yield the smallest estimation error for two-photon absorption absorbance, scaling as 6/n_T^{3.5}, and beat all classical coherent-state strategies.
  • g(1,1) forfeits the quantum scaling advantage, but its precision is essentially unchanged by linear photon loss, making it the safer readout in lossy or poorly characterized setups.
  • The noise reduction factor is the least precise observable, yet it is the only one that can distinguish single-photon losses from two-photon absorption, acting as a built-in loss monitor.
  • The optimal probe state depends strongly on the observable: G(1,1) prefers weak squeezing with strong seeding, g(1,1) prefers a small fixed amount of seeding, and the noise reduction factor requires balanced squeezing and seeding.
  • Squeezing improves precision over coherent states for every observable considered, but the gain is much larger for G(1,1) than for g(1,1) or the noise reduction factor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The identical-loss assumption (one transmittivity η for both modes) is the most fragile point; with unequal losses the normalization in g(1,1) will not cancel perfectly, so its loss immunity and the ranking of G(1,1) versus g(1,1) should be re-examined with two loss parameters.
  • The paper's error-propagation analysis is restricted to the method of moments; a full quantum Fisher information treatment of the same probe states could reveal whether the 6/n_T^{3.5} scaling is the ultimate limit or whether even better estimators exist.
  • The n_T^{-3.5} advantage of raw coincidence counting suggests that in future nonlinear-interferometer versions of two-photon absorption metrology, unnormalized intensity correlations, not normalized ones, are the readout most likely to preserve a quantum advantage.
  • A simple experimental check would place frequency-dependent attenuators in the two arms and map the region where g(1,1) loses its immunity; the paper's predictions are only guaranteed where both modes lose equally.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper analyzes the precision with which the two-photon absorption (TPA) absorbance can be estimated from transmission measurements, comparing three observables: the noise reduction factor (NRF), the intensity correlation G(1,1), and the normalized intensity correlation g(1,1). The input light is a two-mode squeezed state, considered in three configurations: squeezed vacuum, single-seeded squeezed coherent state, and double-seeded squeezed coherent state. Single-photon losses are modeled by beam splitters with a common transmittivity. The authors report that G(1,1) measurements give the best precision, with an optimized double-seeded state yielding Δϵ²_G(1,1) ≈ 6/n_T^3.5, while g(1,1) gives Δϵ² ≈ 1/n_T^2 but is robust to loss, and NRF is the worst observable. The paper includes closed-form expressions for the squeezed-vacuum case, asymptotic scaling laws for seeded states, and a discussion of the trade-off between loss robustness and quantum enhancement.

Significance. If the reported scalings are correct, the paper provides practically useful guidance for choosing both the input state and the measurement observable in quantum-enhanced TPA experiments. The strength of the paper is that the squeezed-vacuum results are given in closed form (Eqs. 21-24) and the error-propagation framework in Appendices A-C is clearly formulated, making the comparison falsifiable. The central claim, however, rests on seeded-state scaling laws and optimization results that are not contained in the manuscript, and the loss model assumes identical losses for the two non-degenerate modes. These issues currently limit the verifiability and generality of the main conclusions.

major comments (3)
  1. [Section III.C-III.D, Eqs. (25)-(30)] The central scaling laws for the seeded states, including the headline Δϵ²_G(1,1) ≈ 6/n_T^3.5 in Eq. (29), are stated to be derived in a companion Mathematica file that is not accessible from the manuscript. Neither the optimized expressions nor the asymptotic expansions are given, so the reader cannot verify that these scalings follow from the stated master equation and beam-splitter transformations. Because Table I and the abstract's trade-off conclusion depend on these results, this is a load-bearing reproducibility gap. The derivations (or a permanent, reviewed supplement) should be included in the paper.
  2. [Section II.A, Eq. (11), and Fig. 3] The loss model uses a single transmittivity η for both modes. For non-degenerate TPA, where ω1 ≠ ω2, losses in the two arms are generally different (η1 ≠ η2). The claims that g(1,1) is robust to loss and that G(1,1) remains the best under loss are only tested for η1 = η2. Since the error-propagation formulas in Appendices B and C are nonlinear functions of the detected photon-number moments, the η1 and η2 dependences do not cancel in general; for example, the TPA signal derivative in G(1,1) scales as η1η2 while the variance can contain terms with different powers of η1 and η2. The equal-loss assumption is therefore load-bearing and should be relaxed or explicitly justified for the experimental regime of interest.
  3. [Section III.D] The optimization over the double-seeded state is not fully specified. The total photon number n_T depends on α1, α2, r, and the relative phase, but the text only states that the squeezing parameter and the relative phase are optimized. It is not stated whether α1 and α2 are fixed, varied, or constrained (e.g., α1 = α2). Without the full optimization domain, the reported 'optimized' scalings in Eqs. (28)-(30) and the phase diagrams in Fig. 6 are not well-defined. This ambiguity is central to the claimed advantage of double seeding and should be clarified.
minor comments (4)
  1. [Throughout] There are several typographical issues, including 'transmitivity' for 'transmittivity' and 'stander deviation' for 'standard deviation' in Appendix A; the paper should be proofread.
  2. [Section II.B] G(1,1) is called the 'first-order intensity correlation function', but ⟨n1 n2⟩ is a second-order intensity correlation; the nomenclature should be aligned with standard quantum-optics usage.
  3. [Fig. 4] The color bar is labeled 'Log Δϵ²_NRF' but the axes are not labeled in the reproduction; please add axis labels and a more complete caption.
  4. [Reference [53]] The reference contains a spurious space ('V ol. 2'); several other references have similar spacing or formatting inconsistencies.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: scaling laws are computed from stated state transformations and error-propagation formulas, with no fitted observable or load-bearing self-citation.

full rationale

The derivation chain is self-contained. Eq. (2) specifies the TPA Lindblad dynamics, Eqs. (8)-(9) define the input two-mode squeezed states, Eq. (10) gives the first-order TPA output, Eq. (11) models single-photon loss via a beam splitter, and Eq. (12) defines the estimation error by standard error propagation. Appendices B and C provide the covariance-matrix expressions used to evaluate Var(N) and Var(g(1,1)). The scaling laws in Table I are obtained by applying these transformations to the specified input states and optimizing squeezing/seeding at fixed total photon number. Crucially, no parameter is fitted to any dataset, and the observables NRF, G(1,1), and g(1,1) are not defined in terms of the target absorbance epsilon or the scaling exponents. The only self-citation is reference [22] for the fictitious-beam-splitter loss model, but that model is also standard and is explicitly implemented in Eqs. (4)-(11); it does not import the paper's central conclusion. The claimed loss robustness of g(1,1) and the superiority of G(1,1) are computed consequences of the stated variance and derivative formulas, not input assumptions. The equal-loss assumption eta for both non-degenerate modes is a scope or modeling limitation for the non-degenerate case, but it is not a circularity: the results would be conditional on that assumption even if the assumption were changed. Therefore no circular step is present.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities and fits no parameters to data. Its central results rest on standard quantum-optics axioms: the Lindblad TPA model, first-order perturbation in epsilon, equal linear losses, and moment-based error propagation. The most fragile input is the equal-loss assumption, which is not relaxed anywhere in the paper.

assumptions (5)
  • domain assumption TPA is modeled by a Markovian Lindblad master equation with jump operator a1 a2 (Eq. 2), valid for weak coupling and a two-level sample.
    This is the standard effective model for resonant non-degenerate two-photon absorption in the weak-coupling limit, but it omits intermediate-state dynamics and any memory effects.
  • domain assumption The TPA absorbance epsilon is small, and all results are first order in epsilon (Eqs. 5 and 10).
    The output operators c1 and c2 are truncated at first order, so the variance and derivative formulas are valid only for epsilon much less than 1.
  • domain assumption Single-photon loss is identical on both modes, modeled by beam splitters with the same transmittivity eta (Eq. 11).
    Non-degenerate TPA involves two different frequencies, so realistic losses would differ; the loss-robustness conclusions are derived under this equal-loss restriction.
  • standard math Measurement precision is assessed by the method of moments, with Var(O) = (d<O>/depsilon)^2 Delta_epsilon^2 evaluated at epsilon=0 (Appendix A).
    Standard linear error propagation; it ignores higher-order dependence of the estimator on epsilon and assumes unbiased estimators.
  • domain assumption Only the resonance condition omega1 + omega2 = omega matters; 2 omega1 and 2 omega2 are non-resonant.
    This justifies the joint loss operator a1 a2 and excludes degenerate TPA channels.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Enhancing Measurement Precision of Non-Degenerate Two-Photon Absorption." pith.science (2026). https://pith.science/paper/E2CM4W3J

@misc{pith2026250607384,
  author       = {Pith},
  title        = {Pith review of: Enhancing Measurement Precision of Non-Degenerate Two-Photon Absorption},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E2CM4W3J}},
  note         = {Machine review of arXiv:2506.07384}
}
read the original abstract

Recent theoretical and experimental studies have shown that squeezed states of light can be engineered to enhance the resolution of nonlinear optical measurements. Here, we analyze non-degenerate two-photon absorption signals obtained from transmission measurements using two-mode squeezed light and compare different measurement strategies. In particular, we investigate how correlations between the light modes may be used to improve the achievable precision. We find that intensity correlation measurements offer the best performance compared to normalized intensity correlation and noise reduction factor approaches. Under experimental imperfections modeled as linear photon losses, the enhancements from intensity and noise reduction measurements are reduced. In contrast, the normalized intensity correlation remains robust to loss, though this comes at the cost of losing the enhancement from non-classical light fields. This establishes a trade-off between robustness to loss and the achievable quantum advantage.

Figures

Figures reproduced from arXiv: 2506.07384 by the authors.

Figure 1
Figure 1. FIG. 1. Panel (a) the setup to calculate the measurement error of the TPA cross-section. Photon losses are modeled as imbalanced beam [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Optimum [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The normalized error, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Estimation error [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Variation of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Phase dependence of the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Optimum [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

56 extracted references · 50 canonical work pages

  1. [1]

    From Eq. (6), variation in expectation value of ˆOwith respect toϵcan be written as ∂⟨ ˆO⟩ ∂ϵ ϵ=0 =tr n e ˆLη ˆL′T PAe ˆLOPA ˆOˆρ′o .(13) We evaluate the intensity measurements in both output ports using the above equations and calculate the following correlation functions: Noise reduction factor: The noise reduction factor (NRF) is defined as [40, 41] N≡...

    work page

  2. [2]

    cosh 2r+ 2α1α2 cosθsinh 2r+2 sinh 2 r) is composed of a spontaneous downconversion contribution (2 sinh 2 r) and photons due to seeded squeezing (α 2 1−α 2 2 +(1+α 2 1 +α 2

    work page

  3. [3]

    cosh 2r+ 2α1α2 cosθsinh 2r). To understand the interrelation between the required squeezing and seeding for the optimal values of ∆ϵ2, we plot the variation of the squeezing parameterrwith nT for the three cases in the lower panels of Fig. 5, showing us that (i) In the case of NRF, we need stronger squeezing for double seeding than the single seeding case...

    work page

  4. [4]

    International Visiting Student Program

    cosh 2r+2α 1α2 cosθsinh 2r≈2 would be satisfied for optimal error measurement. E. Discussions First, we compare the best precision obtained by squeezing for different measurement schemes to their classical counterparts. We give the results in Fig. 7, in which dashed lines correspond to classical transmission measurements with coherent states and the shade...

    work page 2021

  5. [5]

    G ¨oppert-Mayer, ¨Uber elementarakte mit zwei quantenspr¨ungen, Annalen der Physik401, 273 (1931)

    M. G ¨oppert-Mayer, ¨Uber elementarakte mit zwei quantenspr¨ungen, Annalen der Physik401, 273 (1931)

    work page 1931

  6. [6]

    Paul, Photon antibunching, Rev

    H. Paul, Photon antibunching, Rev. Mod. Phys.54, 1061 (1982)

    1982

  7. [7]

    Chandra and H

    N. Chandra and H. Prakash, Anticorrelation in two-photon attenuated laser beam, Phys. Rev. A1, 1696 (1970)

    work page 1970

  8. [8]

    Kaiser and C

    W. Kaiser and C. G. B. Garrett, Two-photon excitation in CaF2: Eu2+, Phys. Rev. Lett.7, 229 (1961)

    work page 1961

Show all 56 references
  1. [9]

    I. D. Abella, Optical double-photon absorption in cesium vapor, Phys. Rev. Lett.9, 453 (1962)

    1962

  2. [10]

    Braunstein and N

    R. Braunstein and N. Ockman, Optical double-photon absorption in CdS, Phys. Rev.134, A499 (1964)

    1964

  3. [11]

    Gea-Banacloche, Two-photon absorption of nonclassical light, Phys

    J. Gea-Banacloche, Two-photon absorption of nonclassical light, Phys. Rev. Lett.62, 1603 (1989)

    1989

  4. [12]

    Javanainen and P

    J. Javanainen and P. L. Gould, Linear intensity dependence of a two-photon transition rate, Phys. Rev. A41, 5088 (1990)

    1990

  5. [13]

    Eshun, O

    A. Eshun, O. Varnavski, J. P. Villabona-Monsalve, R. K. Burdick, and T. Goodson, Entangled photon spectroscopy, Accounts of Chemical Research55, 991 (2022)

    2022

  6. [14]

    K. E. Dorfman, F. Schlawin, and S. Mukamel, Nonlinear optical signals and spectroscopy with quantum light, Rev. Mod. Phys. 88, 045008 (2016)

    2016

  7. [15]

    Schlawin, K

    F. Schlawin, K. E. Dorfman, and S. Mukamel, Entangled two-photon absorption spectroscopy, Accounts of Chemical Research51, 2207 (2018)

    2018

  8. [16]

    Y . Shen, A. J. Shuhendler, D. Ye, J.-J. Xu, and H.-Y . Chen, Two-photon excitation nanoparticles for photodynamic therapy, Chem. Soc. Rev.45, 6725 (2016)

    2016

  9. [17]

    M. Atif, P. Dyer, T. Paget, H. Snelling, and M. Stringer, Two-photon excitation studies of m-thpc photosensitizer and photodynamic activity in an epithelial cell line, Photodiagnosis and Photodynamic Therapy4, 106 (2007)

    2007

  10. [18]

    Srivastava and C

    P. Srivastava and C. G. Elles, A single-shot technique for measuring broadband two-photon absorption spectra in solution, Analytical Chemistry96, 11121 (2024)

    2024

  11. [19]

    Srivastava, D

    P. Srivastava, D. A. Stierwalt, and C. G. Elles, Broadband two-photon absorption spectroscopy with stimulated raman scattering as an internal standard, Analytical Chemistry95, 13227 (2023)

    2023

  12. [20]

    Donegan, Two-photon absorption speeds optical switching, Lightw

    J. Donegan, Two-photon absorption speeds optical switching, Lightw. Europe1, 31 (2002)

    2002

  13. [21]

    P. J. Maguire, L. P. Barry, T. Krug, W. H. Guo, J. O’Dowd, M. Lynch, A. L. Bradley, J. F. Donegan, and H. Folliot, Optical signal processing via two-photon absorption in a semiconductor microcavity for the next generation of high-speed optical communications network, J. Lightw...

    2006

  14. [22]

    D. W. Piston, Imaging living cells and tissues by two-photon excitation microscopy, Trends in Cell Biology9, 66 (1999)

    1999

  15. [23]

    Oheim, D

    M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches, Advanced Drug Delivery Reviews58, 788 (2006), multi-Photon Imaging: Diseases and Therapies

    2006

  16. [24]

    Olesiak-Banska, M

    J. Olesiak-Banska, M. Waszkielewicz, P. Obstarczyk, and M. Samoc, Two-photon absorption and photoluminescence of colloidal gold nanoparticles and nanoclusters, Chem. Soc. Rev. 48, 4087 (2019)

    2019

  17. [25]

    H.-B. Sun, T. Kawakami, Y . Xu, J.-Y . Ye, S. Matuso, H. Misawa, M. Miwa, and R. Kaneko, Real three-dimensional microstructures fabricated by photopolymerization of resins through two-photon absorption, Opt. Lett.25, 1110 (2000)

    2000

  18. [26]

    Panahiyan, C

    S. Panahiyan, C. S. Mu ˜noz, M. V . Chekhova, and F. Schlawin, Two-photon-absorption measurements in the presence of single-photon losses, Phys. Rev. A106, 043706 (2022)

    2022

  19. [27]

    Panahiyan, C

    S. Panahiyan, C. S. Mu ˜noz, M. V . Chekhova, and F. Schlawin, 10 Nonlinear interferometry for quantum-enhanced measurements of multiphoton absorption, Phys. Rev. Lett.130, 203604 (2023)

    2023

  20. [28]

    Landes, B

    T. Landes, B. J. Smith, and M. G. Raymer, Limitations in fluorescence-detected entangled two-photon-absorption experiments: Exploring the low- to high-gain squeezing regimes, Phys. Rev. A110, 033708 (2024)

    2024

  21. [29]

    Pandya, P

    R. Pandya, P. Cameron, C. Verni `ere, B. Courme, S. Ithurria, A. Chin, E. Lhuillier, and H. Defienne, Towards robust detection of entangled two-photon absorption (2024), arXiv:2410.06199 [quant-ph]

    2024 arXiv

  22. [30]

    Lerch and A

    S. Lerch and A. Stefanov, Experimental requirements for entangled two-photon spectroscopy, The Journal of Chemical Physics155, 064201 (2021)

    2021

  23. [31]

    Boitier and et al., Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor, Nature Communications2, 425 (2011)

    F. Boitier and et al., Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor, Nature Communications2, 425 (2011)

    2011

  24. [32]

    Dayan, A

    B. Dayan, A. Pe’er, A. A. Friesem, and Y . Silberberg, Nonlinear interactions with an ultrahigh flux of broadband entangled photons, Phys. Rev. Lett.94, 043602 (2005)

    2005

  25. [33]

    Dayan, A

    B. Dayan, A. Pe’er, A. A. Friesem, and Y . Silberberg, Two photon absorption and coherent control with broadband down- converted light, Phys. Rev. Lett.93, 023005 (2004)

    2004

  26. [34]

    S ´anchez Mu ˜noz, G

    C. S ´anchez Mu ˜noz, G. Frascella, and F. Schlawin, Quantum metrology of two-photon absorption, Phys. Rev. Research3, 033250 (2021)

    2021

  27. [35]

    K. Y . Spasibko, D. A. Kopylov, V . L. Krutyanskiy, T. V . Murzina, G. Leuchs, and M. V . Chekhova, Multiphoton effects enhanced due to ultrafast photon-number fluctuations, Phys. Rev. Lett.119, 223603 (2017)

    2017

  28. [36]

    Z. Yang, P. Saurabh, F. Schlawin, S. Mukamel, and K. E. Dorfman, Multidimensional four-wave-mixing spectroscopy with squeezed light,Applied Physics Letters, Applied Physics Letters116, 244001 (2020)

    2020

  29. [37]

    Zhang, T

    Z. Zhang, T. Peng, X. Nie, G. S. Agarwal, and M. O. Scully, Entangled photons enabled time-frequency-resolved coherent raman spectroscopy and applications to electronic coherences at femtosecond scale, Light: Science & Applications11, 274 (2022)

    2022

  30. [38]

    A. Sone, Q. Zhuang, C. Li, Y .-X. Liu, and P. Cappellaro, Nonclassical correlations for quantum metrology in thermal equilibrium, Phys. Rev. A99, 052318 (2019)

    2019

  31. [39]

    A. Khan, F. Albarelli, and A. Datta, Does entanglement enhance single-molecule pulsed biphoton spectroscopy?, Quantum Science and Technology9, 035004 (2024)

    2024

  32. [40]

    Schaffrath, D

    S. Schaffrath, D. Derr, M. Gr ¨afe, and E. Giese, Quantum imaging beyond the standard-quantum limit and phase distillation, New Journal of Physics26, 023018 (2024)

    2024

  33. [41]

    Schlawin, Two-photon absorption cross sections of pulsed entangled beams, The Journal of Chemical Physics160, 144117 (2024)

    F. Schlawin, Two-photon absorption cross sections of pulsed entangled beams, The Journal of Chemical Physics160, 144117 (2024)

    2024

  34. [42]

    Karsa, R

    A. Karsa, R. Nair, A. Chia, K.-G. Lee, and C. Lee, Optimal quantum metrology of two-photon absorption, Quantum Science and Technology9, 035042 (2024)

    2024

  35. [43]

    Krsti ´c, T

    A. Krsti ´c, T. B. G ¨abler, N. Jain, P. Then, V . F. Gili, S. Saravi, F. Setzpfandt, C. Eggeling, and M. Gr¨afe, Enhancing entangled two-photon absorption of nile red via temperature-controlled spdc (2024), arXiv:2406.01075 [quant-ph]

    2024 arXiv

  36. [44]

    Bondani, A

    M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light, Phys. Rev. A76, 013833 (2007)

    2007

  37. [45]

    T. S. Iskhakov, V . C. Usenko, U. L. Andersen, R. Filip, M. V . Chekhova, and G. Leuchs, Heralded source of bright multi- mode mesoscopic sub-poissonian light, Opt. Lett.41, 2149 (2016)

    2016

  38. [46]

    C. C. Gerry and P. L. Knight,Introductory quantum optics (Cambridge university press, 2023)

    2023

  39. [47]

    Loudon,The Quantum Theory of Light, Oxford science publications (Clarendon Press, 1979)

    R. Loudon,The Quantum Theory of Light, Oxford science publications (Clarendon Press, 1979)

    1979

  40. [48]

    Barnett and P

    S. Barnett and P. Radmore,Methods in Theoretical Quantum Optics(Oxford University Press, 2002)

    2002

  41. [50]

    G. S. Agarwal, Field-correlation effects in multiphoton absorption processes, Phys. Rev. A1, 1445 (1970)

    1970

  42. [51]

    M. S. Zubairy and J. J. Yeh, Photon statistics in multiphoton absorption and emission processes, Phys. Rev. A21, 1624 (1980)

    1980

  43. [52]

    P. D. Drummond and Z. Ficek,Quantum Squeezing(Springer Berlin, Heidelberg, 2004)

    2004

  44. [53]

    R. W. Boyd,Nonlinear Optics, Third Edition, 3rd ed. (Academic Press, Inc., USA, 2008)

    2008

  45. [54]

    Pezz `e, A

    L. Pezz `e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys.90, 035005 (2018)

    2018

  46. [55]

    C. T. Lee, Nonclassical photon statistics of two-mode squeezed states, Phys. Rev. A42, 1608 (1990)

    1990

  47. [56]

    Lemonde, N

    M.-A. Lemonde, N. Didier, and A. A. Clerk, Antibunching and unconventional photon blockade with Gaussian squeezed states, Phys. Rev. A90, 063824 (2014)

    2014

  48. [57]

    J. R. Taylor and W. Thompson,An introduction to error analysis: the study of uncertainties in physical measurements, V ol. 2 (Springer, 1982). 11 Appendix A: Error propagation Let, ˆObe a function ofϵ, its Taylor expansion can be written as ⟨ ˆO⟩=⟨ ˆO⟩ ϵ=0 + ∂⟨ ˆO⟩ ∂ϵ ϵ=0 ϵ.(A...

    1982

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.