Two-photon correlations and HOM visibility from an imperfect single-photon source

Anders S. S{\o}rensen; Eva M. Gonz\'alez-Ruiz; Johannes Bjerlin; Oliver August Dall'Alba Sandberg

REVIEW 3 major objections 4 minor 45 references

Two-photon correlations and HOM visibility from an imperfect single-photon source

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper shows that the commonly used correction factor F = (1 - V)/g^(2) = 2 for relating HOM visibility to two-photon emission is not universal; for a good single-photon source it can take any value between 1 and 3 depending on the…

desk verdict A useful paper with a clear message—g(2) alone doesn't fix HOM visibility—but the printed proof of the central F∈[1,3] bound has a factor-of-four error that must be corrected. read the letter →

arxiv 2412.06679 v1 pith:2HLONM5L submitted 2024-12-09 quant-ph

Eva M. González-Ruiz , Johannes Bjerlin , Oliver August Dall'Alba Sandberg , Anders S. S{o}rensen This is my paper · ORCID

classification quant-ph MSC 81V8081P15 PACS 42.50.Ar42.50.Ex03.67.-a

keywords single-photonsourceHong-Ou-Mandelvisibilitysecond-ordercorrelationg(2)laserleakagewavefunctionansatzfrequencyfilteringphotonindistinguishability

topics The Measurement Problem

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

This paper studies a realistically imperfect single-photon source: a resonantly driven emitter whose excitation laser leaks into the detection path. It shows that the pulse duration and the phase of the leaked field strongly shape both the two-photon component g^(2) and the Hong-Ou-Mandel visibility V, so that leakage cannot be treated as an incoherent background. Its central claim is that the standard relation V = 1 - 2g^(2), used to correct HOM measurements for multi-photon contamination, is unreliable: for a good source (g^(2) << 1) the correction factor F = (1 - V)/g^(2) can be anywhere from 1 to 3, depending on how many photons of the two-photon component sit in modes different from the single photon. A sympathetic reader should care because this means inferred 'intrinsic' indistinguishability from a single HOM measurement is not a well-defined quantity, and sources with the same g^(2) and V can have different physical quality.

What carries the argument

The central object is a two-photon-truncated wavefunction ansatz for a single emitter coupled to a waveguide, solved after a displacement transformation that turns the coherent driving laser into a classical field. The output field operator becomes a sum of the emitter-scattered field and a leaked coherent component with complex amplitude x = |x|$e^{{-i theta}}$; from this, the paper computes the first- and second-order correlation functions G^(1) and G^(2), including the effect of a Lorentzian frequency filter. The argument for the headline claim is carried by a density-matrix decomposition of the output into zero-, one-, and multi-photon components (Appendix D), which yields the bound F in [1,3] and the formula F = 1 + P1<n_{!=psi}>_{n>1}.

What would settle it

Measure V and g^(2) for a single-photon source whose two-photon component is deliberately made indistinguishable from the single photon (e.g., by placing a narrow spectral filter that erases which-photon information) and for a source whose two-photon component is made distinguishable (e.g., by adding a strong, unmodulated laser background). If the paper is right, the first configuration gives F approx 1 and the second F approx 3 (with g^(2) << 1 in both cases); finding F = 2 in both would falsify the claim.

Watch

Extended reading notes

Core claim

The paper's central discovery is that the relation between a single-photon source's HOM visibility V and its two-photon correlation g^(2) is not fixed. Writing V = V1(1 - F g^(2)), where V1 is the visibility of the single-photon component alone, the factor F can attain any value in the interval [1,3] for a good single-photon source (g^(2) << 1), depending on the precise nature of the multiphoton component. Specifically, F = 1 + P1<n_{!=psi}>_{n>1}, i.e., it counts how many photons of the two-photon part occupy modes other than the single-photon mode psi: F = 1 if both extra photons share the signal mode, F = 2 if one is distinguishable, and F = 3 if both are distinguishable. The commonly used value F = 2 is therefore only one special case, and the standard experimental procedure of extracting intrinsic indistinguishability from V and g^(2) is problematic and should not be used; moreover, because systems such as frequency filters modify the single- and two-photon components differently, the decomposition depends on the point where the source is defined, so even the notion of an intrinsic visibility is ambiguous without full state tomography.

Load-bearing premise

The leaked drive is treated as a single coherent field with a fixed complex amplitude x = |x|$e^{{-i theta}}$ and a phase $\theta$ that is stable over the measurement; the interference effects that produce the striking results (e.g., $\theta$ = 0 improving purity when leakage is increased) depend on this definite phase relation, and a true average over shot-to-shot phase drift could wash them out.

Editorial extensions

If this is right

The excitation pulse length that minimizes g^(2) is not universal: it grows roughly linearly with the leakage fraction |x| (sigma_opt proportional to |x|/Gamma), and the minimal achievable impurity scales roughly with |x|, except under destructive-interference conditions.
Laser leakage can interfere constructively or destructively with the emitter field: for phase theta = 0, increasing the leakage can actually lower the two-photon component and improve HOM visibility in some pulse-length windows, while for theta = pi it always degrades them.
Post-emission spectral filtering substantially reduces g^(2) in the short-pulse regime because the leaked field is spectrally broader than the emitter emission, at the cost of losing some of the single-photon signal.
Because F ranges from 1 to 3, a measured (V, g^(2)) pair does not identify a unique intrinsic visibility; extracting V1 requires knowing the mode structure of the multiphoton component and specifying the point at which the source is defined (e.g., before or after a filter).
Full quantum state tomography, rather than a single HOM measurement plus g^(2), is needed to fully characterize the emitted state.

Reading between the lines

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

The bound F in [1,3] could be used as a diagnostic: measuring F on a given source tells whether its multi-photon component is dominated by photons in the signal mode (F near 1, characteristic of emitter re-excitation) or by distinguishable photons (F near 3, characteristic of unfiltered laser leakage).
For sources where the scattering phase drifts between shots (e.g., leakage outside the waveguide), the true phase-averaged behavior may differ from the theta = pi/2 approximation used here; comparing stable-phase and drifting-phase sources of the same emitter could test how much of the interference effects survive averaging.
The pulse-length dependence of F provides a testable signature: near the g^(2) minimum, F should spike for theta = 0 as destructive interference removes the same-mode component of the two-photon field; a similar measurement on a source without a definite leakage phase should lack this spike.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, the paper has a real and useful message: for a good single-photon source, the factor F=(1−V)/g(2) is not fixed at 2 but can range between 1 and 3 depending on where the extra photons sit in mode space, so the standard correction used to extract intrinsic HOM visibility is not reliable. Second, the printed proof of that bound has a factor-of-four error in Appendix D that needs fixing before I'd trust the claim as published.

What's new: the authors take the wavefunction-ansatz approach from Ref. [31] and the V=V1(1−Fg2) framework from Ref. [42] and apply them systematically to a resonantly driven emitter with laser leakage, a complex scattering phase, and spectral filtering. That gives concrete predictions: non-monotonic g(2) versus pulse duration, phase-dependent interference (θ=0 can even make a larger leakage improve purity), and practical rules for choosing pulse length and filter width. The input-output and master-equation steps are clean, and the numerical cross-check against quantum regression for selected parameters is a nice touch.

The soft spots are real but mostly fixable. The stress-test note is correct: Eq. (D11) as printed reads with a P1/2 prefactor, which for a two-photon-dominated multiphoton component gives F=1+P1⟨n_{≠ψ}⟩/4 instead of Eq. (36)'s F=1+P1⟨n_{≠ψ}⟩. The factor is off by four, and the quoted inequality n(n−1)≥n only yields F≤1.5 from that printed formula. The correct prefactor should be 2P1, which does reproduce Eq. (36) and the [1,3] bound. This looks like a typo rather than a conceptual mistake, but it's in the analytic core of the strongest claim. Second, the filtered-case F values in Fig. 8 are computed with Eq. (37) even though the filter makes V1<1; the authors flag this and note F becomes unbounded, but it does make those curves hard to interpret. Third, the two-photon truncation limits the long-pulse predictions, and the θ=π/2 approximation for a drifting phase is not a true average, so the dramatic θ=0 interference effects require a stable phase. Those are caveats, not fatal.

Who is this for: people characterizing quantum-dot or other emitter-based single-photon sources, and anyone who uses the F=2 correction to extract indistinguishability. They should read it carefully after the Appendix D error is fixed.

My recommendation: send it to peer review. The main claim is important and likely right, but the referee needs to check Appendix D and ask for a corrected derivation and a clearer treatment of the filtered F.

Referee Report

3 major / 4 minor

Summary. González-Ruiz et al. study a resonantly driven two-level emitter coupled to a chiral waveguide, with a coherent drive that can leak into the detection path and is described by a complex leakage factor x = |x|e^{-iθ}. Using a wavefunction ansatz truncated at two emitted photons, they compute the integrated second-order correlation g(2), the Hong-Ou-Mandel visibility V, and the effect of Lorentzian post-emission filtering. The central message is that the factor F = (1−V)/g(2), often taken as 2 when correcting HOM visibility for multi-photon emission, can take any value in [1,3] for a good single-photon source depending on the modal structure of the multiphoton component; hence the standard correction procedure is unreliable. The authors also propose a continuous-wave measurement to extract |x| and θ, and show that pulse duration, leakage phase, and filtering have strong, sometimes counterintuitive effects on source purity and visibility.

Significance. If the claims are correct, this is a useful contribution to single-photon-source characterization: it identifies a source-dependent relation between g(2) and HOM visibility and gives a concrete mechanism—the modal overlap between the single-photon component and the additional photons—behind deviations from the common F = 2 rule. The paper contains detailed analytical expressions, a wavefunction-ansatz implementation, a quantum-regression cross-check of the Lorentzian filter results for selected parameters, and a practical fitting procedure for leakage parameters. These strengths make the work potentially publishable, but the analytic proof of the headline F ∈ [1,3] result is not internally consistent as printed.

major comments (3)

[Appendix D, Eqs. (D8)–(D11)] The printed prefactor in Eq. (D11) is inconsistent with Eq. (36) and with the F = 1,2,3 examples in Sec. VI. Substituting the density-matrix decomposition into Eq. (D8) and eliminating P_{n>1} with Eq. (D9) gives F = 1 + 2P1 Σ_l w_l ⟨n̂_{≠l}⟩_{n>1}/⟨n̂(n̂−1)⟩_{n>1}, not F = 1 + (P1/2) Σ_l w_l ⟨n̂_{≠l}⟩_{n>1}/⟨n̂(n̂−1)⟩_{n>1}. With the printed prefactor, the two-photon case would give F = 1 + P1⟨n̂_{≠ψ}⟩_{n>1}/4, contradicting Eq. (36), and the inequality quoted after Eq. (D11) would only bound F ≤ 1.5 rather than F ≤ 3. The corrected prefactor reproduces Eq. (36) and the stated bound. Because this appendix is the analytic basis for the central claim in Sec. VII, the proof must be corrected before publication.
[Section VI, Eq. (37), and Fig. 8] For filtered fields the single-photon component is no longer pure, so V1 < 1 and the relation in Eq. (35) does not apply, yet the filtered values of F are still evaluated from F = (1−V)/g(2). The authors acknowledge the caveat, but the filtered curves in Fig. 8 and the statements that filtering typically decreases F are quantitative claims based on this extrapolation. The Appendix D derivation cannot bound these values, as the text itself notes. Please either compute V1 for the filtered case using the higher-order correlation method of Ref. [42], or present the filtered F curves explicitly as a heuristic that should not be assigned the interpretation of Eq. (35).
[Section II, Eqs. (10)–(11), and Figs. 3–8] The model assumes a leakage field with a time-independent complex amplitude x = |x|e^{-iθ} and a stable phase θ. The text states that for scattering outside the waveguide the phase can drift from shot to shot, and that the θ = π/2 curves are only an approximate average. Since several striking effects (θ = 0 lowering g(2), leakage improving purity, and the sharply peaked F near the g(2) minimum) rely on a definite phase relation between the leaked field and the emitter field, the quantitative predictions are not yet established for drifting-phase sources. Please provide phase-averaged results for representative parameters or explicitly restrict the conclusions to phase-stable leakage scenarios.

minor comments (4)

[Appendix D, Eq. (D12)] In the definition of B, the sum is written with w_1 rather than w_l; this appears to be a typo.
[Appendix B, Eq. (B1)] In the interference term of G(2), the factor φ*_2(t, t−t2, t−t1) is repeated twice; presumably one of the two occurrences should have the time arguments swapped.
[Section VI, final paragraph] The sentence 'it is not possibly to fully characterize the state' should read 'it is not possible to fully characterize the state.'
[Section VI, around Eq. (36)] The notation ⟨n̂_{≠ψ}⟩_{n>1} should explicitly state the decomposition point at which P1 and the photon numbers are evaluated; the text discusses this point only later, and the distinction is important for interpreting the examples.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the F-bounds and V-g(2) relations are derived forward from the stated model.

full rationale

I find no circularity. The paper computes g(2), HOM visibility V, and the factor F = (1-V)/g(2) forward from a stated Hamiltonian, a two-photon wavefunction ansatz, and specified inputs (leakage magnitude |x|, phase theta, pulse width sigma, filter width gamma). No target quantity is used as an input, and no parameter is fitted to the predicted g(2) or V: the leakage parameters are calibrated from the separate CW intensity expression, Eq. (15), and then used to predict the pulsed correlation functions. The central claim about F in [1,3] is derived in Appendix D from a density-matrix decomposition and the inequality 0 <= <n_{!=l}>_{n>1} <= <n>_{n>1} <= <n(n-1)>_{n>1}, not assumed. The self-citations to Refs. [31] and [42] are not load-bearing: the wavefunction ansatz is re-derived and summarized in Sec. III and Appendix A and cross-checked in Appendix E, while Ref. [42] is only cited for consistency of the form of Eq. (35). I note, as a correctness rather than circularity concern, that the printed Eq. (D11) contains an apparent prefactor inconsistency relative to Eq. (36) and the stated bound; correcting or clarifying this would strengthen the proof, but it does not make the derivation circular.

Assumptions & free parameters 6 free parameters · 8 assumptions · 0 invented entities

The central predictions depend on the two-photon truncation, the single-complex-parameter leakage model, the assumption of a stable scattering phase, and the low-efficiency HOM detection limit. These are all stated in the text, and the first and last are acknowledged limitations. No free parameters are fitted to data; they are inputs scanned to map the model behavior.

free parameters (6)

|x|, leakage amplitude = Varied: 0.02, 0.1, 0.2, 0.5
Input parameter controlling leaked coherent field strength; central to all figures; experimental determination suggested via Eq. (15).
θ, scattering phase = 0, π/2, π
Input parameter controlling interference between leaked field and emitter emission; central to the θ=0 results.
σ, Gaussian pulse width = Scanned across Γσ from about 0.01 to 10
Input parameter; causes non-monotonic g2 and determines the optimal operating point.
γ, Lorentzian filter width parameter = γ = 1.66Γ in most figures; varied in Fig. 5
Input parameter for the Lorentzian filter; affects short-pulse g2 and photon number.
Γ_d, pure dephasing rate = Set to 0 in wavefunction simulations
Dephasing is included in the master equation intensity result, but excluded from g2/V/F numerics so that V1=1.
A, efficiency factor = Set to 1 in Fig. 2
Accounts for coupling and detection efficiencies in the CW intensity ratio; not used elsewhere.

assumptions (8)

domain assumption The emitter is a two-level system with spontaneous emission rate Γ and optional pure dephasing Γ_d.
Standard model for a quantum dot; used in the Hamiltonian Eq. (4) and master equation Eqs. (12)-(13).
domain assumption The emitter sits in a chiral one-dimensional waveguide with linear dispersion and frequency-independent coupling G_k ≈ G.
Justifies the input-output relation Eq. (11); paper argues results depend only on the ratio of emitted to leaked field, so geometry is not essential.
ad hoc to paper Laser leakage is fully described by a time-independent complex number x = |x|e^{-iθ} that is independent of the incident light.
Introduced in Sec. II after Eq. (10) to model scattering of the drive into the waveguide; the physical mechanism is left unspecified.
domain assumption Photon emission is truncated at two photons: the wavefunction ansatz Eq. (17) contains no three-photon amplitudes.
Valid for weak driving or short pulses; the paper acknowledges in Sec. IV and Fig. 3 that it fails for σ ~ 1/Γ and g2 ≳ 0.5.
standard math The excitation pulse is a Gaussian π-pulse with ∫Ω(t)dt = π.
Pulse shape and normalization chosen in Sec. IV, Eq. (20); gives a perfect inversion in the short-pulse limit.
domain assumption HOM visibility is computed in the low-efficiency detection limit, so Pcc is evaluated with two-point correlations and three-or-more-photon coincidences are neglected.
Stated in Sec. VI before Eq. (28); high-efficiency sources need additional corrections.
domain assumption A Lorentzian spectral filter with transmission T(ω-ω_c) = γ/(i(ω-ω_c)-γ) models a filter cavity.
Used in Sec. V, Eq. (27); equivalence with a cavity quantum regression calculation verified only for some parameters (Appendix E).
ad hoc to paper For filtered fields, the factor F is still extracted from F = (1-V)/g2 although V1 < 1 after filtering.
Acknowledged in Sec. VI; this F is not the same quantity as the derived F in Eq. (36), and the paper notes it can become unbounded.

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Cite this review

Pith. "Pith review of Two-photon correlations and HOM visibility from an imperfect single-photon source." pith.science (2026). https://pith.science/paper/2HLONM5L

@misc{pith2026241206679,
  author       = {Pith},
  title        = {Pith review of: Two-photon correlations and HOM visibility from an imperfect single-photon source},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2HLONM5L}},
  note         = {Machine review of arXiv:2412.06679}
}

read the original abstract

We study the single photon purity of a resonantly driven single-photon source in the realistic scenario where the excitation laser can leak into the detection path. We find that the duration of the excitation pulse strongly influences the quality of the single-photon source. We calculate the influence of this on the effective parameters describing the most relevant properties, including the two-photon component and Hong-Ou-Mandel (HOM) visibility. Furthermore, we analyze how these properties can be strongly affected by frequency filtering of the outgoing field. Our results highlight that the relation between the two-photon component of the emission and the HOM visibility is more complicated than typically assumed in the literature, and depends on the specific details of the source.

Figures

Figures reproduced from arXiv: 2412.06679 by the authors.

**Figure 2.** FIG. 2. Input-output intensity ratio [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Second-order two-photon correlation, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4. Minimum two-photon contribution of the single [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. Two-photon contribution and filtered output photon [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 7.** Figure 7: FIG. 7. Relation between HOM visibility [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 6.** Figure 6: FIG. 6. HOM visibility of a single photon source subject to [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 8.** Figure 8: FIG. 8. Ratio between lack of visibility and multi-photon [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 36 canonical work pages

[31]

Heuck, K

M. Heuck, K. Jacobs, and D. R. Englund, Physical Re- view Letters 124, 160501 (2020)

work page 2020
[42]

Sekatski, E

P. Sekatski, E. Oudot, P. Caspar, R. Thew, and N. San- gouard, Quantum 6, 875 (2022)

work page 2022
[1]

Thomas and P

S. Thomas and P. Senellart, Nature Nanotechnology 16, 367 (2021)

work page 2021
[2]

Knill, R

E. Knill, R. Laflamme, and G. J. Milburn, nature 409, 46 (2001)

2001
[3]

J. L. O’brien, Science 318, 1567 (2007)

2007
[4]

Aspuru-Guzik and P

A. Aspuru-Guzik and P. Walther, Nature physics 8, 285 (2012)

work page 2012
[5]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001)

2001
[6]

Sangouard, C

N. Sangouard, C. Simon, H. De Riedmatten, and N. Gisin, Reviews of Modern Physics 83, 33 (2011)

2011

Show all 45 references

[7]

H. J. Kimble, Nature 453, 1023 (2008)

2008
[8]

N. Tomm, A. Javadi, N. O. Antoniadis, D. Najer, M. C. L¨ obl, A. R. Korsch, R. Schott, S. R. Valentin, A. D. Wieck, A. Ludwig, and R. J. Warburton, Nature Nan- otechnology 16, 399 (2021)

2021
[9]

Aharonovich, D

I. Aharonovich, D. Englund, and M. Toth, Nature Pho- tonics 10, 631 (2016)

2016
[10]

Senellart, G

P. Senellart, G. Solomon, and A. White, Nature nan- otechnology 12, 1026 (2017)

2017
[11]

Wang, Z.-C

H. Wang, Z.-C. Duan, Y.-H. Li, S. Chen, J.-P. Li, Y.- M. He, M.-C. Chen, Y. He, X. Ding, C.-Z. Peng, et al., Physical Review Letters 116, 213601 (2016)

2016
[12]

Arakawa and M

Y. Arakawa and M. J. Holmes, Applied Physics Reviews 7, 021309 (2020)

2020
[13]

Ollivier, I

H. Ollivier, I. Maillette de Buy Wenniger, S. Thomas, S. C. Wein, A. Harouri, G. Coppola, P. Hilaire, C. Millet, A. Lema ˆ ıtre, I. Sagnes, O. Krebs, L. Lanco, J. C. Loredo, C. Ant´ on, N. Somaschi, and P. Senellart, ACS Photonics 7, 1050 (2020)

2020
[14]

Laferri` ere, E

P. Laferri` ere, E. Yeung, I. Miron, D. B. Northeast, S. Haf- fouz, J. Lapointe, M. Korkusinski, P. J. Poole, R. L. Williams, and D. Dalacu, Scientific Reports 12, 6376 (2022)

2022
[15]

Unfortunately, the often challenging experimental real- ization of single-photons sources deviate from generating identical and pure single photons on demand

and fault-tolerant quantum computing [20]. Unfortunately, the often challenging experimental real- ization of single-photons sources deviate from generating identical and pure single photons on demand. To improve on these properties, it is essential to have a thorough understa...

2024 arXiv
[16]

Lu and J.-W

C.-Y. Lu and J.-W. Pan, Nature Nanotechnology 16, 1294 (2021)

2021
[17]

Valeri, P

M. Valeri, P. Barigelli, B. Polacchi, G. Rodari, G. D. San- tis, T. Giordani, G. Carvacho, N. Spagnolo, and F. Sciar- rino, Quantum Science and Technology9, 025002 (2024)

2024
[18]

R. Uppu, F. T. Pedersen, Y. Wang, C. T. Olesen, C. Pa- pon, X. Zhou, L. Midolo, S. Scholz, A. D. Wieck, A. Lud- wig, et al., Science advances 6, eabc8268 (2020)

2020
[19]

E. M. Gonz´ alez-Ruiz, S. K. Das, P. Lodahl, and A. S. Sørensen, Physical Review A 106, 012222 (2022)

2022
[20]

Device Inde- pendent Quantum Key Distribution with realistic single- photon source implementations,

E. M. Gonz´ alez-Ruiz, J. Rivera-Dean, M. F. B. Cenni, A. S. Sørensen, A. Ac ´ ın, and E. Oudot, “Device Inde- pendent Quantum Key Distribution with realistic single- photon source implementations,” (2022)

2022
[21]

Maring, A

N. Maring, A. Fyrillas, M. Pont, E. Ivanov, P. Stepanov, N. Margaria, W. Hease, A. Pishchagin, A. Lema ˆ ıtre, I. Sagnes, T. H. Au, S. Boissier, E. Bertasi, A. Baert, M. Valdivia, M. Billard, O. Acar, A. Brieussel, R. Mezher, S. C. Wein, A. Salavrakos, P. Sinnott, D. A. Fioret...

2024
[22]

Hong, Z.-Y

C.-K. Hong, Z.-Y. Ou, and L. Mandel, Physical review letters 59, 2044 (1987)

1987
[23]

Somaschi, V

N. Somaschi, V. Giesz, L. De Santis, JC. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, et al., Nature Photonics 10, 340 (2016)

2016
[24]

Wang, Y.-M

H. Wang, Y.-M. He, T.-H. Chung, H. Hu, Y. Yu, S. Chen, X. Ding, M.-C. Chen, J. Qin, X. Yang, et al., Nature Photonics 13, 770 (2019)

2019
[25]

Ollivier, SE

H. Ollivier, SE. Thomas, SC. Wein, I. M. de Buy Wen- niger, N. Coste, JC. Loredo, N. Somaschi, A. Harouri, A. Lemaitre, I. Sagnes, et al., Physical Review Letters 126, 063602 (2021)

2021
[26]

J. C. Loredo, C. Ant´ on, B. Reznychenko, P. Hi- laire, A. Harouri, C. Millet, H. Ollivier, N. Somaschi, L. De Santis, A. Lema ˆ ıtre, I. Sagnes, L. Lanco, A. Auff` eves, O. Krebs, and P. Senellart, Nature Photon- ics 13, 803 (2019), publisher: Nature Publishing Group

2019
[27]

I. M. d. B. Wenniger, S. C. Wein, D. Fioretto, S. E. Thomas, C. Ant´ on-Solanas, A. Lema ˆ ıtre, I. Sagnes, A. Harouri, N. Belabas, N. Somaschi, P. Hilaire, J. Senel- lart, and P. Senellart, Optica Quantum 2, 404 (2024), publisher: Optica Publishing Group

2024
[28]

Trivedi, K

R. Trivedi, K. A. Fischer, J. Vuˇ ckovi´ c, and K. M¨ uller, Advanced Quantum Technologies 3, 1900007 (2020)

2020
[29]

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, 14 C. Dory, J. J. Finley, J. Vuˇ ckovi´ c, and K. M¨ uller, Nature Physics 13, 649 (2017)

2017
[30]

Trivedi, K

R. Trivedi, K. Fischer, S. Xu, S. Fan, and J. Vuckovic, Physical Review B 98, 144112 (2018)

2018
[32]

S. Das, L. Zhai, M. ˇCepulskovskis, A. Javadi, S. Mah- moodian, P. Lodahl, and A. S. Sørensen, arXiv preprint arXiv:1912.08303 (2019), arxiv:1912.08303

2019 arXiv
[33]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature physics 3, 807 (2007)

2007
[34]

Shen and S

J.-T. Shen and S. Fan, Physical Review A 76, 062709 (2007)

2007
[35]

Witthaut and A

D. Witthaut and A. S. Sørensen, New Journal of Physics 12, 043052 (2010)

2010
[36]

B. R. Mollow, Physical Review A 12, 1919 (1975)

1975
[37]

˘Cepulkovskis, Nonlinear photon interactions in waveguides, Master’s thesis, Niels Bohr Institute, Uni- versity of Copenhagen (2017)

M. ˘Cepulkovskis, Nonlinear photon interactions in waveguides, Master’s thesis, Niels Bohr Institute, Uni- versity of Copenhagen (2017)

2017
[38]

L. Zhai, Characterisation of Single-Photon sources: fromPulse- Width and Power Dependence of Single- Photon Purity to Effect of Spectral Filtering ,Master’s thesis, Niels Bohr Institute, University of Copenhagen (2017)

2017
[39]

Kiraz, M

A. Kiraz, M. Atat¨ ure, and A. Imamo˘ glu, Physical Re- view A 69, 032305 (2004)

2004
[40]

Giesz, N

V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaitre, et al., Nature communications 7, 1 (2016)

2016
[41]

C. W. Gardiner and M. J. Collett, Physical Review A 31, 3761 (1985)

1985
[43]

E. R. Hellebek, K. Mølmer, and A. S. Sørensen, Phys. Rev. A 110, 023728 (2024). 15 Appendix A: Master equation and equations of motion In this section, we first explicitly derive the stationary state ˆ ρ. From Eqs. (12) and (13) we obtain the following set of differential equa...

2024
[44]

G(2)(t1, t2) terms Evaluating G(2)(t1, t2) with the output operator aout gives several terms, which we write collected by powers of the leaked field x. I. κ2 4 Tr a(t2)a(t1)ρa†(t1)a†(t2) II. κ3/2α(t1)x∗ 2 √ 2 Tr a(t2)a(t1)ρa†(t2) + H.c κ3/2α(t2)x∗ 2 √ 2 Tr a(t2)a(t1)ρa†(t1) + ...
[45]

κ 2 Tr a(t1)ρa†(t2) II

G(1)(t1, t2) and |G(1)(t1, t2)|2 Evaluating G(1)(t1, t2) with the output operators yields, in powers of x I. κ 2 Tr a(t1)ρa†(t2) II. x √κ√ 2 α(t1)Tr ρa†(t2) + H.c. III. |x|2α(t1)α(t2). (E11) To compute the visibility, we require the squared modulus |G(1)(t1, t2)|2 = Tr a(t1)ρa...

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [31]

Heuck, K

M. Heuck, K. Jacobs, and D. R. Englund, Physical Re- view Letters 124, 160501 (2020)

work page 2020

[2] [42]

Sekatski, E

P. Sekatski, E. Oudot, P. Caspar, R. Thew, and N. San- gouard, Quantum 6, 875 (2022)

work page 2022

[3] [1]

Thomas and P

S. Thomas and P. Senellart, Nature Nanotechnology 16, 367 (2021)

work page 2021

[4] [2]

Knill, R

E. Knill, R. Laflamme, and G. J. Milburn, nature 409, 46 (2001)

2001

[5] [3]

J. L. O’brien, Science 318, 1567 (2007)

2007

[6] [4]

Aspuru-Guzik and P

A. Aspuru-Guzik and P. Walther, Nature physics 8, 285 (2012)

work page 2012

[7] [5]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001)

2001

[8] [6]

Sangouard, C

N. Sangouard, C. Simon, H. De Riedmatten, and N. Gisin, Reviews of Modern Physics 83, 33 (2011)

2011