Hong-Ou-Mandel interferometry with cavity QED-based single-photon sources: A Quantum Jump Analysis

Caden McCollum; Imran M. Mirza; Lexi Dudones

REVIEW 3 major objections 6 minor 33 references

Hong-Ou-Mandel interferometry with cavity QED-based single-photon sources: A Quantum Jump Analysis

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Cavity-QED single-photon sources can produce a perfect Hong-Ou-Mandel effect, with the final post-jump state fixed to |g1g2,00>.

desk verdict The perfect-HOM conclusion is right, but Eq. (16) is invalid and the claimed 'excellent agreement' with numerics is unsupported. read the letter →

arxiv 2507.03803 v1 pith:FYNKFAG3 submitted 2025-07-04 quant-ph physics.atom-ph

Lexi Dudones , Caden McCollum , Imran M. Mirza This is my paper · ORCID

classification quant-phphysics.atom-ph

keywords Hong-Ou-MandeleffectquantumjumpscavityQEDsingle-photonsourcestwo-photoninterferenceJaynes-CummingsmodelMonteCarlotrajectoriesphotonindistinguishability

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 asks whether single-photon sources that are physically realistic—excited atoms, or atoms inside optical cavities—still produce the standard Hong-Ou-Mandel effect when the dissipative emission process is modeled explicitly. Using quantum jump theory, the authors derive analytic post-jump states for both source types and support them with Monte Carlo simulations. They find that two identical excited-atom sources yield a perfect effect with unit visibility, and that two identical atom-cavity sources also yield a perfect effect whose final state is |g1g2,00>, independent of the atom-cavity coupling strength except for time-dependent coefficients. The result matters because tests of photon indistinguishability and linear-optics quantum computing often assume idealized single-photon inputs; this analysis probes whether the way photons are generated changes the interference.

What carries the argument

The analysis runs on the quantum jump (trajectory) formalism: between photon detections the system evolves under a non-Hermitian Hamiltonian built from the Jaynes-Cummings interaction plus photon-leakage and spontaneous-emission loss terms, and each detection applies a jump operator formed by the 50/50 beam-splitter combination of the two cavity fields (or, for the atom case, the two atomic lowering operators). The beam-splitter combination enforces the Hong-Ou-Mandel bunching: after the first jump, the antisymmetric jump combination carries zero amplitude, so the second click must occur at the same output port, leaving the system in the ground-ground state with both cavities empty.

What would settle it

Solve the exact two-cavity non-Hermitian Schrodinger equation for the model of Section III without factorizing the loss operators away from the Jaynes-Cummings interaction, and evaluate the second-jump amplitude for the jump operator that was not used in the first jump. If that amplitude is nonzero for any G, kappa, or gamma, the claimed perfect Hong-Ou-Mandel effect fails; if it is identically zero, the claim survives this test.

Watch

Extended reading notes

Core claim

For two initially excited two-level atoms, the first photodetection collapses the two-atom system into a maximally entangled Bell state, and the second detection is then guaranteed to occur at the same output port, giving unit visibility. For two identical atom-cavity systems starting with one photon in each cavity, the same structure repeats: after both detections the surviving amplitude is proportional to |g1g2,00>, and the amplitude for clicks at different detectors is zero. The authors interpret this as a perfect Hong-Ou-Mandel effect for cavity-QED sources, with the post-jump state depending on the source only through time-dependent prefactors involving the cavity leakage rate and the atom-cavity coupling. The analytic results are corroborated by quantum-jump Monte Carlo trajectories, which also show Rabi oscillations in the strong-coupling regime and a drop of coincidence counts toward 50% as the two cavity leakage rates become very different.

Load-bearing premise

The central perfect-HOME result assumes that, between jumps, the lossy evolution can be split into undamped Jaynes-Cummings dynamics multiplied by independent exponential decays for the photon and the atomic excitation; if that split is not valid, the zero cross-detector amplitude behind Eq. (21) would need to be re-derived from the exact non-Hermitian evolution.

Editorial extensions

If this is right

For two identical initially excited atoms, the visibility parameter is V = 1: the second photon is never detected at a different output port, and the first click leaves the atoms in a maximally entangled Bell state.
For two identical atom-cavity sources, the final post-jump state is proportional to |g1g2,00> and the opposite-detector amplitude is zero, so the perfect Hong-Ou-Mandel effect holds at the analytic level in both strong- and weak-coupling regimes.
Making the two cavity leakage rates unequal reduces the coincidence percentage from 100% toward 50%, quantifying how source distinguishability erodes two-photon interference; stronger atom-cavity coupling slows that erosion.
Monte Carlo trajectories reproduce the analytic post-jump states and, in the strong-coupling regime, show damped Rabi oscillations in the atomic and cavity excitation probabilities.
For two entirely independent cavity sources run separately, coincidence and anti-coincidence counts are equal, signaling the absence of any two-photon interference between them.

Reading between the lines

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

Beyond the paper, the perfect-HOME claim can be stress-tested by solving the exact non-Hermitian evolution without the factorization used to write Eq. (16); the cross-detector amplitude is the decisive observable to check.
Beyond the paper, generalizing the jump construction to asymmetric sources (different atom-cavity couplings or different leakage rates on the two sides) would turn the coincidence curve into a quantitative indistinguishability metric for certifying single-photon sources.
Beyond the paper, the Bell state produced by the first click in the excited-atom case suggests a heralded entanglement-preparation protocol in which the first detection event triggers a useable entangled atom pair rather than merely recording an outcome.

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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

Worth knowing: the headline conclusion—perfect HOM for identical cavity-QED sources—is correct, but the analytic derivation that supposedly supports it is not. Eq. (16) is obtained by multiplying the ideal Jaynes-Cummings evolution by independent decay factors; that factorization fails because [κa†a + γσ†σ, G(a†σ + σ†a)] = G(κ − γ)(a†σ − σ†a) ≠ 0. Even in the commuting case κ = γ the exponents in (16) are wrong: the exact no-jump evolution has a common decay e^(−κt) for all components of the initial |g1g2;11⟩ state, not three different factors. Worse, Eq. (17) does not normalize to Eq. (18); the decay factors only cancel if γ = 2κ, which is never assumed. So Eqs. (19)–(21) and the repeated claim of agreement with Monte Carlo are unsupported. This is not a footnote-level slip: the quantitative content of Section III rests on these equations.

What the paper does well: it is clearly written, the excited-atom section is correct (though it reproduces the known Bell-state result, Ref. [24], as the authors acknowledge), and the numerical Monte Carlo study of coincidence percentage versus leakage-rate ratio and the time-delay analysis are useful new calculations. The qualitative behavior—coincidence drops to 50% for very asymmetric leakage—is physically right and consistent with standard distinguishability arguments.

The saving grace is that the perfect-HOM claim does not need the flawed state. With identical parameters, the exact evolution factorizes as U1⊗U2, the initial state is exchange-symmetric, and a J+ or J− first jump leaves a symmetric or antisymmetric one-excitation state; the opposite jump operator then annihilates it. That symmetry argument is airtight and shows the central conclusion is robust.

Target audience: people working on single-photon source indistinguishability and cavity-QED-based quantum information. The coincidence-vs-leakage curves will be of interest if re-derived; the paper would also make a good teaching example of why damping operators must be exponentiated together with the coupling.

Recommendation: send to peer review after major revision. A referee with open-systems experience should require the corrected no-jump evolution and a re-run of the numerics before publication. The qualitative result is worth keeping, but the current analytic apparatus is not.

Referee Report

3 major / 6 minor

Summary. The manuscript presents a quantum jump/trajectory analysis of Hong-Ou-Mandel interferometry for two classes of single-photon sources: two initially excited two-level atoms and two independent cavity QED systems prepared with one photon per cavity. For the atomic sources, the authors derive a Bell state after the first detection and a unit visibility for identical atoms. For the cavity QED sources, they write an analytic no-jump evolution, post-jump states, and a final state proportional to |g1g2;00⟩, claiming a perfect HOME whose amplitude depends on the cavity leakage rate κ and the atom-cavity coupling G, and they support this with Monte Carlo simulations of excitation probabilities, coincidence counts, and detection-time delays.

Significance. If correct, this would provide a compact analytic illustration of how source dynamics enter two-photon interference and would be useful for source-indistinguishability tests and linear-optics quantum information. The paper is self-contained, requires no fitted parameters for the analytic results, and includes explicit Monte Carlo simulations over 10,000 trajectories. The main limitation is that the analytic cavity-QED evolution is not the solution of the stated non-Hermitian Hamiltonian, so the quantitative predictions and the claimed agreement with simulation are not established; the qualitative perfect-HOME conclusion for identical sources may still be recoverable from symmetry, but the present derivation cannot support it.

major comments (3)

[III.A, Eq. (16)] Equation (16) is not the solution of the no-jump evolution generated by H_NH. The damping terms do not commute with the Jaynes-Cummings coupling: [κ a†a + γ σ†σ, G(a†σ + σ†a)] = G(κ-γ)(a†σ - σ†a), which vanishes only when κ=γ. In the single-excitation subspace {|g,1⟩, |e,0⟩} the exact evolution has a common decay prefactor exp(-(κ+γ)t/4) and an oscillation frequency Ω = sqrt(G² - (κ-γ)²/16), so for the two-cavity product all amplitudes carry exp(-(κ+γ)t/2), not the three different exponents exp(-κt), exp(-(κ/2+γ/4)t), and exp(-γt/2) appearing in Eq. (16). Since Eq. (16) is the basis for Eqs. (17)-(21), the analytic amplitudes and the claimed quantitative agreement are unsupported.
[III.A, Eqs. (17)-(18)] Equation (18) does not follow from Eq. (17) by normalization. After normalizing Eq. (17), the ratio of the coefficient of (|g1g2;10⟩+|g1g2;01⟩)/√2 to that of (|e1g2;00⟩+|g1e2;00⟩)/√2 is exp(-(κ/2 - γ/4)t1) cot(Gt1), whereas Eq. (18) gives cot(Gt1); equality would require κ=γ/2, which is not assumed. Thus the normalized state loses the unequal decay factors and also changes cos² to cos, so the subsequent evolution in Eqs. (19)-(21) and the final amplitude in Eq. (21) are not derived.
[III.B] The claimed 'excellent agreement' between analytic and Monte Carlo results is not demonstrated: Figs. 6-9 present only simulation data, with no overlay or quantitative comparison to Eqs. (16)-(21). Given the errors in the analytic state, the agreement claim is load-bearing for the quantitative content and needs to be either substantiated after correction or removed.

minor comments (6)

[III.A, Eq. (15)] The operator expression for the Jaynes-Cummings evolution is not the standard one; the term connecting |g⟩ to |e⟩ should involve a† sin(Gt√N)/√N, and the expression as written does not reproduce U(t)|g,1⟩ = cos(Gt)|g,1⟩ - i sin(Gt)|e,0⟩.
[III.A, Eq. (16)] The notation is inconsistent: t1 appears in the decay prefactors while t appears inside cos(Gt) and sin(Gt); the state is supposed to be evaluated just before t1.
[III.A, Eq. (19)] The arguments of the trigonometric functions mix t and t1; from the preceding text, cos(Gt) should be cos(Gt1) and sin(Gt) should be sin(Gt1) if Δt = t - t1.
[Throughout Section III] The coupling is denoted G in equations but g in the text and figures; please standardize the notation.
[Introduction] The phrase 'perfect homodyne detection (HOME)' should read 'perfect Hong-Ou-Mandel effect'; the acronym HOME is already defined.
[Fig. 7] The text reports '10 · 10^4 trajectories,' which is presumably 10^5; please clarify the number of trajectories used.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the cavity-QED HOME result follows from the stated model and standard quantum-jump rules, not from fitted parameters or self-citation.

full rationale

The paper's analytic chain (Sec. III A) starts from a non-Hermitian Hamiltonian built from Jaynes-Cummings couplings and beam-splitter jump operators J± = √(κ/2)(a1 ± a2), evolving the initial state |g1g2;11> between jumps. The claimed perfect HOME in Eq. (21) does not reduce to any fitted input: no parameter is adjusted to match the target coincidence, and the beam-splitter operators are fixed by the standard 50/50 transformation. The only self-citation, Ref. [32] (Mirza & van Enk), appears as a general citation for photon bunching and is not load-bearing. The reader-identified defect—that the decay terms do not commute with the Jaynes-Cummings Hamiltonian, making Eq. (16) and the normalization from Eq. (17) to Eq. (18) algebraically suspect—concerns mathematical correctness of the no-jump propagator, not circularity. The conclusion that two identical sources give perfect bunching is also structurally robust because J− annihilates the symmetric single-photon state produced after the first jump, independent of the disputed prefactors. Thus no 'prediction' is equivalent by construction to its inputs; the derivation is self-contained and the circularity burden is low.

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

The model uses standard quantum optics ingredients: the Jaynes-Cummings Hamiltonian, input-output theory, and the quantum jump formalism. No free parameters are fitted to data. The questionable assumption is that decay factors factor out of the Jaynes-Cummings evolution, which is used to write Eq. (16).

assumptions (5)

domain assumption Quantum jump/trajectory formalism (Carmichael, Ref. [18]) correctly describes photodetection in open quantum systems.
Used throughout to define non-Hermitian evolution and stochastic jumps; cited but not derived.
domain assumption Collett-Gardiner input-output theory allows construction of jump operators from system operators (Eqs. 3, 14).
Used to write J1, J2 and J+/- as simple combinations of atomic and cavity lowering operators.
domain assumption Jaynes-Cummings interaction for each atom-cavity system (Eq. 15).
Standard model for a two-level atom coupled to a single cavity mode; only the single-excitation subspace is considered.
ad hoc to paper The damping terms in the non-Hermitian Hamiltonian can be factored out of the Jaynes-Cummings evolution as independent exponential decay factors.
Assumed implicitly in Eq. (16); the damping operators do not commute with the Jaynes-Cummings Hamiltonian, so this factorization is not valid.
domain assumption Both sources are identical for the analytic results (gamma1 = gamma2, kappa1 = kappa2, G1 = G2).
Simplifies the state evolution; stated in Sec. III A.

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Cite this review

Pith. "Pith review of Hong-Ou-Mandel interferometry with cavity QED-based single-photon sources: A Quantum Jump Analysis." pith.science (2026). https://pith.science/paper/FYNKFAG3

@misc{pith2026250703803,
  author       = {Pith},
  title        = {Pith review of: Hong-Ou-Mandel interferometry with cavity QED-based single-photon sources: A Quantum Jump Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FYNKFAG3}},
  note         = {Machine review of arXiv:2507.03803}
}

read the original abstract

We present a quantum jump/trajectory analysis of the two-photon interference phenomenon in the context of the Hong-Ou-Mandel effect (HOME). In particular, we consider the standard setup of HOME, which consists of two-photon sources firing single photons from the opposite sides of a 50/50 beam splitter and two perfect detectors placed at the output ports to record photodetection events. For single-photon sources, we consider two special cases: (1) two excited two-level atoms and (2) two atom-cavity setups with initially present single photons in both cavities. For both cases, we report analytic results as well as quantum jump-based Monte Carlo simulations to demonstrate the signatures of these single-photon sources on the HOME under different working conditions (for example, strong- and weak-coupling regimes of cavity quantum electrodynamics). Our results may have interesting applications in linear optics quantum computing as well as in protocols that test the indistinguishability of single-photon sources.

Figures

Figures reproduced from arXiv: 2507.03803 by the authors.

**Figure 2.** FIG. 2: (Color online) The diagram of the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3: (Color online) A timeline summarizing the main steps of the quantum jump protocol. The system starts [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: FIG. 4: (Color online) The experimental setup, as [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5: (Color online) Quantum jump-based evolution timeline outlining the different steps involved in the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6: (Color online) Expectation values of the number operator and excitation operators as a function of time [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7: (Color online) A plot showing the [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: FIG. 8: (Color online) Coincidence percentage for (a) atom-cavity- and (b) case-III atom-based single photon [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

**Figure 9.** Figure 9: FIG. 9: (Color online) (a) Coincidence counts as a function of the time delay between the two clicks recorded at [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [24]

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N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of Modern Physics, vol. 86, no. 2, pp. 419–478, 2014

work page 2014

[2] [1]

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work page 1987

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F. Bouchard, A. Sit, Y. Zhang, R. Fickler, F. M. Mi- atto, Y. Yao, F. Sciarrino, and E. Karimi, “Two-photon interference: the Hong-Ou-Mandel effect,” Reports on Progress in Physics, vol. 84, no. 1, p. 012402, 2020

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S. Walborn, A. De Oliveira, S. Pádua, and C. Monken, “Multimode Hong-Ou-Mandel interference,”Physical Re- view Letters, vol. 90, no. 14, p. 143601, 2003

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