Fringe visibility and which-way information in Young's double slit experiments with light scattered from single atoms

Hanzhen Lin; Jiahao Lyu; Vitaly Fedoseev; Wolfgang Ketterle; Yoo Kyung Lee; Yu-Kun Lu

Fringe visibility and which-way information in Young's double slit experiments with light scattered from single atoms

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Pith's one-line read Reduced fringe visibility in single-atom double-slit experiments is not always which-way information.

desk verdict A careful, honest theory note that sharpens the Bohr–Einstein recoiling-slit story by distinguishing population-stored from phase-stored which-way information; the central claim holds, though the B-versus-C eraser contrast is conditional on an energy-offset assumption. read the letter →

arxiv 2507.19801 v2 pith:SK5VAINJ submitted 2025-07-26 quant-ph physics.atom-ph

Hanzhen Lin , Yu-Kun Lu , Vitaly Fedoseev , Yoo Kyung Lee , Jiahao Lyu , Wolfgang Ketterle This is my paper · ORCID

classification quant-phphysics.atom-ph

keywords complementaritywhich-wayinformationfringevisibilitysingle-atomscatteringquantumeraserrecoilingslitharmonicoscillatorinterferencecontrast

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 compares Young's double-slit setups in which the slits are single atoms held in harmonic traps and can recoil when a photon scatters. It argues that a loss of fringe visibility is not automatically evidence that the photon's path was recorded: in a mobile single-slit configuration, the contrast reduction for long light pulses comes from entangling the unshifted and $\pi$-shifted interference patterns with different atomic oscillator states, while the phase that would encode which-way information is never recorded. In the two-independent-slits configuration, by contrast, the recoil excitation itself is a which-way marker, and the lost contrast can only be recovered with a quantum eraser. The distinction matters for interpreting recent single-atom scattering experiments and for what kind of measurement counts as a which-way measurement.

What carries the argument

The argument is carried by a mechanical-oscillator model in which a slit is a mass $m$ in a harmonic trap, with displacement operator $D=\exp(iQR)$ that transfers momentum recoil $\hbar Q$ to the atom when a photon scatters. After short pulses the atomic wavepackets become coherent states $|\pm\beta\rangle$ with $\beta=iQx_0/\sqrt{2}$, where $x_0=\sqrt{\hbar/m\omega_{\rm trap}}$; after long pulses, Fermi's golden rule turns the superposition into a mixture. For small $\beta$, expanding $|\pm\beta\rangle\approx|0\rangle\pm\beta|1\rangle$ reduces configuration C to an entangled state $|0\rangle\otimes(\text{symmetric pattern})+\beta|1\rangle\otimes(\pi\text{-shifted pattern})$, so the contrast $1-2|\beta|^2$ is set by the atomic-state overlap rather than by any stored path label.

What would settle it

Take two independent atomic slits with exactly equal trap frequencies, scatter long pulses, and apply the quantum-eraser rotation; if full fringe contrast reappears after erasure, the claimed unconditional which-way recording in the independent-slit configuration is falsified. Alternatively, in the single-mobile-slit configuration, detect the scattered photon's frequency with resolution better than the trap period and sort the two frequency components: if each component already shows full contrast without any eraser, the long-pulse contrast reduction is confirmed to be entanglement rather than which-way information.

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Extended reading notes

Core claim

The central claim is that in the configuration with one mobile slit (or a rigid double slit moving as one unit), the partial fringe visibility $1-2|\beta|^2$ observed with pulses much longer than the trap period is not due to which-way information. The long-pulse scattering produces a mixture in which one component keeps the symmetric interference pattern while the atom stays in $|0\rangle$, and the other component carries a $\pi$-shifted pattern while the atom is excited to $|1\rangle$; which-way information would have to reside in the relative phase between these two atomic states, which is not recorded on such timescales. Full contrast is restored by detecting the two frequency components separately or by inserting a dispersive element that gives a relative $\pi$ phase shift, without any erasure operation. This is different from the two-independent-atom configuration, where the excitation sits on one of two slits and always constitutes which-way information; there the contrast can only be restored by actively erasing that information.

Load-bearing premise

The distinction between the independent two-atom setup and the single-atom setup rests on the two atoms having a small but non-zero potential energy offset; if the two atoms were exactly degenerate, the independent setup would behave like the coupled-slit setup and a quantum eraser would restore full contrast.

Editorial extensions

If this is right

In single-mobile-slit experiments with pulses longer than the trap period, a measured contrast of $1-2|\beta|^2$ should not be read as evidence that which-way information was obtained.
Full contrast can be recovered in that configuration by frequency-resolving the scattered light or applying a $\pi$ dispersive phase shift, without any quantum eraser.
In two-independent-atom slits, the recoil site always encodes which-way information, so the quantum eraser is necessary to restore full contrast.
Adding a longitudinal common-mode recoil to the mobile single slit (configuration D) gives a detectable signal that carries no path information and does not reduce contrast.
Two slits coupled by a weak spring (configuration E) interpolate between B and C: with short pulses they record which-way information, but with long pulses the eigenstates are symmetric and antisymmetric and full contrast can be regained by coincidence detection.

Reading between the lines

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

This suggests that textbook statements equating reduced fringe visibility with available which-way information need a qualifier: the path label must be stored in an eigenstate of the measuring device to survive slow measurements, not merely in a relative phase.
The same oscillator model could be extended to matter-wave interferometers and cavity-QED setups with a single trapped particle as the slit, predicting when frequency-resolved detection restores contrast without erasure.
A direct test would be to time-tag scattered photons in configuration C with resolution better than the trap period: as the atomic phase becomes resolvable, true which-way information should appear and the naive no-which-way-information interpretation should fail.
Because the B-versus-C distinction relies on a small energy offset between the two atoms, experiments with exactly degenerate traps may actually realize configuration E; the apparatus classification should be checked by measuring the splitting.

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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

This note is worth having on record. The authors do exactly what they say: they compare configurations B and C (and D and E) of the recoiling-slit gedankenexperiment under short and long pulses using one simple model, and they show that a reduction in fringe visibility is not always a signature of which-way information. In configuration C with long pulses, the 1−2|β|² contrast arises from entanglement of the unshifted and π-shifted interference patterns with the atomic states |0⟩ and |1⟩; the which-way information, which would have to live in the phase between those states, is not recorded. That claim is internally consistent and well-supported by the derivation. The paper also makes a nice point with configuration D: common-mode longitudinal recoil carries no path information, so detecting it with high probability does not reduce contrast. This is a genuinely useful clarification for people reading the recent single-atom experiments.

What is new here is not any single ingredient but the explicit side-by-side comparison with a unified formalism. The authors are frank that every component exists in textbooks or prior work, and they do not dress it up as a new result. The derivations are straightforward and the math checks out. The self-citation to [4] is modest and used only as an illustration, not as an input to the model; there is no circularity.

The main soft spot is footnote 17. The sharp distinction between B and C—specifically the claim that in B a quantum eraser cannot restore contrast after a long pulse—relies on a small but non-zero energy offset between the two atoms, so that |1,0⟩ and |0,1⟩ are the unique eigenstates. If the atoms are exactly degenerate, the long-pulse state can retain coherence in the which-path basis, and an eraser can restore full contrast, making B resemble configuration E. This is a real conditionality, and the paper could be more explicit that the B-versus-C eraser contrast is an experimental condition, not a universal one. It does not, however, undermine the central claim about C, because configuration C alone demonstrates the visibility-versus-which-way distinction.

The other limitations are idealized assumptions (equal and opposite recoil, harmonic traps, single-mode scattering), which are acceptable for a pedagogical note of this scope. The citation pattern is broad and fair.

This is a solid, clearly written note that deserves a serious referee. It will be most useful to experimentalists in quantum optics and trapped-atom interferometry who want a crisp conceptual map of these configurations. I would send it to peer review and, modulo a small tweak to footnote 17, would accept it.

Referee Report

0 major / 7 minor

Summary. The paper analyzes four configurations of Young's double-slit experiments in which the slits are realized by trapped atoms that can recoil when a photon is scattered. In configuration B (two independent mobile slits), the which-way information is stored in which atom is excited, and the interference contrast is 1−|β|², with a quantum eraser capable of restoring full contrast only for short pulses. In configuration C (a single mobile slit or a rigid double slit), the paper derives that the long-pulse contrast is 1−2|β|², and argues that this reduction does not arise from which-way information but from entanglement of the unshifted and π-shifted interference patterns with the atomic ground and excited states, since the phase between |0⟩ and |1⟩ is not recorded in the long-pulse limit. The paper extends the analysis to 2D motion (configuration D) and to coupled slits (configuration E), and concludes that a visibility decrease is not always a signature of which-way information. The derivations are simple, transparent, and free of fitted parameters.

Significance. If the conclusions hold, the paper provides a useful clarification of a subtle point in complementarity: not all contrast reductions in which-way experiments are due to path information. The contrast formulas (1−|β|² and 1−2|β|²) and the distinction between robust which-way storage (configuration B) and phase-sensitive storage (configurations C and E) are derived from a first-principles model and connect directly to recent experiments [4,5]. The paper is honest in stating its assumptions, and the derivations in Eqs. (1)–(7) are internally consistent and easy to follow. The main value is pedagogical and conceptual, but the distinction is important for interpreting single-atom scattering experiments.

minor comments (7)

[Equation (2)] The notation "ϵ|0,0⟩ a ⊗ (γ1 |1,0⟩ γ + γ2 |0,1⟩ γ)" places the subscript 'a' in an easily misread position; please use parentheses or a clear spacing to indicate that |0,0⟩ is the atomic state and the following term is the photonic state.
[Configuration B, long-pulse paragraph] The phrase "with shows interference" should read "which shows interference".
[Configuration C, coherent-state projection] The sentence "the probability for a positive measurement is exp(−|δ∓β|²) for |±β⟩ states" is ambiguous; it should state explicitly that the probability is exp(−|δ−β|²) for |+β⟩ and exp(−|δ+β|²) for |−β⟩.
[First paragraph after Eq. (1)] "frequency 1/ω trap" should be "frequency ω_trap".
[Footnote 17] The assumption of a small non-zero potential energy offset between the two atoms is load-bearing for the claim that configuration B "always records which-way information" in the long-pulse limit; this condition should be stated prominently in the main text, not only in a footnote.
[References] Reference [5] is incomplete: "Phys. Rev. Lett., (2025)" lacks volume, page numbers, and DOI; please provide the full citation.
[Throughout] There is an extra closing parenthesis in "short light pulse with duration ≪1/ω trap)" and a few similar typographical slips; proofreading is recommended.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central claims are derived from first-principles oscillator/QED states, and the sole self-citation [4] is used only as an illustrative experiment, not as a load-bearing input.

full rationale

The paper's derivation chain is self-contained. Configuration B is analyzed by writing the state after a short pulse as |ψ⟩ = |0,0;0,0⟩ + ε(γ1|β,0;1,0⟩ + γ2|0,−β;0,1⟩), expanding for small β, and then treating long pulses via Fermi's golden rule; the contrast and the quantum-eraser behavior follow from these equations, not from any fitted parameter. Configuration C is similarly expanded to |ψ⟩ = |0;0,0⟩ + ε|0⟩_a⊗(γ1|1,0⟩_γ+γ2|0,1⟩_γ) + εβ|1⟩_a⊗(γ1|1,0⟩_γ−γ2|0,1⟩_γ), from which the 1−2|β|² contrast and the statement that the visibility loss is due to atom-photon entanglement rather than which-path information are direct consequences. The 'prediction' of 1−2|β|² is compared with the external experiment [5], not fitted to it. The only self-citation is [4], described as one of two 'recent experiments' being analyzed and generalized; it is used as an example of scheme B, not as a justification for any formula or as a uniqueness proof. Footnote 17 is an explicitly stated assumption (small non-zero energy offset between the two atoms), not an imported theorem from the authors' prior work, and it affects only the B-versus-C eraser comparison, leaving the central configuration-C claim intact. No step of the derivation reduces by construction to its input, and no fitted quantity is renamed as a prediction. Hence no circularity; the score reflects only the presence of a minor, non-load-bearing self-citation.

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

The central claim rests on standard quantum optical model assumptions: a two-level atom in a harmonic trap, displacement operator for photon recoil, short-pulse coherent evolution, and Fermi's golden rule for long pulses. The key assumption of a small energy offset to lift degeneracy in configuration B (footnote 17) is explicitly acknowledged. No free parameters are fitted; β is defined from physical constants.

assumptions (5)

standard math Standard quantum mechanics: harmonic oscillator states, coherent states, and displacement operator D=exp(iQR) describe photon recoil.
Used throughout the model (first page, after Fig.1) to derive states and contrast.
domain assumption Small-momentum expansion |±β⟩ ≈ |0⟩ ± β|1⟩, keeping only first order in β.
Used to derive the simplified states in Eqs. (2), (5)-(7) and the contrast formulas 1-|β|² and 1-2|β|².
domain assumption Fermi's golden rule applies for long light pulses, producing a mixture of energy eigenstates.
Invoked to analyze the long-pulse limit in configurations B, C, and E.
domain assumption The two photon paths impart equal and opposite recoil to the atom(s).
Stated for simplicity before Eq. (1); central to the |±β⟩ symmetry in configuration C.
ad hoc to paper In configuration B, a small but non-zero potential energy offset lifts the degeneracy between |0,1⟩ and |1,0⟩, so these are the unique eigenstates.
Footnote [17] introduces this assumption to make which-way information robust in B and prevent the quantum eraser from restoring contrast, a key distinction from C.

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Pith. "Pith review of Fringe visibility and which-way information in Young's double slit experiments with light scattered from single atoms." pith.science (2026). https://pith.science/paper/SK5VAINJ

@misc{pith2026250719801,
  author       = {Pith},
  title        = {Pith review of: Fringe visibility and which-way information in Young's double slit experiments with light scattered from single atoms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SK5VAINJ}},
  note         = {Machine review of arXiv:2507.19801}
}

read the original abstract

Young's double slit experiment has often been used to illustrate the concept of complementarity in quantum mechanics. If information can in principle be obtained about the path of the photon, then the visibility of the interference fringes is reduced or even destroyed. This Gedanken experiment discussed by Bohr and Einstein can be realized when the slit is replaced by individual atoms sensitive to the transferred recoil momentum of a photon which "passes through the slit". Early pioneering experiments were done with trapped ions and atom pairs created via photo-dissociation. Recently, it became possible to perform interference experiments with single neutral atoms cooled to the absolute ground state of a harmonic oscillator potential. The slits are now single atoms representing a two-level system, and the excitation in the harmonic oscillator potential is the which-way marker. In this note, we analyze and generalize two recent experiments performed with single atoms and emphasize the different ways they record which-way information.

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Pith tools

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

[1] [4]

Fedoseev, H

V. Fedoseev, H. Lin, Y.-K. Lu, Y. K. Lee, J. Lyu, and W. Ketterle, Coherent and incoherent light scat- tering by single-atom wavepackets, arXiv preprint arXiv:2410.19671 (2024)

arXiv 2024

[2] [1]

Bohr, Library of living philosophers, in Albert Einstein : Philosopher - Scientist, Vol

N. Bohr, Library of living philosophers, in Albert Einstein : Philosopher - Scientist, Vol. 7, edited by P. A. Schilpp (Open Court, 1970) Chap. Discussion with Einstein on Epistemological Problems in Atomic Physics, pp. 215–220

work page 1970

[3] [2]

Bohr, Niels bohr collected works, in Foundations of Quantum Physics I, edited by J

N. Bohr, Niels bohr collected works, in Foundations of Quantum Physics I, edited by J. Kalckar (The Niels Bohr Institute, Copenhagen, 1985)

work page 1985

[4] [3]

Jammer, The philosophy of’quantum mechanics: The interpretations of qm in historical perspective

M. Jammer, The philosophy of’quantum mechanics: The interpretations of qm in historical perspective. (John Wi- ley and Sons, 1974) Chap. The Bohr-Einstein Debate, pp. 121–132

work page 1974

[5] [5]

Zhang, H.-W

Y.-C. Zhang, H.-W. Cheng, Z.-Q. Zengxu, Z. Wu, R. Lin, Y.-C. Duan, J. Rui, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, Tunable einstein-bohr recoiling-slit gedankenexper- iment at the quantum limit, Phys. Rev. Lett. , (2025)

work page 2025

[6] [6]

W. M. Itano, J. C. Bergquist, J. J. Bollinger, D. J. Wineland, U. Eichmann, and M. Raizen, Complemen- tarity and young’s interference fringes from two atoms, Physical Review A57, 4176 (1998)

work page 1998

[7] [7]

Eichmann, J

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. 5 Gilligan, W. M. Itano, D. J. Wineland, and M. G. Raizen, Young’s interference experiment with light scat- tered from two atoms, Phys. Rev. Lett.70, 2359 (1993)

work page 1993

[8] [8]

Grangier, A

P. Grangier, A. Aspect, and J. Vigue, Quantum Interfer- ence Effect for Two Atoms Radiating a Single Photon, Phys. Rev. Lett.54, 418 (1985)

work page 1985