Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2507.19801 · Physical Review A

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

Hanzhen Lin, Yu‐Kun Lu, Vitaly Fedoseev, Yoo Kyung Lee, Jiahao Lyu, Wolfgang Ketterle

Published Dec 3, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.1103/dyg4-vswk

Related papers

Interference and partial which-way information: A quantitative test of duality in two-atom resonance

Yonatan Abranyos, Matthias Jakob, János A. Bergou

We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.

Physical Review A•Dec 8, 1999•8 citations

Young’s interference experiment with light scattered from two atoms

U. Eichmann, Jonas Bergquist, J. J. Bollinger +4 more

We report the first observation of interference effects in the light scattered from two trapped atoms. The visibility of the fringes can be explained in the framework of Bragg scattering by a harmonic crystal and simple ``which path'' considerations of the scattered photons. If the light scattered by the atoms is detected in a polarization-sensitive way, then it is possible to selectively demonstrate either the particle nature or the wave nature of the scattered light.

Physical Review Letters•Apr 19, 1993•293 citations

Young`s interference experiment with light scattered from two atoms

U. Eichmann, Jonas Bergquist, J. J. Bollinger +1 more

We report the first observation of interference in the light scattered from two trapped atoms ({sup 198}Hg{sup +} ions localized in a linear Paul trap). The visibility of the interference fringes can be explained in the frame-work of Bragg scattering by a harmonic crystal, but with important differences compared to the case of a large crystal. Comparison of the experimental data with theory shows that the interference pattern offers another method to determine ion temperatures and separations. Furthermore, by exploiting the atom`s internal structure we have found a way to obtain {open_quotes}which path{close_quotes} information without invoking the position-momentum uncertainty relation. If the light scattered by the atoms is detected in a polarization-sensitive way, then it is possible to selectively demonstrate either the particle-nature or the wave-nature of the scattered photons.

Bulletin of the American Physical Society•May 1, 1993•0 citations

Observation of Which-Way-2D-Cross-Double-Slit Experiments: Violation of Bohr’s Complementarity Principle

Hui Peng

Young’s one-dimension-double-slit experiment represents the basic mystery of quantum world and was extended to which-way-1D-double-slit experiment. To explore the mystery, 2D-cross-double-slit apparatuses have been proposed, which consists of more than one double-slits intersecting to each other. In this article, we report which-way-2D-cross-double-slit experiments by detecting which slit of a double-slit of 2D-cross-double-slit apparatus a photon would pass through. The experimental results show that photons passing through the detected double-slit behave as particle, while photons passing through other undetected double-slit(s) distribute as wave in the same experiment with the same apparatus. Namely the particle nature and wave distribution coexist, which violates Bohr’s complementarity principle. We suggest that photon’s “particle nature” is intrinsic, while the term “wave nature” represents a wave-like distribution, which is a consequence of movement of photon as particle. It is a challenge to interpret mathematically those observations consistently.

International Journal of Physics•Nov 27, 2020•3 citations

Objective Recoil and Complementarity in the Single-Atom Einstein–Bohr Experiment: A Physical–Observation Dual-Axis Formulation

Xianwei Meng

Nearly a century after the 1927 Solvay exchange, the Einstein–Bohr recoiling-slit experiment has been realized with a single optically trapped 87Rb atom. The atom is light enough for one scattered photon to leave a resolvable motional record, and sufficiently controllable for the overlap of the two opposite recoil states to be tuned across the quantum regime. The resulting visibility curve is commonly read as an experimental confirmation of Bohr. That reading is correct, but incomplete: the same experiment also makes visible the objective recoil carrier on which Einstein’s argument rested. We develop a physical–observation dual-axis formulation in which the photon path x ∈ X and the atomic motional state s ∈ S enter as irreducible state coordinates of the observed fact r = F(x,s). The joint photon atom state then gives a complex cross-axis coherence kernel γS = ⟨s−|s+⟩. Its modulus is the photon visibility, its phase transports the fringe origin, and the distinguishability of the same two recoil records supplies the available path information. For a Gaussian motional ground state the construction yields V = exp(−2η2), with η = hk /(2∆p), reproducing the dependence tested in the experiment. We also prove that, whenever controlled atomic states generate different complex kernels at fixed photon preparation, no photon-only response map can represent the complete phase-resolved family of observations. Standard quantum mechanics satisfies this requirement by retaining the composite state; the dual-axis formulation makes its observational structure explicit. The resulting synthesis is precise: Einstein was right about the reality and physical location of the recoil record, while Bohr was right about the bound governing its coexistence with interference. Neither the necessity of a classical apparatus cut nor the completeness of quantum single-event dynamics follows from the experiment. Phase-sensitive and closed-loop extensions are proposed to probe the complex cross-axis response beyond visibility alone.

•Sep 10, 2026•0 citations

Einstein–Bohr recoiling double-slit gedanken experiment performed at the molecular level

X.-J. Liu, Quan Miao, Faris Gel’mukhanov +6 more

Double-slit experiments illustrate proof for wave–particle complementarity. The essence of Einstein–Bohr's debate about wave–particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. We realized this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled slits). Interference is observed in the former case, while the electron momentum transfer quenches the interference in the latter case.

Journal of Physics Conference Series•Sep 7, 2015•1 citation
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.
We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.
We report the first observation of interference in the light scattered from two trapped atoms ({sup 198}Hg{sup +} ions localized in a linear Paul trap). The visibility of the interference fringes can be explained in the frame-work of Bragg scattering by a harmonic crystal, but with important differences compared to the case of a large crystal. Comparison of the experimental data with theory shows that the interference pattern offers another method to determine ion temperatures and separations. Furthermore, by exploiting the atom`s internal structure we have found a way to obtain {open_quotes}which path{close_quotes} information without invoking the position-momentum uncertainty relation. If the light scattered by the atoms is detected in a polarization-sensitive way, then it is possible to selectively demonstrate either the particle-nature or the wave-nature of the scattered photons.
Young’s one-dimension-double-slit experiment represents the basic mystery of quantum world and was extended to which-way-1D-double-slit experiment. To explore the mystery, 2D-cross-double-slit apparatuses have been proposed, which consists of more than one double-slits intersecting to each other. In this article, we report which-way-2D-cross-double-slit experiments by detecting which slit of a double-slit of 2D-cross-double-slit apparatus a photon would pass through. The experimental results show that photons passing through the detected double-slit behave as particle, while photons passing through other undetected double-slit(s) distribute as wave in the same experiment with the same apparatus. Namely the particle nature and wave distribution coexist, which violates Bohr’s complementarity principle. We suggest that photon’s “particle nature” is intrinsic, while the term “wave nature” represents a wave-like distribution, which is a consequence of movement of photon as particle. It is a challenge to interpret mathematically those observations consistently.
Nearly a century after the 1927 Solvay exchange, the Einstein–Bohr recoiling-slit experiment has been realized with a single optically trapped 87Rb atom. The atom is light enough for one scattered photon to leave a resolvable motional record, and sufficiently controllable for the overlap of the two opposite recoil states to be tuned across the quantum regime. The resulting visibility curve is commonly read as an experimental confirmation of Bohr. That reading is correct, but incomplete: the same experiment also makes visible the objective recoil carrier on which Einstein’s argument rested. We develop a physical–observation dual-axis formulation in which the photon path x ∈ X and the atomic motional state s ∈ S enter as irreducible state coordinates of the observed fact r = F(x,s). The joint photon atom state then gives a complex cross-axis coherence kernel γS = ⟨s−|s+⟩. Its modulus is the photon visibility, its phase transports the fringe origin, and the distinguishability of the same two recoil records supplies the available path information. For a Gaussian motional ground state the construction yields V = exp(−2η2), with η = hk /(2∆p), reproducing the dependence tested in the experiment. We also prove that, whenever controlled atomic states generate different complex kernels at fixed photon preparation, no photon-only response map can represent the complete phase-resolved family of observations. Standard quantum mechanics satisfies this requirement by retaining the composite state; the dual-axis formulation makes its observational structure explicit. The resulting synthesis is precise: Einstein was right about the reality and physical location of the recoil record, while Bohr was right about the bound governing its coexistence with interference. Neither the necessity of a classical apparatus cut nor the completeness of quantum single-event dynamics follows from the experiment. Phase-sensitive and closed-loop extensions are proposed to probe the complex cross-axis response beyond visibility alone.
Double-slit experiments illustrate proof for wave–particle complementarity. The essence of Einstein–Bohr's debate about wave–particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. We realized this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled slits). Interference is observed in the former case, while the electron momentum transfer quenches the interference in the latter case.