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arXiv:2605.28038

Squeezed-slit Bohr-Einstein Interferometer

Hao-Wen Cheng, Xu-Zhao-Qiu Zeng, Yu-Chen Zhang, Yu-Hao Deng, Zhan Wu, Rui Lin, Yu-Cheng Duan, Zi-Han Chen, Jun Rui, Ming-Cheng Chen, Chao-Yang Lu, Jian-Wei Pan

quant-phphysics.atom-phphysics.opticsphysics.pop-phSubmitted May 27, 2026• Announced May 28, 2026• 0 citations
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Abstract

The Einstein-Bohr recoiling-slit gedankenexperiment, a cornerstone of quantum complementarity, has long been constrained by the zero-point fluctuations of the atomic slit -- the spatial Standard Quantum Limit (SQL). Here we transcend this fundamental boundary through active quantum state engineering of a single-atom slit. By implementing a non-adiabatic quench-evolve-quench protocol, we prepare the atomic motion in a squeezed state, dynamically redistributing phase-space uncertainty to suppress which-path information and restore high-visibility interference beyond the static vacuum limit. We report an intrinsic visibility of $0.938_{-0.008}^{+0.004}$, violating the SQL ($0.819$) by over 10 standard deviations, corresponding to $7.6(2)$ dB of effective squeezing. Our work reveals Kerr-induced non-Gaussian dynamics and reinterprets the traditional interferometer as a powerful tool for continuous-variable Wigner tomography, bridging the gap between quantum foundations and advanced metrology.

Related papers

Tunable Einstein-Bohr Recoiling-Slit Gedankenexperiment at the Quantum Limit

Yu-Chen Zhang, Haowen Cheng, Zhao-Qiu Zengxu +7 more

In 1927, during the fifth Solvay Conference, Einstein and Bohr described a double-slit interferometer with a "movable slit" that can detect the momentum recoil of one photon. Their debate centered on this Gedankenexperiment has provided profound insights into the central concepts of quantum mechanics. Despite many efforts to reproduce this conceptual experiment, a linear-optical version with a movable, quantum-limited slit and tunable momentum width remained challenging. Here, we report a realization of the Einstein-Bohr interferometer using a single atom in an optical tweezer, which is cooled to the motional ground state in three dimensions such that its momentum uncertainty is comparable to that of a single photon. We design an interferometric configuration where the single atom serves as an ultralight, quantum-limit beam splitter that is momentum entangled with the input photon. By varying the trap depth of the optical tweezer, we dynamically tune the atom's intrinsic momentum uncertainty, thus enabling the observation of a gradual shift in the visibility of single-photon interference. The interferometer also allows us to distinguish the classical noise caused by atom heating from the quantum-limited noise due to the momentum transfer, illustrating a quantum-to-classical transition.

arXiv:2410.10664•Physical Review Letters•Oct 17, 2025•10 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

Context-Induced Metric Geometry and Complementarity in the Recoiling-Slit Limit

Joseph Julian

Recent experimental realizations of the Einstein–Bohr recoiling-slit thought experiment have demonstrated a continuous tradeoff between interference visibility and recoil-induced distinguishability, often interpreted as a definitive empirical vindication of Bohr’s complementarity principle. In this work, we propose an alternative but compatible interpretation in which the effective geometry of distinguishability is induced by the experimental context itself. By introducing a context-dependent metric operator on the slit’s motional Hilbert space, we show that the standard recoil-limited visibility law emerges as a limiting case, while allowing for experimentally testable deviations when coherence bandwidth and accessibility constraints are varied. This formulation preserves complementarity while reframing its enforcement as a mechanistic, geometric process rather than an axiomatic postulate.

•Jan 1, 2025•0 citations

Entanglement For Atom Interferometers

Alexander Idel

Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.

•Jan 1, 2021•0 citations

Near-unitary spin squeezing with ytterbium (Conference Presentation)

Boris Braverman, Akio Kawasaki, Edwin Pedrozo-Peñafiel +9 more

State of the art atomic sensors operate near the standard quantum limit (SQL) of projection noise, and overcoming this limit by using atom-atom entanglement such as spin squeezing is a major goal in quantum metrology. By coupling an ensemble of approximately 1000 Yb-171 atoms to a high-finesse asymmetric micromirror cavity with single-atom cooperativity of 1.8., we produce a near-unitary spin squeezed state. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4) dB and 6.5(4) dB, respectively, while the generated states offer a spin noise suppression of 15.9(6) dB and a metrological gain of 12.9(6) dB over the standard quantum limit, limited by the curvature of the Bloch sphere. When requiring the squeezing process to be within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2).

Optical and Quantum Sensing and Precision Metrology II•Mar 9, 2020•0 citations

A New Interpretation of the Recoiling-Slit Quantum Interference Experiment

Jiaqing Yan

In December 2025, Pan Jianwei’s research team reproduced the Einstein-Bohr recoiling-slit thought experiment proposed in 1927 at the quantum limit. They observed that the interference fringe contrast changes continuously with the momentum of the slit. Mainstream physical theories currently regard this phenomenon as critical evidence for the quantum complementarity principle. Based on the Light Primitive Theory, this paper points out that all relevant theoretical models established since the century-long debate at the Solvay Conference contain two fundamental idealized simplifications: first, physical slits are abstracted as two-dimensional geometric holes with zero thickness; second, the inherent continuous spatial oscillation of photons is ignored. Photons are not point-like particles moving along fixed straight lines. Their persistent oscillation enables continuous momentum coupling between photons and the photon self-locked matter forming the slit walls throughout the whole passage through the physically thick slit channel. The inverse correlation between path detectability and interference fringe visibility observed in the experiment can be self-consistently explained by continuous photon-slit wall interaction, without abstract hypotheses such as wave-particle complementarity or quantum superposition. This paper supplements the objective physical conditions missing from traditional models and provides a brand-new interpretative framework for quantum interference phenomena at the underlying mechanism level.

•Jul 25, 2026•0 citations
The Einstein-Bohr recoiling-slit gedankenexperiment, a cornerstone of quantum complementarity, has long been constrained by the zero-point fluctuations of the atomic slit -- the spatial Standard Quantum Limit (SQL). Here we transcend this fundamental boundary through active quantum state engineering of a single-atom slit. By implementing a non-adiabatic quench-evolve-quench protocol, we prepare the atomic motion in a squeezed state, dynamically redistributing phase-space uncertainty to suppress which-path information and restore high-visibility interference beyond the static vacuum limit. We report an intrinsic visibility of 0.938−0.008+0.0040.938_{-0.008}^{+0.004}0.938−0.008+0.004​, violating the SQL (0.8190.8190.819) by over 10 standard deviations, corresponding to 7.6(2)7.6(2)7.6(2) dB of effective squeezing. Our work reveals Kerr-induced non-Gaussian dynamics and reinterprets the traditional interferometer as a powerful tool for continuous-variable Wigner tomography, bridging the gap between quantum foundations and advanced metrology.
In 1927, during the fifth Solvay Conference, Einstein and Bohr described a double-slit interferometer with a "movable slit" that can detect the momentum recoil of one photon. Their debate centered on this Gedankenexperiment has provided profound insights into the central concepts of quantum mechanics. Despite many efforts to reproduce this conceptual experiment, a linear-optical version with a movable, quantum-limited slit and tunable momentum width remained challenging. Here, we report a realization of the Einstein-Bohr interferometer using a single atom in an optical tweezer, which is cooled to the motional ground state in three dimensions such that its momentum uncertainty is comparable to that of a single photon. We design an interferometric configuration where the single atom serves as an ultralight, quantum-limit beam splitter that is momentum entangled with the input photon. By varying the trap depth of the optical tweezer, we dynamically tune the atom's intrinsic momentum uncertainty, thus enabling the observation of a gradual shift in the visibility of single-photon interference. The interferometer also allows us to distinguish the classical noise caused by atom heating from the quantum-limited noise due to the momentum transfer, illustrating a quantum-to-classical transition.
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.
Recent experimental realizations of the Einstein–Bohr recoiling-slit thought experiment have demonstrated a continuous tradeoff between interference visibility and recoil-induced distinguishability, often interpreted as a definitive empirical vindication of Bohr’s complementarity principle. In this work, we propose an alternative but compatible interpretation in which the effective geometry of distinguishability is induced by the experimental context itself. By introducing a context-dependent metric operator on the slit’s motional Hilbert space, we show that the standard recoil-limited visibility law emerges as a limiting case, while allowing for experimentally testable deviations when coherence bandwidth and accessibility constraints are varied. This formulation preserves complementarity while reframing its enforcement as a mechanistic, geometric process rather than an axiomatic postulate.
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
State of the art atomic sensors operate near the standard quantum limit (SQL) of projection noise, and overcoming this limit by using atom-atom entanglement such as spin squeezing is a major goal in quantum metrology. By coupling an ensemble of approximately 1000 Yb-171 atoms to a high-finesse asymmetric micromirror cavity with single-atom cooperativity of 1.8., we produce a near-unitary spin squeezed state. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4) dB and 6.5(4) dB, respectively, while the generated states offer a spin noise suppression of 15.9(6) dB and a metrological gain of 12.9(6) dB over the standard quantum limit, limited by the curvature of the Bloch sphere. When requiring the squeezing process to be within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2).
In December 2025, Pan Jianwei’s research team reproduced the Einstein-Bohr recoiling-slit thought experiment proposed in 1927 at the quantum limit. They observed that the interference fringe contrast changes continuously with the momentum of the slit. Mainstream physical theories currently regard this phenomenon as critical evidence for the quantum complementarity principle. Based on the Light Primitive Theory, this paper points out that all relevant theoretical models established since the century-long debate at the Solvay Conference contain two fundamental idealized simplifications: first, physical slits are abstracted as two-dimensional geometric holes with zero thickness; second, the inherent continuous spatial oscillation of photons is ignored. Photons are not point-like particles moving along fixed straight lines. Their persistent oscillation enables continuous momentum coupling between photons and the photon self-locked matter forming the slit walls throughout the whole passage through the physically thick slit channel. The inverse correlation between path detectability and interference fringe visibility observed in the experiment can be self-consistently explained by continuous photon-slit wall interaction, without abstract hypotheses such as wave-particle complementarity or quantum superposition. This paper supplements the objective physical conditions missing from traditional models and provides a brand-new interpretative framework for quantum interference phenomena at the underlying mechanism level.