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

Physics

Measuring the Tidal Force on a Particle’s Matter Wave

Matt Jaffe, Holger Müller

Published May 1, 2017• 3 citations
Publisher

Abstract

Spacetime curvature induces tidal forces on the wave function of a single quantum system.Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces.The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold.Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.

DOI
10.1103/physics.10.47

Related papers

Phase Shift in an Atom Interferometer due to Spacetime Curvature across its Wave Function

Peter Asenbaum, Chris Overstreet, Tim Kovachy +3 more

Spacetime curvature induces tidal forces on the wave function of a single quantum system. Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces. The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold. Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.

arXiv:1610.03832•Physical Review Letters•May 1, 2017•250 citations

Viewpoint: Measuring the Tidal Force on a Particle’s Matter Wave

Matt Jaffe, Holger Müller

The effect of the tidal force, which is directly related to the curvature of spacetime, on an individual particle’s wave function has been measured with an atom interferometer.

•May 1, 2017•0 citations

Local measurement scheme of gravitational curvature using atom interferometers

Michael Werner, Ali Lezeik, Dennis Schlippert +3 more

Abstract Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we provide a theoretical analysis of the phase resulting in a complex gravitational environment and introduce a novel interferometer geometry which singles out the phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.

Communications Physics•Nov 14, 2025•2 citations

Gravitationally induced phase shift on a single photon

Christopher Hilweg, Francesco Massa, Д. В. Мартынов +3 more

The effect of the Earth's gravitational potential on a quantum wave function has only been observed for massive particles. In this paper we present a scheme to measure a gravitationally induced phase shift on a single photon traveling in a coherent superposition along different paths of an optical fiber interferometer. To create a measurable signal for the interaction between the static gravitational potential and the wave function of the photon, we propose a variant of a conventional Mach–Zehnder interferometer. We show that the predicted relative phase difference of 10 −5 rad is measurable even in the presence of fiber noise, provided additional stabilization techniques are implemented for each arm of a large-scale fiber interferometer. Effects arising from the rotation of the Earth and the material properties of the fibers are analysed. We conclude that optical fiber interferometry is a feasible way to measure the gravitationally induced phase shift on a single-photon wave function, and thus provides a means to corroborate the equivalence of the energy of the photon and its effective gravitational mass.

arXiv:1612.03612•New Journal of Physics•Feb 28, 2017•33 citations

Curvature effects in interferometry

J. Anandan

The phase shift in interferometry due to the space-time curvature is computed in nonrelativistic and relativistic physics. This treatment is applied to an interferometer analogous to the perfect crystal interferometer used in the Colella-Overhauser-Werner experiment with thermal neutrons, an interferometer consisting of only horizontal mirrors, suitable for ultracold neutrons, and optical interferometry. Experiments are proposed to detect the effect of the tidal forces of the Earth, Moon, and the Sun, for the first time in interferometry. The phase shift in neutron interferometry due to terrestrial objects is considered and an experiment is proposed with superfluid helium as the source of gravity. This would provide, for the first time, direct evidence concerning the gravitational interaction between two quantum-mechanical states. The possibility of detecting purely general-relativistic effects due to curvature, by means of neutron interferometry, is also explored.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 1, 1984•29 citations

Observation of a gravitational Aharonov-Bohm effect

Chris Overstreet, Peter Asenbaum, Joseph Curti +2 more

Gravity curves space and time. This can lead to proper time differences between freely falling, nonlocal trajectories. A spatial superposition of a massive particle is predicted to be sensitive to this effect. We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg’s error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.

Science•Jan 14, 2022•132 citations
Spacetime curvature induces tidal forces on the wave function of a single quantum system.Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces.The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold.Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.
Abstract Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we provide a theoretical analysis of the phase resulting in a complex gravitational environment and introduce a novel interferometer geometry which singles out the phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.
The effect of the Earth's gravitational potential on a quantum wave function has only been observed for massive particles. In this paper we present a scheme to measure a gravitationally induced phase shift on a single photon traveling in a coherent superposition along different paths of an optical fiber interferometer. To create a measurable signal for the interaction between the static gravitational potential and the wave function of the photon, we propose a variant of a conventional Mach–Zehnder interferometer. We show that the predicted relative phase difference of 10 −5 rad is measurable even in the presence of fiber noise, provided additional stabilization techniques are implemented for each arm of a large-scale fiber interferometer. Effects arising from the rotation of the Earth and the material properties of the fibers are analysed. We conclude that optical fiber interferometry is a feasible way to measure the gravitationally induced phase shift on a single-photon wave function, and thus provides a means to corroborate the equivalence of the energy of the photon and its effective gravitational mass.
The phase shift in interferometry due to the space-time curvature is computed in nonrelativistic and relativistic physics. This treatment is applied to an interferometer analogous to the perfect crystal interferometer used in the Colella-Overhauser-Werner experiment with thermal neutrons, an interferometer consisting of only horizontal mirrors, suitable for ultracold neutrons, and optical interferometry. Experiments are proposed to detect the effect of the tidal forces of the Earth, Moon, and the Sun, for the first time in interferometry. The phase shift in neutron interferometry due to terrestrial objects is considered and an experiment is proposed with superfluid helium as the source of gravity. This would provide, for the first time, direct evidence concerning the gravitational interaction between two quantum-mechanical states. The possibility of detecting purely general-relativistic effects due to curvature, by means of neutron interferometry, is also explored.
Gravity curves space and time. This can lead to proper time differences between freely falling, nonlocal trajectories. A spatial superposition of a massive particle is predicted to be sensitive to this effect. We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg’s error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.