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arXiv:2504.15409

Magnetic recoil interferometer in a uniform gravitational field. Comment on Observation of the quantum equivalence principle for matter-waves

Peter Asenbaum, Chris Overstreet

Published Apr 21, 2025• 0 citations
arXivHTMLPDF

Abstract

The calculation of the phase shift of a matter-wave interferometer looks different for different coordinate choices or the addition of a uniform gravitational field, but the final result of the observable phase shift does not depend on the coordinate choices or the uniform gravitational field. We find that the phase shift observed in ``Observation of the quantum equivalence principle for matter-waves'' is a magnetic recoil phase shift, similar to the recoil phase shift in light-pulse interferometers. Recoil phase shifts are inversely proportional to the inertial mass and do not depend on the gravitational mass. Our analysis highlights the difference between magnetic and gravitational acceleration in quantum mechanics.

DOI
10.48550/arxiv.2504.15409

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The calculation of the phase shift of a matter-wave interferometer looks different for different coordinate choices or the addition of a uniform gravitational field, but the final result of the observable phase shift does not depend on the coordinate choices or the uniform gravitational field. We find that the phase shift observed in ``Observation of the quantum equivalence principle for matter-waves'' is a magnetic recoil phase shift, similar to the recoil phase shift in light-pulse interferometers. Recoil phase shifts are inversely proportional to the inertial mass and do not depend on the gravitational mass. Our analysis highlights the difference between magnetic and gravitational acceleration in quantum mechanics.
Abstract In a uniform gravitational field, classical test objects fall universally. Any reference object or observer will fall in the same universal manner. Therefore, a uniform gravitational field cannot create dynamics between observers and classical test objects. The influence of a uniform gravitational field on matter waves and clocks, however, is described inconsistently throughout research and education. To illustrate, we discuss the behavior of a matter-wave interferometer and a clock redshift experiment in a uniform gravitational field. As a consistent formulation of the equivalence principle implies, a uniform gravitational field has no observable influence on these systems and is physically equivalent to the absence of gravity.
One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment.
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.
There now exists in the literature two different expressions for the phase shift of a matter-wave interferometer caused by the passage of a gravitation wave. The first, a commonly accepted expression that was first derived in the 1970s, is based on the traditional geodesic equation of motion (EOM) for a test particle. The second, a more recently derived expression, is based on the geodesic deviation EOM. The power-law dependence on the frequency of the gravitational wave for both expressions for the phase shift is different, which indicates fundamental differences in the physics on which these calculations are based. Here we compare the two approaches by presenting a series of side-by-side calculations of the phase shift for one specific matter-wave-interferometer configuration that uses atoms as the interfering particle. By looking at the low-frequency limit of the different expressions for the phase shift obtained, we find that the phase shift calculated via the geodesic deviation EOM is correct, and the ones calculated via the geodesic EOM are not.
Abstract We use a quantum variant of the Sagnac interferometer to argue for the quantum nature of gravity assuming the equivalence principle, which we formulate in its quantum version. We first present an original derivation of the phase acquired in the conventional Sagnac matter-wave interferometer, within the Hamiltonian formalism. Then we modify the interferometer in two crucial respects. The interfering matter wave is interfered along two different distances from the centre and the interferometer is prepared in a superposition of two different angular velocities. We argue that if the radial and angular degrees of freedom of the matter wave become entangled through this experiment, then, via the equivalence principle, the gravitational field must be non-classical.