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Fundamental Research

Designing precision measurement of the gravitational Aharonov-Bohm effect in microgravity

Yuan Sun, Liang Liu

Published May 25, 2024• 1 citation
Publisher

Abstract

The gravitational Aharonov-Bohm (GAB) effect serves as the gravitational counterpart to the electromagnetic Aharonov-Bohm effect. Despite the concept's inception in 1967, a rigorous experimental test of the GAB effect remains elusive. While recent endeavors with ground-based apparatus show promise in uncovering hints of the GAB effect, we propose a precise yet practical experiment to deterministically measure the GAB phase shift using cold atom interferometry in a microgravity environment, such as an orbital space station or drop tower. We conduct a thorough analysis of the experiment's principles and derive key parameters. Our calculations suggest that it is feasible to precisely measure a significant GAB phase shift within known engineering constraints. Additionally, our design of the cold atom interferometer possesses a unique sensitivity to potential but insensitivity to force, which can be further refined to effectively mitigate adverse effects associated with nonzero inertial forces acting on the cold atoms. These endeavors will ultimately pave the way for experimental exploration into the quantum nature of gravity.

DOI
10.1016/j.fmre.2024.05.006

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The gravitational Aharonov-Bohm (GAB) effect serves as the gravitational counterpart to the electromagnetic Aharonov-Bohm effect. Despite the concept's inception in 1967, a rigorous experimental test of the GAB effect remains elusive. While recent endeavors with ground-based apparatus show promise in uncovering hints of the GAB effect, we propose a precise yet practical experiment to deterministically measure the GAB phase shift using cold atom interferometry in a microgravity environment, such as an orbital space station or drop tower. We conduct a thorough analysis of the experiment's principles and derive key parameters. Our calculations suggest that it is feasible to precisely measure a significant GAB phase shift within known engineering constraints. Additionally, our design of the cold atom interferometer possesses a unique sensitivity to potential but insensitivity to force, which can be further refined to effectively mitigate adverse effects associated with nonzero inertial forces acting on the cold atoms. These endeavors will ultimately pave the way for experimental exploration into the quantum nature of gravity.
Testing whether gravity is quantum or classical remains a cornerstone challenge in fundamental physics. We introduce a practical tabletop experiment to probe gravity's quantum nature via the gravitational Aharonov-Bohm (AB) effect in atom interferometry. Our approach hinges on two pivotal insights: First, unlike electromagnetic AB effects where constant charge ensures gauge-invariant phases for closed paths, semiclassical gravity couples to the particle's total energy, rendering the AB phase gauge-dependent and unobservable when energies differ between paths due to environmental noise or controlled perturbations. Second, in quantum gravity—treating source, particle, and field as quantum—the total phase splits into a gauge-dependent particle contribution and a gauge-invariant source backreaction, yielding precisely half the nominal AB phase as observable. This halved phase discriminates quantum from classical gravity without requiring massive superpositions, aligning with existing technology. Remarkably, Overstreet et al.'s (Science 375, 226 (2022)) data already reveal a nonzero measured AB phase, providing the first experimental evidence for gravitational quantization.
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We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.
Atom interferometry provides a unique platform for testing fundamental physics. Building on the successful realization of the gravitational Aharonov-Bohm (gAB) effect in a large-baseline atom interferometer, I propose a next-generation experiment adapting this precise setup by adding a controllable electric potential. This experiment enables a background-free search for Beyond Standard Model (BSM) physics manifesting as a phenomenological composition-dependent coupling to both a gravitational and an electric potential (LBSM∝qφgφe\mathcal{L}_{BSM} \propto q \varphi_g \varphi_eLBSM​∝qφg​φe​). I show that the analogous Standard Model (SM) effect, a gravitationally-modified Stark shift, vanishes identically due to parity conservation; as the atomic ground state has even parity, the expectation value of this interaction is zero. To detect the target microradian-scale signal beneath milliradian-scale technical noise and gigaradian-scale inertial backgrounds, the experimental design integrates three crucial solutions: (1) a simultaneous dual-isotope (85^{85}85Rb/87^{87}87Rb) interferometer to reject technical common-mode noise, (2) optimal spin-squeezed states providing N−2/3^{-2/3}−2/3 sensitivity scaling to surpass the Standard Quantum Limit, and (3) a four-point differential quadrature (±V0,±keff\pm V_0, \pm k_{\text{eff}}±V0​,±keff​) to algebraically cancel the dominant inertial phase and all k-odd systematics. A Monte Carlo analysis validates this complete protocol's robustness against systematics and projects a realistic path to a 5-sigma discovery within a 3-month integration time. This model-independent search, particularly sensitive to neutron-coupled forces like U(1)B−L_{B-L}B−L​ gauge bosons, constitutes a high-precision null test that further solidifies the Aharonov-Bohm intuition that potentials are more fundamental than fields.
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.
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom’s Compton frequency. In analogy to the AharonovBohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.