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arXiv:2311.07764 · Physical review. D/Physical review. D.

Gravitational Aharonov-Bohm effect

R. Y. Chiao, Nader A. Inan, Michael Scheibner, Jay E. Sharping, Douglas Singleton, Michael Edmund Tobar

Published Mar 25, 2024• 17 citations
arXivHTMLPDF

Abstract

We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time---it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the Aharonov-Bohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes.

DOI
10.1103/physrevd.109.064073

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We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time---it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the Aharonov-Bohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes.
Recently we showed that quantum systems in orbit around a massive body may be compared to ground clocks to test the gravitational Aharonov-Bohm effect. To be sensitive, orbits must have non-zero eccentricity, so geometric phase effects related to the time varying gravitation potential will be present. Since the quantum system will be in free-fall, by the equivalence principle, the quantum system is locally screened from the gravitational field. However, the time varying gravitational potential will change the energy levels of the quantum system and develop side bands, which are harmonics of the orbit frequency and is the signature of the scalar Aharonov-Bohm effect. Experiments that have the potential to measure such geometric phases include atomic clocks in space, such as the ACES mission, as well as other missions that propose optical clocks in space. Also, worth investigating is the possible use of data from Galileo clocks with non-zero eccentricity.
Abstract In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.
The Aharonov–Bohm effect is a quantum mechanical phenomenon that demonstrates how potentials can have observable effects even when the classical fields associated with those potentials are absent. Initially proposed for electromagnetic interactions, this effect has been experimentally confirmed and extensively studied over the years. More recently, the effect has been observed in the context of gravitational interactions using atom interferometry. Additionally, recent predictions suggest that temporal variations in the phase of an electron wave function will induce modulation sidebands in the energy levels of an atomic clock, solely driven by a time-varying scalar gravitational potential. In this study, we consider the atomic clock as a two-level system undergoing continuous Rabi oscillations between the electron's ground and excited state. We assume the photons driving the transition are precisely frequency-stabilized to match the transition, enabling accurate clock comparisons. Our analysis takes into account, that when an atom transitions from its ground state to an excited state, it absorbs energy, increasing its mass according to the mass-energy equivalence principle. Due to the mass difference between the two energy levels, we predict that an atomic clock in an eccentric orbit experiencing a time-varying gravitational potential, will exhibit a constant frequency redshift relative to a ground clock, corresponding to the orbit's average gravitational redshift. Additionally, modulation sidebands will appear, and detecting these predicted sidebands would confirm the scalar gravitational Aharonov–Bohm effect.
The Aharonov-Bohm (AB) effect underscores the fundamental role of electromagnetic and gravitational potentials in quantum mechanics, even in regions where classical fields vanish.In this article, we summarize and expand on our recent work on the AB effect.We explore the gravitational AB effect as a generalization of gravitational redshift, considering a quantum system in orbit around a massive body.In this scenario, time-dependent gravitational potentials give rise to sidebands in the energy spectrum, which could be detected using precision atomic clocks aboard satellites.In parallel, we extend recent investigations of the electric-scalar AB effect.By using a balanced interferometric excitation scheme in a microwave cavity, on resonance, we achieve 25 dB suppression of the electromagnetic fieldwhile enhancing the time-varying scalar electric potential.This offers a promising platform to directly probe the electricscalar AB effect under conditions of a null electric field and a finite scalar potential.Also, it enables the realization of a resonant system exhibiting extreme dispersion.These complementary approaches provide new experimental pathways to test fundamental quantum effects in electromagnetic and gravitational potentials.
The gravitational Aharonov-Bohm (AB) effect is examined in the weak-field approximation to general relativity. In analogy with the electromagnetic AB effect, we find that a gravitoelectromagnetic 4-vector potential gives rise to interference effects. A matter wave interferometry experiment, based on a modification of the gravity-induced quantum interference experiment of Colella, Overhauser and Werner (COW), is proposed to explicitly test the gravitoelectric version of the AB effect in a uniform gravitational field.
The electric Aharonov-Bohm effect is a special case of the general Ab effect. However, when inserting a gravitational potential in the place of the time dependent potential, a different understanding of the phase shift could be gained. The usual topological phase is replaced by a phase with origin in the red shift of the particle at one of the paths taken relative to the other path. In this case, the change in the geometrical measure is the source of the phase shift, which therefore has a local interpretation along with the non-local topological explanation.