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Temporal Topological Aharonov-Bhom Phase in Quantum-Systems under Electric and Gravitational Scalar Potentials

M. E. Tobar, M. T. Hatzon, G. R. Flower, Maxim Goryachev, J. F. Bourhill, R. Y. Chiao, Nader A. Inan, Michael Scheibner, Jay E. Sharping, D. A. Singleton

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

We present results that shed light on a quantum system's scalar Aharonov-Bohm (AB) phase and how the effect can be measured. We show that the electric-scalar effect is the temporal dual of the vector-magnetic effect and propose a setup using a Faraday cage, where the observable is the modification of a quantum system's energy levels. For the scalar gravitational potential, we propose a quantum system in an eccentric orbit, which manifests as a temporal generalization of the gravitational redshift.

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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.

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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.

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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.

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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.

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Electrodynamic Aharonov-Bohm effect

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We propose an electrodynamic Aharonov-Bohm (AB) scheme where a nonzero AB phase difference appears even if the interferometer paths do not enclose a magnetic flux and are subjected to negligible scalar potential differences during the propagation of the quantum charged particle. In the proposal, the current in a solenoid outside the interferometer varies in time while the quantum particle is in a superposition state inside two Faraday cages, such that it is always subjected to negligible electromagnetic fields. At first glance, this result could challenge the topological nature of the AB effect. However, by considering the topology of the electromagnetic field configuration and the possible particle trajectories in spacetime, we demonstrate the topological nature of this situation.

arXiv:2302.14542•Physical Review A•Dec 22, 2023•7 citations
We present results that shed light on a quantum system's scalar Aharonov-Bohm (AB) phase and how the effect can be measured. We show that the electric-scalar effect is the temporal dual of the vector-magnetic effect and propose a setup using a Faraday cage, where the observable is the modification of a quantum system's energy levels. For the scalar gravitational potential, we propose a quantum system in an eccentric orbit, which manifests as a temporal generalization of the gravitational redshift.
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.
A version of the electric Aharonov-Bohm effect is proposed where the quantum system which picks up the Aharonov-Bohm phase is confined to a Faraday cage with a time-varying spatially uniform scalar potential. The electric and magnetic fields in this region are effectively zero for the entire period of the experiment. The observable consequence of this version of the electric Aharonov-Bohmn effect is to shift the energy levels of the quantum system rather than shift the fringes of the two-slit interference pattern. We show a strong mathematical connection between this version of the scalar electric ABABAB effect and the ac Stark 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.
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.
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.
We propose an electrodynamic Aharonov-Bohm (AB) scheme where a nonzero AB phase difference appears even if the interferometer paths do not enclose a magnetic flux and are subjected to negligible scalar potential differences during the propagation of the quantum charged particle. In the proposal, the current in a solenoid outside the interferometer varies in time while the quantum particle is in a superposition state inside two Faraday cages, such that it is always subjected to negligible electromagnetic fields. At first glance, this result could challenge the topological nature of the AB effect. However, by considering the topology of the electromagnetic field configuration and the possible particle trajectories in spacetime, we demonstrate the topological nature of this situation.