Scalar Gravitational Aharonov-Bohm Effect: Generalization of the Gravitational Redshift

Abstract: 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 [1]. 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 will exhibit a constant frequency shift relative to a ground clock corresponding to the orbit's average gravitational redshift, with additional modulation sidebands due to the time-varying gravitational potential.