Gravitational Aharonov-Bohm Effect Research Articles

Temporal Pound–Rebka experiment as gravitational Aharonov–Bohm effect

One of the classical tests of general relativity is the precision measurements by Pound and Rebka of red-shift/blue-shift of photons in a gravitational field. In this essay, we lay out a temporal version of the Pound–Rebka experiment. The emission and absorption of photons occurs at different times, rather than at different spatial locations as in the original Pound–Rebka experiment. This temporal Pound–Rebka experiment is equivalent to a gravitational Aharonov–Bohm Effect and is testable via current or near future satellite experiments.

Scalar gravitational Aharonov–Bohm effect: 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.

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

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.

Gravitational Aharonov–Bohm effect in a matter-wave interferometer

Gravitational Aharonov–Bohm effect in a matter-wave interferometer

Observation of a gravitational Aharonov-Bohm effect.

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.

Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect

The main objective of this work is to present a theoretical proposal for an implementation of the $(2 + 1)$-dimensional Dirac equation in classical gravitational and electromagnetic backgrounds in a two-dimensional waveguide array. For this, a framework for achieving site-dependent effective coupling constants in two-dimensional waveguide arrays is developed. Implementability of the Dirac equation under the proposed scheme puts minor demands on gauge and spacetime backgrounds; however, a wide array of physical spacetimes, such as all vacuum and static solutions, prove to be implementable. As an interesting and instructive example, we discuss a tabletop realization of the gravitational Aharonov-Bohm effect: After devising a thought experiment in which signatures of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss how the analogue of such a setting can in principle be implemented using the proposed waveguide setup.

Testing sub-gravitational forces on atoms from a miniature in-vacuum source mass

Gravity is the weakest fundamental interaction and the only one that has not been measured at the particle level. Traditional experimental methods, from astronomical observations to torsion balances, use macroscopic masses to both source and probe gravitational fields. Matter wave interferometers have used neutrons, atoms and molecular clusters as microscopic test particles, but initially probed the field sourced by the entire earth. Later, the gravitational field arising from hundreds of kilograms of artificial source masses was measured with atom interferometry. Miniaturizing the source mass and moving it into the vacuum chamber could improve positioning accuracy, allow the use of monocrystalline source masses for improved gravitational measurements, and test new physics, such as beyond-standard-model ("fifth") forces of nature and non-classical effects of gravity. In this work, we detect the gravitational force between freely falling cesium atoms and an in-vacuum, centimeter-sized source mass using atom interferometry with state-of-the-art sensitivity. The ability to sense gravitational-strength coupling is conjectured to access a natural lower bound for fundamental forces, thereby representing an important milestone in searches for physics beyond the standard model. A local, in-vacuum source mass is particularly sensitive to a wide class of interactions whose effects would otherwise be suppressed beyond detectability in regions of high matter density. For example, our measurement strengthens limits on a number of cosmologically-motivated scalar field models, such as chameleon and symmetron fields, by over two orders of magnitude and paves the way toward novel measurements of Newton's gravitational constant G and the gravitational Aharonov-Bohm effect

Quantum superposition at the half-metre scale.

The quantum superposition principle allows massive particles to be delocalized over distant positions. Though quantum mechanics has proved adept at describing the microscopic world, quantum superposition runs counter to intuitive conceptions of reality and locality when extended to the macroscopic scale, as exemplified by the thought experiment of Schrödinger's cat. Matter-wave interferometers, which split and recombine wave packets in order to observe interference, provide a way to probe the superposition principle on macroscopic scales and explore the transition to classical physics. In such experiments, large wave-packet separation is impeded by the need for long interaction times and large momentum beam splitters, which cause susceptibility to dephasing and decoherence. Here we use light-pulse atom interferometry to realize quantum interference with wave packets separated by up to 54 centimetres on a timescale of 1 second. These results push quantum superposition into a new macroscopic regime, demonstrating that quantum superposition remains possible at the distances and timescales of everyday life. The sub-nanokelvin temperatures of the atoms and a compensation of transverse optical forces enable a large separation while maintaining an interference contrast of 28 per cent. In addition to testing the superposition principle in a new regime, large quantum superposition states are vital to exploring gravity with atom interferometers in greater detail. We anticipate that these states could be used to increase sensitivity in tests of the equivalence principle, measure the gravitational Aharonov-Bohm effect, and eventually detect gravitational waves and phase shifts associated with general relativity.

Gravitational Aharonov–Bohm effect due to noncommutative BTZ black hole

In this paper we consider the scattering of massless planar scalar waves by a noncommutative BTZ black hole. We compute the differential cross section via the partial wave approach, and we mainly show that the scattering of planar waves leads to a modified Aharonov–Bohm effect due to spacetime noncommutativity.

A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time

Abstract. A new approach to path integral quantum mechanics in curved space-time is presented for scalar particle propagation, expressed in terms of Lie transport and Fermi or Riemann normal co-ordinates to describe local curvature. While the presence of local curvature results in a strictly non-unitary representation of local time translation, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new terms that predict a simultaneous breakdown of time-reversal symmetry and a quantum violation of the weak equivalence principle at the particle’s Compton wavelength scale. Furthermore, the formalism reveals the prediction of a gauge-invariant phase factor interpreted as the gravitational Aharonov-Bohm effect and Berry’s phase.

A NEW PERSPECTIVE ON PATH INTEGRAL QUANTUM MECHANICS IN CURVED SPACETIME

A fundamentally different approach to path integral quantum mechanics in curved spacetime is presented for scalar particle propagation on a locally curved background, as described by Fermi or Riemann normal coordinates. While using a strictly non-unitary form of local time translation involving Lie transport, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved spacetime, plus new contributions. All the probability violating terms due to curvature contribute to a quantum violation of the weak equivalence principle at the particle's Compton wavelength scale and the propagator yields a gauge-invariant phase factor interpreted as the gravitational Aharonov–Bohm effect and Berry's phase.

Gravitational Aharonov-Bohm Effect

We study a purely gravitational Aharonov-Bohm effect. The space-time curvature is concentrated in the quasiregular singularity of a cosmic string, outside of which space-time is (locally) flat. The symmetries of this field configuration are described by the groupoid symmetries rather than by the usual group symmetries. The groupoid in question is formed by homotopy classes of piecewise smooth paths in the cosmic string region. A gravitational counterpart of the Aharonov-Bohm effect occurs if the symmetry of the system, with respect to the groupoid action, is broken down.

Gravitational Aharonov-Bohm effect due to weak fields

We study the behavior of relativistic quantum particles in the space-times generated by a rotating massive body and a moving mass current, in the weak field approximation. We solve the Dirac equation in these gravitational fields and calculate the currents associated with the particles. It is shown that these solutions and the currents depend on the angular momentum and on the velocity of the sources, in the cases of a massive rotating body and a moving mass current, respectively. These effects may be looked upon as a gravitational analog of the Aharonov-Bohm effect.

AHARONOV–BOHM EFFECT AND DISCLINATIONS IN AN ELASTIC MEDIUM

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov–Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov–Bohm effect. We analyze this effect in an elastic medium with one and N defects.

Global Properties of the Black Cigar Spacetime

In this work, we use parallel transport of vectors to study global characteristics of the Schwarzschild spacetime, in the context of the five-dimensional Randall-Sundrum braneworld, in the spacetime known as black cigar. We examine constant time circular orbits, where the parallel transport matrix indicates the existence of the analogue gravitational Aharonov-Bohm effect, except for some particular radii, where this matrix is trivial. Parallel transport along radial and time displacements are also obtained, reducing, in all cases to the usual results of ordinary Schwarzschild spacetime. On the other hand, the parallel transport matrix for a circular orbit in the Schwarzschild-AdS spacetime, an alternative solution for the black hole on the brane, keeps a ``memory" of the higher dimension.

Vortex versus spinning string: Iordanskii force and gravitational Aharonov—Bohm effect

We discuss the transverse force acting on the spinning cosmic string, moving in the background matter. It comes from the gravitational Aharonov-Bohm effect and corresponds to the Iordanskii force acting on the vortex in superfluids, when the vortex moves with respect to the normal component of the liquid.

The gravitational Aharonov–Bohm effect with photons

The analogy between general relativity and electromagnetism suggests that there is a gravitational analog of the Aharonov–Bohm effect. There is indeed such an effect. Since gravitation couples to all fields, the effect should exist for photons. There is a close connection with the Sagnac effect. Both the electromagnetic field and the gravitational field are classical fields, so the effect could have been predicted in the interval between the publication of the theory of general relativity in 1915 and the discovery of quantum mechanics in the mid 1920s.

An Experiment to Test the Gravitational Aharonov-Bohm Effect

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.

A particular realization of a gravitational anyon

We discuss the situation, frequently arisen in general relativity, in which the background spacetime is multiply connected. The associated gravitational Aharonov-Bohm effect can induce a small, but arbitrary phase factor turning a massive point particle into an anyon. Possible implications of this are outlined.

Gravitational Aharonov-Bohm effect in a locally flat spacetime

A quantum particle is considered in the background gravitational field due to a tubular matter source with axial interior magnetic field and vanishing exterior magnetic field. It is shown that in the locally flat spacetime around this tubular matter source, the wavefunction, the energy spectrum and the probability current depend on the amount of matter and magnetic field. These dependences represent gravitational analogues of the Aharonov-Bohm effect in electrodynamics.