Mass-energy equivalence in gravitationally bound quantum states of the neutron

TL;DR

This paper incorporates relativistic mass-energy equivalence into models of gravitationally bound neutrons, revealing small energy shifts and proposing enhanced measurement strategies for future experiments in fundamental physics.

Contribution

It introduces a relativistic correction to the Hamiltonian of gravitationally bound neutrons and analyzes its impact on experimental measurements and precision estimation.

Findings

Mass-energy equivalence causes measurable energy shifts in neutron states.

Joint measurements of spin and motion improve precision in detecting relativistic effects.

Relativistic corrections influence experimental searches for new physics.

Abstract

Gravitationally bound neutrons have become an important tool in the experimental searches for new physics, such as modifications to Newton's force or candidates for dark matter particles. Here we include the relativistic effects of mass-energy equivalence into the model of gravitationally bound neutrons. Specifically, we investigate a correction in a gravitationally bound neutron's Hamiltonian due to the presence of an external magnetic field. We show that the neutron's additional weight due to mass-energy equivalence will cause a small shift in the neutron's eigenenergies and eigenstates, and examine how this relativistic correction would affect experiments with trapped neutrons. We further consider the ultimate precision in estimating the relativistic correction to the precession frequency and find that, at short times, a joint measurement of both the spin and motional degrees of freedom provides a metrological enhancement as compared to a measurement of the spin alone.