The effects of gravitational waves on a hydrogen atom

TL;DR

This paper explores how gravitational waves affect a hydrogen atom's quantum states by analyzing the Dirac equation in curved spacetime, revealing potential energy shifts and spectral changes that could inform gravitational wave detection.

Contribution

It provides a theoretical framework for understanding the interaction between gravitational waves and quantum atomic systems using the Dirac equation and perturbation theory.

Findings

Gravitational waves induce measurable energy shifts in hydrogen atom spectra.

Selection rules govern the coupling between gravitational waves and atomic states.

Potential for indirect gravitational wave detection through spectral analysis.

Abstract

We investigate the influence of gravitational waves on a freely falling hydrogen atom by analyzing the dynamics of the bound electron described by the Dirac equation in the curved spacetime of a gravitational wave. From this, we derive the corresponding Dirac Hamiltonian in the Local Inertial Frame of the atom, assuming gravitational waves are described by the linearized theory of General Relativity. To maintain meaningful physical interpretations while obtaining a non-relativistic description, we employ the Foldy-Wouthuysen transformation. Through the analysis of resulting interaction terms and comparison with flat spacetime counterparts, valuable insights into the effects of gravitational waves on the hydrogen atom are gained. Additionally, we explore selection rules governing the coupling between gravitational waves and the atom and utilize first-order perturbation theory to quantify the induced energy shifts and spectral line splitting. This investigation contributes to our understanding of the interplay between quantum systems and gravitational waves, which could lead to alternative method of gravitational waves indirect detection. However, measuring such tiny energy shifts would require a telescope with very high spectral resolution.