Gravitational effects on a dissipative two-level atom in the weak-field regime

TL;DR

This work analyzes how a classical, weak gravitational field modifies dissipation in an open quantum system by studying a two-level atom coupled to a thermal scalar field. Using the Feynman–Vernon influence functional, it derives a GKSL master equation with gravity-modified transition rates and computes the dissipation rate, showing that the spontaneous emission rate $\gamma_g$ deviates from its flat-space value due to terms involving $\Phi(\mathbf{R})$, $f_1(R\Omega)$, and $f_2(R\Omega)$. The results reveal regimes where gravity enhances or suppresses emission, with distinct behavior in the $R\Omega\ll1$ and $R\Omega\gg1$ limits and dependence on dipole orientation relative to the gravitational source. These findings provide a theoretical bridge between quantum open systems and gravitational physics, suggesting potential routes for detecting gravitational or dark matter effects via quantum sensors and for testing quantum field theory in curved spacetime.

Abstract

We investigate the dissipative dynamics of a two-level atom in a weak gravitational field. Using the Feynman--Vernon influence functional formalism, we derive a quantum master equation describing the two-level atom interacting with a scalar field in a Newtonian gravitational field, and compute the energy dissipation rate of the atom. We find that the spontaneous emission rate (the dissipation rate in vacuum) is modified by the gravitational field. Specifically, this modification depends on the atom's dipole, the position of the atom relative to the source of the gravitational field, and the frequency of the scalar radiation emitted by the atom. Furthermore, we identify the parameter regimes in which the spontaneous emission rate is enhanced or suppressed by gravity. We also discuss how the modification arises from time dilation and dipole radiation in a weak gravitational field. These findings provide a theoretical basis for exploring gravitational effects in open quantum systems.

Figures (2)

• Figure 1: Schematic thought experiment illustrating how a distant observer compares decay signals from two atoms: one located near a gravitational source and another located near the distant observer. By repeatedly detecting decay events from the distant atom, the observer can infer its dissipation rate and compare it with the reference rate obtained from the atom, thereby identifying gravitational effects.
• Figure 2: Behavior of the ratio $\gamma_g/\gamma$ as a function of $R\Omega$. The left panel is the parallel case $\bm{d}\parallel\bm{R}$, and the right panel is the perpendicular case $\bm{d}\perp\bm{R}$. In the low- and high-frequency limits, the ratio becomes constant. In the parallel case (the left panel), the ratio is greater than one around $R\Omega \sim 1$.