Gravitational wave imprints on spontaneous emission

Abstract

Despite growing interest, there is a scarcity of known predictions in the regime where both quantum and general relativistic effects become observable. Here, we investigate a combined atom-field system in a curved spacetime, with a specific focus on gravitational-wave backgrounds. We demonstrate that a plane gravitational wave alters spontaneous emission from a single atom, manifesting itself as a direction-dependent change in the emission spectrum. Although the total decay rate remains unchanged, implying that no information about the gravitational wave is stored in the atomic internal state alone, the wave leaves imprints on the evolution of the composite atom-field system. To quantify how well this effect can be measured, we analyze both the classical Fisher information associated with photon number measurements and the quantum Fisher information. Our analysis indicates that the effect could be measured in state-of-the-art cold-atom experiments and points to spontaneous emission as a potential probe of low-frequency gravitational waves.

Figures (1)

• Figure 1: Functions $f(\delta_k,T)$ and $g(\theta,\varphi)$ governing frequency and angular dependence of the GW correction to the photon emission. Their values are indicated by color, with blue and red corresponding to negative and positive values. From (a), it is apparent that the GW gives rise to positive and negative corrections on the sides of the carrier frequency ($\delta_k=0$). The corrections are antisymmetric with respect to the carrier frequency. The red dashed lines in the plot correspond to $\delta_kT=\pm2\pi$, designating the width of the flat spacetime contribution $\langle\tilde{n}_{\boldsymbol{k}}\rangle$. From the function $g(\theta, \varphi)$ in panel (b), it is apparent that the effect is maximal along the positive $z$ direction (direction of GW propagation) and vanishes in the opposite direction. It exhibits a quadrupolar pattern in the $xy$ plane with opposite signs along the $x$ and $y$ axes. The distance from the origin additionally highlights the absolute value of the function $g(\theta,\varphi)$ at given $\theta$ and $\varphi$.