Phase Diffusion of Light Immersed In Quantum Tides: Open Quantum System Approach

Abstract

The interaction between quantum gravitational waves (GWs) and electromagnetic (EM) fields is investigated within the open quantum system formalism, where GWs are considered as a heat bath reservoir occupying a generic state $\hat{\ddot{I}}{}_{\text{gws}}$. Following the quantum Langevin equations, it turns out that the correlations of the Langevin noise operator associated with the GW background directly determine the statistical properties of the EM phasor $\ddot{I}•(t)$. We apply this formalism to the background of inflationary-generated primordial gravitational waves (PGW). Since this background has an astronomically large correlation time, of the order of the Hubble time $H_0^{-1}$, we show that it leads to a non-Markovian dynamics of the EM field, which causes memory effects. As a result of the Gaussianity of PGW, it turns out that the EM phasor goes through a stochastic process, which is a manifestation of the fluctuation-dissipation in EM-GW system. The variance of the EM phase smears out as $\hat{I}{”}^2\ddot{I}†(t)=\hat{I}{”}^2\ddot{I}{†}_0+4(t/\ddot{I}{„}_c{)}^4$, where the characteristic time scale $\ddot{I}{„}_c$ is associated with the diffusion rate caused by PGWs. The specific quartic growth of the phase noise is thus attributed to the two-mode squeezed nature of PGWs, which is inherently different from the phase diffusion induced by vacuum fluctuations of spacetime or a thermal heat bath of gravitons.

23 pages, 1 figure