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

TL;DR

This work connects quantum spacetime fluctuations to electromagnetic phase diffusion by treating gravitational waves as a Gaussian, two-mode squeezed bath within an open quantum systems framework. Using a Heisenberg-Langevin approach and a c-number stochastic description, it shows that GW noise correlations directly govern EM phase statistics, with memory effects arising from the PGW background’s long correlation time. The central result is a quartic-in-time growth of the EM phase variance, $\Delta^2\phi(t) = \Delta^2\phi_0 + 4\,(t/\tau_c)^4$, where the decoherence time $\tau_c$ depends on the PGW spectrum and squeezing parameters, distinguishing it from vacuum- or thermal-induced diffusion. While the estimated decoherence timescale $\tau_c \sim 10^4\,\text{s}$ exceeds current interferometric capabilities, the findings reveal a fundamental quantum-gravity limit on phase coherence and offer a novel pathway to probe the quantum nature of the inflationary GW background through precision optical measurements.

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 $\hatρ_{\text{gws}}$. 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 $φ(t)$. 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 $Δ^2\varphi(t)= Δ^2\varphi_0+ 4(t/τ_c)^4$, where the characteristic time scale $τ_c$ 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.

Figures (1)

• Figure 1: Schematic view of the experiment. Panel (a): The coherent laser beam is sent from a sender located at $\mathbf{x}_s$, and received at a receiver at $\mathbf{x}_r$. $\hat{\mathbf{k}}$ and $\hat{\mathbf{K}}$ show the direction of propagation of the EM field and GWs with respect to some coordinate system. Panel (b): spatial extension of the EM field. It is assumed that the transverse profile of the EM field is much smaller than GW's wavelength, while the propagation length $L \equiv z_r - z_s$ can be arbitrarily large. The polar angles $(\Theta_K, \Phi_K)$ represent the direction of GW propagation with respect to $\hat{\mathbf{K}}$.