Dynamical Casimir effect under the action of gravitational waves

TL;DR

This work analyzes how a plane gravitational wave modifies the dynamical Casimir effect inside a 3D cavity with a moving mirror by deriving the scalar-field dynamics in TT gauge and constructing instantaneous mode functions. It identifies gravity-induced resonance channels beyond the standard mechanical DCE and provides analytic expressions for the particle number $N_{\mathbf{k}}(T)$ under five resonances, with $N_{\mathbf{k}}(T)=\sinh^2(\chi_{\mathbf{k}}T)$. The study highlights the extreme smallness of the GW contribution due to $h_+\sim 10^{-20}-10^{-21}$ and discusses the distinct spectral sidebands that could, in principle, distinguish gravity-driven signals in high-Q or analogue-gravity platforms. It also points to future directions involving quantum-gravity considerations and experimental realizations in controlled analogue systems.

Abstract

Several nontrivial phenomena emerge when a quantum field is subjected to dynamical perturbations, with prominent examples including the Hawking and Unruh effects, as well as the dynamical Casimir effect. In this work, we compute the number of particles produced via the dynamical Casimir effect in an ideal cavity, where one of the mirrors is allowed to move under the influence of a gravitational wave. Assuming an oscillatory mirror motion and a plane gravitational wave, we identify the resonance conditions that lead to an exponential increase in the number of created particles through parametric amplification.

Figures (2)

• Figure 1: The system. A 3-dimensional cavity that confines the quantum scalar field $\Phi$. We assume that the boundaries of the cavity are formed by perfect mirrors, thus imposing the Dirichlet boundary conditions $\Phi(0,y,z,t)~=~\Phi(L_x,y,z,t)~=~0$, $\Phi(x,0,z,t)~=~\Phi(x,L_y,z,t)~=~0$, and $\Phi(x,y,0,t)~=~\Phi(x,y,L_z(t),t)~=~0$.
• Figure 2: Effective amplification rate. The figure shows coefficient $\chi_{\mathbf{k}}/\epsilon \kappa$ as a function of the cavity frequency $\Omega_c$ for different values of $\Omega_g$ (assuming $h=\kappa \Omega_g^2$, as typically expected for an oscillating binary system). We considered a cubic cavity of length $L$ and a fixed pair of modes $\mathbf{k}=(2,1,2)$ and $\mathbf{j}=(2,1,1)$, computing $\chi_{\mathbf{k}}/\epsilon \kappa$ solely as a function of $\Omega_c$. This was done by expressing the unperturbed field frequencies in terms of the cavity length $L(\Omega_c)$ required to satisfy the resonance conditions. The dashed lines indicate the values of $\Omega_c$ for which the corresponding cavity length violates the approximation $L_z \Omega_g \ll 1$ (here we imposed $L_z \Omega_g < 10^{-3}$ for graphical purposes), meaning that our analytical formulas cease to reliably describe the physics of the system in that regime. We emphasize that these results isolate the purely gravitational contribution. In a realistic experimental setup, the standard dynamical Casimir effect (driven by mechanical mirror motion) would dominate the total particle production rate. However, as discussed in the main text, the gravitational contribution possesses a distinct spectral signature which allows, at least in principle, to be distinguished from the mechanical input. Finally, this figure is intended to illustrate the qualitative behaviour, parametric dependencies, and resonant structure of the gravitational interaction in an idealized regime.