Cavity-QED Transducer of Gravitons

Abstract

We develop a quantum description of the resonant interaction between electromagnetic (EM) and gravitational waves (GW). We first show that Lorentz invariance together with polarization selection rules forbids any photon-graviton mixing in free space. We demonstrate that confining the EM field within a cavity quantum electrodynamics (cavity-QED) environment breaks translational symmetry and isotropy, leading to non-vanishing mode coupling between EM and gravitational degrees of freedom. Within this framework, we identify multiple photon-graviton scattering channels, including photon up- and down-conversion and photon creation. In the semiclassical limit of the trilinear interaction where GW acts as a classical pump and the EM field is in a vacuum, spontaneous parametric photon amplification and two-mode squeezing occur. When the gravitational field is quantized, however, the back-action and energy exchange between photons and gravitons result in saturation of amplification, in contrast to exponential growth, and the loss of purity in the photonic subsystem. The characteristic timescale scales as $t_{\text{sp}}\sim (g\sqrt{n_g})^{-1}$, where $g$ and $n_g$ refer to the coupling strength and the mean graviton number, demonstrating collective enhancement of the interaction with the graviton occupation number. In the stimulated regime, where one EM mode is initially populated, the effective coupling is further enhanced, analogous to Dicke-type superradiant emission. This work introduces a cavity-based graviton transducer for probing quantum aspects of GWs.

Figures (3)

• Figure 1: Schematic view of a rectangular cavity of size $V=L_xL_yL_z$ illuminated by a plus-polarized mono-mode GW propagating in $\hat{\mathbf{K}}=(\sin\Theta_K\cos\Phi_K, \sin\Theta_K\sin\Phi_K,\cos\Theta_K)$ direction.
• Figure 2: The mean number of particles in GW mode $K$, collective EM mode $\hat{c}$ and EM degenerate modes $\hat{a}_{\beta_1}, \hat{a}_{\beta_2}, \hat{a}_{\beta_2}$ versus the dimensionless timescale $\tau = g t$, shown in purple, black, red, blue and green, respectively. Initial graviton content in coherent state is taken $n_g=50$. Note that the classical hyperbolic amplification is $2\sinh^2(r) = \sinh^2 (|g|\,\sqrt{24}\, t) = \sinh^2(\sqrt{24} \,\tau)$, as shown by the gray dashed line.
• Figure 3: The purity $\mu_{\alpha c}(\tau)$ versus the reduced timescale $\tau=gt$. The reference purity (classical GW) $\mu_{\alpha c}=1$ is shown by the gray dashed line. The inset shows the early-time abrupt decrease of purity.