Entanglement and squeezing of gravitational waves

Abstract

We show that the self-interactions present in the effective field theory formulation of general relativity can couple gravitational wave modes and generate nonclassical states. The output of gravitational nonlinear processes can also be sensitive to quantum features of the input states, indicating that nonlinearities can act both as sources and detectors of quantum features of gravitational waves. Due to gauge and quantization issues in strongly curved spacetimes, we work in the geometric optics limit of gravitational radiation, but we expect the key ideas extend to situations of astrophysical interest. This offers a new direction for probing the quantum nature of gravity, analogous to how the quantumness of electrodynamics was established through quantum optics.

Figures (3)

• Figure 1: Nonlinear interactions as sources of nonclassical GWs. Top: mean number of gravitons as a function of time for modes $\vec{k}_{0}, \vec{k}_{0} + \vec{k}_{L}$ and $\vec{k}_{0} +2\vec{k}_{L}$. The initial number of quanta in mode $\vec{k}_{0}$ is $N_{0}= 10^{38}$. Middle: Squeezing degree $\mathcal{S}$ and squeezed variance $V_{\mathrm{sq}}$ of mode $\vec{k}_{0}$. Bottom: Entanglement of modes $\vec{k}_{0}$ and $\vec{k}_{0}+\vec{k}_{L}$, quantified by the logarithmic negativity $\mathcal{N}(\vec{k}_{0}, \vec{k}_{0}+\vec{k}_{L})$.
• Figure 2: Nonlinear interactions as detectors of nonclassical GWs. Mean number of gravitons in mode $\vec{k}_{0}+\vec{k}_{L}$ as a function of time for different initial states of mode $\vec{k}_{0}$. All initial states have the same mean number of quanta $N_{0}$.
• Figure 3: Maximum logarithmic negativity as a function of the amplitude $\mathcal{A}$ for different values of the perturbation parameter $\epsilon$.