Sensing Quantum Nature of Primordial Gravitational Waves Using Quantum Electromagnetic Fields.

We establish a new formalism to describe the interaction of an optical system with a background of gravitational waves based on optical medium analogy. Besides reproducing the basic formula for the response of a LISA-type interferometer in terms of the phase shift of light, other classical observables of the electromagnetic field such as light-bending, walk-off angle and Stokes parameters are investigated. At the quantum level, this approach enables us to construct a full quantum Hamiltonian describing both electromagnetic and gravitational waves as quantum entities. It turns out that the effective coupling between the electromagnetic field and gravitational wave background resembles an opto-mechanical coupling. This points to a new strategy to evident non-classical nature of gravity within the reach of future optical experiments. As an illustrative application, we investigate the optical quadrature variance as well as the power spectrum of a laser field interacting with a background of primordial gravitational wave. The effect of the relic background of quantized gravitational waves on the optical variance is analogous to the effect of a classical mechanical oscillator, which stabilizes the optical variance. It also acts similar to a Doppler-broadening mechanism which broadens the line-width of the laser field of optical frequency by $10^{-6}$Hz. This line-width broadening and also appearance of side-bands in the spectrum of light could serve as signatures of the highly squeezed nature of primordial gravitational waves.