Sensing Quantum Nature of Primordial Gravitational Waves Using Quantum Electromagnetic Fields
Abstract
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 LISAtype interferometer in terms of the phase shift of light, other classical observables of the electromagnetic field such as lightbending, walkoff 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 optomechanical coupling. This points to a new strategy to evident nonclassical 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 Dopplerbroadening mechanism which broadens the linewidth of the laser field of optical frequency by $10^{6}$Hz. This linewidth broadening and also appearance of sidebands in the spectrum of light could serve as signatures of the highly squeezed nature of primordial gravitational waves.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10962
 Bibcode:
 2021arXiv211010962S
 Keywords:

 General Relativity and Quantum Cosmology;
 81V10
 EPrint:
 11 pages, 3 figures