  Based on optical medium analogy, we establish a formalism to describe the
interaction between an electromagnetic (EM) system with gravitational waves
(GWs) background. After a full discussion on the classical treatment of the
EM-GW interaction and finding the EM field mode-functions in the presence of
the magneto-dielectric media caused by GWs, the governing quantum interaction
Hamiltonian is obtained. Investigation of the optical quadrature variance as
well as the visibility of a laser field interacting with the multi-mode
squeezed primordial gravitational waves imply that the inflationary primordial
gravitational waves (PGWs) act as a decoherence mechanism that destroy EM
coherency after a characteristic time scale, $\tau_{c}$, which depends on the
inflationary parameters $(\beta,\beta_s,r)$, or equivalently, the fractional
energy density of PGWs, $\Omega_{gw,0}$. The decoherency mechanism overcomes
the coherent effects, such as revivals of optical squeezing, thus leaving their
confirmation out of reach. Influenced by the continuum of the squeezed PGWs,
the laser field suffers a line-width broadening by $\gamma=
\tau_{\text{c}}^{-1}$. The most peculiar property of the EM spectrum is the
apparition of side bands at $\omega\sim \omega_0\pm 1.39 \tau_c^{-1}$Hz,
stemming from the squeezed nature of PGWs. The laser phase noise induced by the
squeezed PGWs grows with time squarely, $\Delta\phi=(t/\tau_c)^2$, that can
most possibly be sensed within a finite flight time.
