Interference phenomena in the photon production between two oscillating walls

We study the photon production in a 1D cavity whose left and right walls oscillate with the frequency $\Omega_{L}$ and $\Omega_{R}$, respectively. For $\Omega_{L} \neq \Omega_{R},$ the number of generated photons by the parametric resonance is the sum of the photon numbers produced when the left and the right wall oscillates separately. But for $\Omega_{L} = \Omega_{R}$, the interference term proportional to $\cos \phi$ is found additionally, where $\phi$ is the phase difference between two oscillations of the walls.