Analysis and estimation of the threshold for a microwave "pellicle mirror" parametric oscillator, via energy conservation

An experiment is proposed to observe the dynamical Casimir effect by means of two tandem, high Q, superconducting microwave cavities, which are separated from each other by only a very thin wall consisting of a flexible superconducting membrane that can be driven into motion by means of resonant "pump" microwaves injected into the left cavity. Degenerate "signal" and "idler" microwave signals can then be generated by the exponential amplification of vacuum fluctuations in the initially empty right cavity, above a certain threshold. The purpose of this paper is calculate the threshold for this novel kind of opto-mechanical parametric oscillation, using energy considerations.