Analysis of stability and near-equilibrium dynamics of self-assembled Casimir cavities

Vacuum fluctuations are a fundamental and irremovable property of a quantized electromagnetic field. These fluctuations are the cause of the Casimir effect---mutual attraction of two electrically neutral metallic plates in vacuum in the absence of any other interactions. For most geometries and materials, the Casimir effect is strictly attractive, leading to the only stable equilibrium configuration with merged plates. Recent observation showed, however, that this unavoidable vacuum-induced attraction can be mitigated by the presence of electrostatic repulsion produced by the formation of double electric layers, and a stable equilibrium between two charged metallic plates in a solution of an organic salt can be reached Munkhbat et al., Nature (London) 597, 214 (2021). Here, we study theoretically in detail equilibrium configurations and their dynamical behavior in the system of two parallel metallic films coupled by the Casimir and electrostatic interactions. We analyze the effect of various parameters of the system---such as the salt concentration and temperature---on the equilibrium cavity thicknesses, inspect resonant properties of the resulting optomechanical system near equilibrium, and examine its stochastic dynamics under thermal fluctuations of the environment.