Photon Generation and Squeezing in a Cavity with Vibrating Walls

Abstract

The problem of the electromagnetic field inside cavities with moving walls attracted the attention of researchers beginning with early sixties. Exact solutions for uniformly moving boundaries were found in [1] for the classical field and in [5] for the quantized field. Approximate solutions valid for an arbitrary nonrelativistic law of motion of a boundary were proposed in [3] (quantized field) and [4] (classical field) . They were used to investigate the case of an oscillating boundary (which seems the most interesting from the point of view of possible experimental realizations) in [5]. However, these solutions hold only in the adiabatic case, when the frequency of wall’s vibrations is much smaller than the frequency of some unperturbed electromagnetic mode. Consequently, no photons can be created under such conditions. The evolution of the classical field in the case when both the frequencies were close to each other was investigated in [6]. Here the solution of the quantum problem in the resonance case is presented.