Dynamics of the quantized radiation field in an oscillating cavity in the harmonic resonance case

Abstract

We investigate the dynamics of the quantized radiation field in an oscillating cavity described by the effective resonance Hamiltonians H = Omega Sigma(k=1)(infinity) ka(k)(dagger)a(k) + epsilon Omega Sigma(k=1)(infinity) root k(k + j)[a(k)(dagger)a(k+j) + a(k+j)(dagger)a(k)] + epsilon Omega H-(p) where epsilon characterizes the oscillating amplitude of the moving boundary of the cavity, the boundary oscillates with the jth unperturbed eigenfrequency (j = 1, 2, 3,...) and the parametric oscillator part H(p) contains only a few terms to be specified in the main text. We present the exact diagonalization forms of the effective Hamiltonians for j = 1, 2, 3,... in the absence of the parametric oscillator part H-(p). A systematic procedure is then developed to obtain the analytical solutions of the Hamiltonians in the presence of the part H(p) accurate up to order epsilon(k) for an arbitrary positive integer k. In this way, we can investigate the dynamics of the corresponding quantized radiative field by explicitly presenting the analytical expressions of the diagonalized Hamiltonians, the time-varying annihilation and creation operators as well as photon number operators for the radiative field, accurate up to any desired order of the dimensionless oscillating amplitude. The analytical expressions of these quantities up to order epsilon(4) are also explicitly presented.