Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field

We perform a theoretical investigation into the classical and quantum dynamics of an optical field in a cavity containing a moving membrane (“membrane-in-the-middle” setup). Our approach is based on the Maxwell wave equation and complements previous studies based on an effective Hamiltonian. The analysis shows that for slowly moving and weakly reflective membranes the classical field dynamics can be approximated by first-order-in-time evolution …