Generalization of damping theory for cavities with mirrors of finite transmittivity

Standard damping theory is generalized to incorporate the effects of finite mirror transmittivity. The correction to the standard Langevin equation for the quasimode annihilation operator is determined in first order in the transmittivity of the mirrors. From the Langevin equation an effective master equation is derived. As an example, we study the decay of a single two-level atom at a fixed position in a nonideal cavity. For this case we find a modification of the damped Rabi oscillations, which depends on the atomic position. {} 1996 The American Physical Society.