PATH INTEGRAL APPROACH TO A DAMPED AND DRIVEN OSCILLATOR COUPLED WITH ANOTHER ONE

Abstract

We approach the case of two coupled oscillators where the first one may correspond to a photonic field, while the second one is damped and driven. We model the oscillator's damping via a bath and consider the relevant master equation. We use perturbation theory to handle it. We then path integrate over the effective Hamiltonian of the two oscillators and derive the path integrated density matrix. We suppose that initially both of the oscillators are in coherent states and study the quadrature squeezing effect of the second oscillator.