Optomechanical simulation of a time-dependent parametric oscillator

Abstract

We explore a finite element model of a standard one-dimensional photonic crystal cavity etched on a nanobeam designed to enhance optomechanical coupling. We theoretically demonstrate that polychromatic driving of the mechanical sidebands produces an effective Hamiltonian model showing optical self- and cross-Kerr terms and parametric interaction between the optical and mechanical modes. For the sake of providing an example, we show that bi-chromating driving, near the first and second red-sidebands, produces an analog simulation of a mechanical parametric oscillator that exhibits a squeezed vacuum ground state in the time-independent case, and in the time-dependent case, the evolution of the mechanical ground state produces displaced squeezed vacuum.