Dynamics and spectral response of linear-quadratic optomechanical interaction: effects of pure dephasing

Abstract In this paper, the decoherence dynamics and spectral response of an optomechanical system, with linear and quadratic couplings, is addressed. The decoherence considered arises from pure dephasing, described by the Milburn stochastic evolution of the Schrödinger equation. In the first part of this paper, it is shown how the decoherence rate influences the evolution of the number of phonons, and the quadrature of the mechanical resonator. In the second part of the paper, an attempt to look at the spectral response of the mechanical part of the system is given using non-stationary spectroscopy. The response of the resonator in its equilibrium position is emphasized when the single-photon regime is considered. Coherent states in the cavity field and the mechanical resonator are also represented. Results and discussion comparing the inclusions of the linear, quadratic, and linear-quadratic couplings are given, regarding the influence of the dephasing in the decoherence mechanism.