Master-equation treatment of nonlinear optomechanical systems with optical loss

TL;DR

This paper develops an analytical solution to the Lindblad master equation for nonlinear optomechanical systems with optical loss, enabling better understanding of decoherence effects on intracavity states.

Contribution

It introduces a novel Lie-algebra based method to solve the master equation for nonlinear optomechanical Hamiltonians with optical decoherence.

Findings

Analytical solution for the Lindblad master equation in nonlinear optomechanics.

Assessment of optical decoherence impact on optical cat states.

Method applicable to a broad class of nonlinear quantum systems.

Abstract

Open-system dynamics play a key role in the experimental and theoretical study of cavity optomechanical systems. In many cases, the quantum Langevin equations have enabled excellent models for optical decoherence, yet a master-equation approach to the fully nonlinear optomechanical Hamiltonian has thus far proven more elusive. To address this outstanding question and broaden the mathematical tool set available, we derive a solution to the Lindblad master equation that models optical decoherence for a system evolving with the nonlinear optomechanical Hamiltonian. The method combines a Lie-algebra solution to the unitary dynamics with a vectorization of the Lindblad equation, and we demonstrate its applicability by considering the preparation of optical cat states via the optomechanical nonlinearity in the presence of optical loss. Our results provide a direct way of analytically assessing the impact of optical decoherence on the optomechanical intracavity state.