Non-Gaussian mean-field method for self-sustaining optomechanical system

Abstract We introduce a simulation method based on a mean-field theory to treat the entire dynamical process of an oscillator in a self-sustaining optomechanical system, including the absorbed energy, up to the formation of a stable limit cycle. Higher-order nonlinear effects are taken into account and the non-Gaussian amplitude (phase) distribution is characterized by analyzing a set of linearized fluctuation equations in amplitude–phase representation. This method has the same applicability as full numerical simulations with stochastic Langevin equations, but it can greatly reduce the required computational resources. The non-Gaussian dynamics of the oscillator can be largely understood from the evolution of the phase fluctuation in the non-stationary phase, which cannot be described by a constant diffusion factor. Finally, we discuss the generalization of this method to multi-mode systems and show the potential of this method to solve complex quantum problems, such as quantum synchronization.