Kerr-like nonlinearities in an optomechanical system with an asymmetric anharmonic mechanical resonator

Abstract

A typical optomechanical system with a mechanical resonator realizing anharmonic oscillations in linear and cubic potentials is studied. Using the Bogoliubov averaging method in the nonsecular perturbation theory, the effective Hamiltonian of the system is constructed. The cross-Kerr interaction of photons and vibration quanta as well as the Kerr-like mechanical self-interaction arises in the Hamiltonian. The Kerr and Kerr-like interactions are induced by both the cubic nonlinearity of oscillations of the mechanical resonator and the cavity-resonator interaction linear in mechanical displacements. This approach correctly describes also the hybrid system consisting of a quantum dot and a nanocavity mediated by a mechanical resonator without leading to non-Hermitian terms in the effective Hamiltonian. The obtained results offer new possibilities for describing optomechanical systems with asymmetric mechanical oscillations.