Generalized Rotating‐Wave Approximation for the Quantum Rabi Model with Optomechanical Interaction

Abstract

AbstractThe spectrum of energy and eigenstates of an hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction are investigated. In the spirit of approximations developed for the quantum Rabi model beyond rotating‐wave approximation (RWA), the so‐called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings is implemented. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a Rabi model with dressed atom‐field states (polaritons) coupled to mechanical modes through reparametrized coupling strength and Rabi frequency. A more accurate energy spectrum for a wide range of values of the atom‐photon and photon–phonon couplings, when compared to the RWA results is found. The fidelity between the numerical eigenstates and its approximated counterparts is also calculated. The degree of polariton‐phonon entanglement of the eigenstates presents a non‐monotonic behavior as the atom‐photon coupling varies, in contrast to the characteristic monotonic increase in the RWA treatment.