Master equation for photon mediated phonon–atom coupled system

Achieving phonon–atom couplings in cavity optomechanical system could lead to fundamentally new regimes of phonon–matter interaction and the development of sensitive mass and force sensors. Here we derive a master equation to describe the phonon–atom system and numerically simulate the equation. The phonon–atom coupling is mediated by a driven cavity mode. A crossover from the bad cavity limit, which validates the master equation, to the limit of small cavity loss rate is studied.