Coherent feedback ground-state cooling for a mechanical resonator assisted by an atomic ensemble

We propose a coherent feedback cooling method to cool a mechanical resonator to the ground-state energy level in an optomechanical setup working in unresolved sideband regime (USR). The proposed system is composed of a strongly pumped optomechanical cavity coupled to a weakly excited ensemble of two-level atoms and the mechanical resonator is the moving mirror of the cavity. A coherent feedback loop is applied by feeding back a fraction of the output field of the cavity through a controllable beam splitter to the input mirror of the cavity. Under the condition of weak optomechanical coupling, the fluctuation spectrum of the optical force is derived by solving the rate equations of the system in the steady-state mode. The optimal conditions for ground-state cooling to achieve the best cooling performance are obtained by analyzing the optical spectrum of the cavity. The results show that due to the presence of coherent feedback, the effect of the anti-stokes transitions is enhanced which yields better cooling performance. Also, the proposed scheme can work well in the USR and cool down the mechanical resonator almost to the quantum limit of cooling. Moreover, results demonstrate that for non-optimal conditions, the proposed scheme can improve the results significantly.