Electromagnetically and optomechanically induced transparency and amplification in an atom-assisted cavity optomechanical system

We propose an atom-assisted cavity optomechanical system consisting of a single $\mathrm{\ensuremath{\Lambda}}$-type three-level atom, a mechanical resonator, and a sideband-driven cavity. The analytic expression of the system's evolution is constructed under the consideration of sideband-driven fields, then steady-state solution of electromagnetically and optomechanically induced transparency and amplification is presented. In the resolved red sideband case, we demonstrate the appearance of electromagnetically and optomechanically induced transparency when the two sets of two-photon resonances are satisfied. Moreover, we set up the eigenstate structure for this atom-assisted cavity optomechanical system, which gives an explicit explanation for the mechanism of the transparency. In the resolved blue sideband case, we can achieve the controllable amplification of the probe light, which is induced by the constructive interactions of photon, atom, and phonon. The proposed scheme offers insight for the tripartite coherent interaction among photons, atoms, and phonons, which will provide great flexibility for phonon storage and motivate the development of quantum information processing.