Preparation of a nonlinear coherent state of the mechanical resonator in an optomechanical microcavity

We propose a scheme for generation of a nonlinear coherent state (NCS) of a mechanical resonator (MR) in an optomechanical micro-cavity, in which a two-level quantum dot (QD) and the microcavity are respectively driven by a strong laser and a weak laser. This microcavity can be engineered within a photonic band-gap (PBG) material. By properly tuning the frequency of the weak driving field, two-photon blockade phenomenon occurs. The QD-cavity subsystem can evolve into a dark state due to the damping of the microcavity and the elimination of the decay rate of the QD at selected frequencies in the PBG material. In this situation, the phonon mode of the MR can be prepared into a NCS, which is a non-classical state and possesses the sub-Poisson statistics. We also demonstrate the Wigner function of the NCS, which negativity implies its non-classicality.