Optomechanical Entanglement Between an Ion and an Optical Cavity Field

I study an optomechanical system in which the mechanical motion of a single trapped ion is coupled to a cavity field for the realization of a strongly quantum correlated two-mode system. I show that for large pump intensities the steady state photon number exhibits bistable behaviour. I further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the ion motion which indicates a coherent energy exchange. I also find that in the parameter regime where NMS exists, the steady state of the system shows continuous variable entanglement. Such a two-mode optomechanical system can be used for the realization of continuous variable quantum information interfaces and networks.