Generation of hybrid entanglement between a mirror and a trapped ion

Abstract: We present a scheme for cavity-assisted generation of hybrid entanglement between a moving mirror belonging to an optomechanical cavity and a single trapped ion located inside a second cavity. Due to radiation pressure, it is possible to entangle the moving mirror with one of the cavity fields. Also, by tuning the second cavity field with the internal degrees of freedom of the ion, an entangled state of the cavity field/ion can be independently generated. The fields leaking from each cavity are then combined in a beam-splitter, and following the detection of the outgoing photons by conveniently placed photodetectors, we show that it is possible to generate entangled states of the moving mirror and the single trapped ion subsystems. In our scheme the generated states are hybrid entangled states, in the sense that they are constituted by discrete (Fock) states and continuous variable (coherent) states.