Preparation of Nonclassical States in Cavities with a Moving Mirror

We describe how a quantum system composed of a cavity field interacting with a movable mirror can be utilized to generate a large variety of nonclassical states of both the cavity field and the mirror. First we consider state preparation of the cavity field. The system dynamics will prepare a single mode of the cavity field in a multicomponent Schr\"{o}dinger cat state, in a similar manner to that in a Kerr medium. In addition, when two or more cavity modes interact with the mirror, they may be prepared in an entangled state which may be regarded as a multimode generalisation of even and odd coherent states. We show also that near-number states of a single mode may be prepared by performing a measurement of the position of the mirror. Secondly we consider state preparation of the mirror, and show that this macroscopic object may be placed in a Scr\"{o}dinger cat state by a quadrature measurement of the light field. In addition we examine the effect of the damping of the motion of the mirror on the field states inside the cavity, and compare this with the effect of cavity field damping.