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We provide a general quantum theory to describe the coupling of light withthe motion of a dielectric object inside a high finesse optical cavity. Inparticular, we derive the total Hamiltonian of the system as well as a masterequation describing the state of the center of mass mode of the dielectric andthe cavity field mode. In addition, a quantum theory of elasticity is used inorder to study the coupling of the center of mass motion with internalvibrational excitations of the dielectric. This general theory is applied tothe recent proposal of using an optically levitating nanodielectric as a cavityoptomechanical system [Romero-Isart et al. NJP 12, 033015 (2010), Chang et al.PNAS 107, 1005 (2010)]. On this basis, we also design a light-mechanicsinterface to prepare non-Gaussian states of the mechanical motion, such asquantum superpositions of Fock states. Finally, we introduce a directmechanical tomography scheme to probe these genuine quantum states by time offlight experiments.

Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols