Optically levitating dielectrics in the quantum regime

We provide a general quantum theory to describe the coupling of light with the motion of a dielectric object inside a high-finesse optical cavity. In particular, we derive the total Hamiltonian of the system as well as a master equation describing the state of the center-of-mass mode of the dielectric and the cavity-field mode. In addition, a quantum theory of elasticity is used to study the coupling of the center-of-mass motion with internal vibrational excitations of the dielectric. This general theory is applied to the recent proposal of using an optically levitating nanodielectric as a cavity optomechanical system [see Romero-Isart, New J. Phys.NJOPFM1367-263010.1088/ 1367-2630/12/3/033015 12, 033015 (2010); Chang, Proc. Natl. Acad. Sci. USAPNASA60027-842410.1073/pnas.0912969107 107, 1005 (2010)]. On this basis, we also design a light-mechanics interface to prepare non-Gaussian states of the mechanical motion, such as quantum superpositions of Fock states. Finally, we introduce a direct mechanical tomography scheme to probe these genuine quantum states by time-of- flight experiments.