We propose to optically levitate a dielectric nano-dielectric inside a high-finesse optical cavity in order to couple its mechanical center-of-mass motion to the optical cavity field. This opto-mechanical system has the unique feature of not
having thermal contact to other objects. We analyze the main sources of decoherence: scattering of the surrounding gas, scattering of light, and coupling to the other modes, and show that for sufficiently small objects these sources of noise are also negligible. Therefore, the center-of-mass is effectively isolated. Then we propose different protocols to couple the mechanical motion with the field out of the cavity, and to use non-Gaussian states of light to prepare non-Gaussian states of the mechanical object, such as superposition of Fock states. This is an effective way to obtain non-linearities in quantum opto-mechanical systems. We analyze how tomography of the mechanical state can be performed by time-of-flight experiments, exploiting the analogy of levitating objects with atomic physics. We also argue that time-of-flight experiments can be used to prepare macroscopic superposition states of nano-spheres (preparing the center-of-mass in a superposition of two positions separated by a distance of the order of the radius of the sphere), and discuss how this can be used to test objective reduction of the wave-function models. Finally, we argue that the theory presented here for dielectric nano-spheres can be extended to arbitrarily shaped dielectric objects, and in particular even to microorganisms.