Dynamics of levitated nanospheres: towards the strong coupling regime

The use of levitated nanospheres represents a new paradigm for the optomechanical cooling of a small mechanical oscillator, with the prospect of realizing quantum oscillators with unprecedentedly high quality factors. We investigate the dynamics of this system, especially in the so-called self-trapping regime, where one or more optical fields simultaneously trap and cool the mechanical oscillator. The determining characteristic of this regime is that both the mechanical frequency omega(M) and single-photon optomechanical coupling strength parameters g are a function of the optical field intensities, in contrast to usual set-ups where omega(M) and g are constant for the given system. We also measure the characteristic transverse and axial trapping frequencies of different sized silica nanospheres in a simple optical standing wave potential, for spheres of radii r = 20-500 nm, illustrating a protocol for loading single nanospheres into a standing wave optical trap that would be formed by an optical cavity. We use these data to confirm the dependence of the effective optomechanical coupling strength on sphere radius for levitated nanospheres in an optical cavity and discuss the prospects for reaching regimes of strong light-matter coupling. Theoretical semiclassical and quantum displacement noise spectra show that for larger nanospheres with r greater than or similar to 100 nm a range of interesting and novel dynamical regimes can be accessed. These include simultaneous hybridization of the two optical modes with the mechanical modes and parameter regimes where the system is bistable. We show that here, in contrast to typical single-optical mode optomechanical systems, bistabilities are independent of intracavity intensity and can occur for very weak laser driving amplitudes.