determines whether one can attain strong coupling regimes in levitated systems such as recently observed in a non-levitated set-up [@strong]. It determines too whether one may access other interesting dynamics, both in the semiclassical and quantum regimes. We consider in particular the possibility of simultaneous hybridization of the two optical modes with the mechanical mode; here, we consider also the implications of a static bistability, which, unusually, occurs also in the limit of quite weak driving in the levitated self-trapped system.

In the present work, we investigate theoretically and experimentally the strength of the optomechanical coupling. In particular, we present experimental measurements of the mechanical frequency of a nanosphere trapped in an optical standing wave in order to investigate the optical coupling as a function of the size of the nanosphere.

In section 1 we review the theory of the cavity cooling and dynamics of a self-trapped system, and in section 2 we employ the experimentally measured size dependence of the coupling to determine the range of optomechanical coupling strengths accessible in a cavity. The data suggests that the most effective means to attain stronger coupling will be to employ larger nanospheres of typical radii $r=200-300$nm. Our work suggests that 