Dynamics of Nano-Particles Inside an Optical Cavity in the Quantum Regime

We investigate the optomechanical effect on a single nano-particle inside an optical cavity, by deriving forces acting cavity from quantum theory. obtain steady state of system and found that force contains three terms associated with gradient force, back-action resulting intra-cavity photon energy change, as well reactive coupling between external field cavity. Moreover, we solve dynamical for dielectric particle in small mode volume which is characterized quasi-periodic pattern. These results are important understanding control various types levitated nano-particles through coupling.