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