Steady-state entanglement in levitated optomechanical systems coupled to a higher order excited atomic ensemble

We investigate the steady-state entanglement in an optomechanical system with a levitated dielectric nanosphere and a higher order excited atomic ensemble. The single nanosphere is trapped by an external harmonic dipole trap and coupled to the single-mode cavity field by the effective optomechanical coupling, which depends on the steady-state position of the nanosphere. We show that the steady-state optomechanical entanglement can be generated via the effective optomechanical interaction between the mechanical motion and the cavity mode. Further, these exist an optimal effective cavity detuning that maximizes the optomechanical entanglement. We also analyze in detail the influences of the excitation number of atoms, the radius of the nanosphere and the thermal noise strength on the steady-state optomechanical entanglement. It is found that the steady-state entanglement can be enhanced by increasing the excitation number of atoms and the radius of the nanosphere.