Abstract
We investigate the effect of the Casimir force on the entanglement in an optomechanical system formed by a Fabry-P\'erot cavity with a dielectric nanosphere trapped near the cavity mirror by external driving laser beams. We find that steady-state optomechanical entanglement can be generated via the Casimir interaction between the nanosphere and the mirror, even with only one driving laser. With two driving lasers that are simultaneously responsible for trapping and cooling, the Casimir effect may enhance or reduce the degree of the steady-state optomechanical entanglement, depending on the cavity detunings, the strength of the Casimir interaction, the driving powers, and the cavity decay rates. The Casimir effect leads to an oscillation frequency shift of the nanosphere in the optomechanical system, which could be used for estimating the magnitude of the Casimir force between a sphere and a plane.
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