Dispersive interaction of a Bose-Einstein condensate with the movable mirror of an optomechanical cavity in the presence of the laser phase noise

TL;DR

This paper models the dispersive interaction between a Bose-Einstein condensate and a movable mirror in an optomechanical cavity, highlighting how laser phase noise affects mode coupling and entanglement.

Contribution

It introduces an effective two-mode model capturing the impact of laser phase noise on BEC-mirror interactions in optomechanics.

Findings

Laser phase noise acts as a classical stochastic pump.

Strong mirror-atom entanglement occurs in dispersive regimes.

Entanglement is resilient when modes are in resonance with low noise influence.

Abstract

We theoretically investigate the dispersive interaction of a Bose-Einstein condensate (BEC) trapped inside an optomechanical cavity with a moving end mirror in the presence of the laser phase noise (LPN) as well as the atomic collisions. We assume that the effective frequency of the optical mode is much greater than those of the mechanical and the Bogoliubov modes of the movable mirror and the BEC . In the adiabatic approximation where the damping rate of the cavity is faster than those of the other modes, the system behaves as an effective two-mode model in which the atomic and mechanical modes are coupled to each other through the mediation of the optical field by an effective coupling parameter. We show that in the effective two-mode model, the LPN appears as a classical stochastic pump term which drives the amplitude quadratures of the mechanical and the Bogoliubov modes. It is also shown that a strong stationary mirror-atom entanglement can be established just in the dispersive and Doppler regimes where the two modes come into resonance with each other and the effect of the LPN gets very low.