Generating Asymmetric Einstein–Podolsky–Rosen Steering between Two movable Mirrors Exploiting Correlated-Emission Laser

Abstract

Quantum steering is a form of quantum correlation that exhibits an inherent asymmetry, distinguishing it from entanglement and Bell nonlocality. It is now understood that quantum steering plays a pivotal role in asymmetric quantum information tasks. In this work, a scheme is proposed to generate asymmetric steering between two mechanical modes by transferring quantum coherence from a correlated-emission laser. To accomplish this, quantum Langevin equations is derived to describe the optomechanical coupling between two cavity modes and two mechanical modes along with the master equation of two-mode laser. By examining the case where the cavity modes scatter at the anti-Stokes sidebands, it is demonstrated that both two-way and one-way steering can be achieved by adjusting the strength of the field driving the gain medium of the laser. Furthermore, it is showed that the direction of one-way steering can be controlled by varying the temperatures of the mechanical baths or the strengths of the optomechanical couplings. Additionally, it is revealed that the directionality of one-way steering depends on the modes fluctuation levels of the modes, with the mode exhibiting larger fluctuations determining the direction. This highly controllable scheme could potentially be realized with current technology, offering a promising platform for implementing one-way quantum information tasks.