Hybrid Einstein-Podolsky-Rosen steering in an atom-optomechanical system

Einstein-Podolsky-Rosen steering manifests a type of quantum correlations intermediate between entanglement and Bell nonlocality. In this paper we propose a scheme for realizing hybrid atom-mechanical quantum steering in the steady-state regime. In our scheme, an optomechanical two-mode cavity is coupled to a distant ensemble of double- atoms in a cascade way, which induces the dissipative interaction between the mechanics and the internal atomic states. We show that strong cavity dissipation can lead to two-way atom-mechanical steering and the optimal steering exhibited in an approximate two-mode squeezed-vacuum atom-mechanical state. Moreover, we find that for the present cascade coupling scheme, the one-way steering from the mechanical oscillator to the atoms is achievable under certain conditions, while the reverse one-way steering is impossible to obtain. The reason for achieving the asymmetric steering is analyzed and the effect of mechanical thermal noise on the steering is also studied.