Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system

Abstract

We study multi-partite entanglement, the generation of EPR states and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beamsplitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other.

Quantum steering and entanglement in three-mode triangle Bose–Hubbard system

“…They were considered in discussions of various physical systems. For example, there were three-mode optomechanical system composed of an atomic ensemble located in a cavity comprising oscillating mirror [43], double-cavity optomechanical model with two separate electromagnetic fields mediated by a mechanical oscillator [44] or optical cavity field and the mechanical oscillator system [45].…”

Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling

“…The steering strengths in two directions may not be the same [22], especially, a special type is known as one-way EPR steering where the entangled states show steering in one direction but not in the other [7,23]. The asymmetric EPR steering has attracted considerable attention recently for both theory [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and experiment [14,23,[41][42][43][44][45][46]. One important method used in above studies to produce directional steering is making the states asymmetric by adding different amount of losses or noises on the subsystems.…”

Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir

“…Reservoir engineering has earlier been the subject of significant theoretical study in the context of optical and atomic systems [7,[21][22][23][24][25][26], culminating in the experimental demonstration by Krauter and coworkers of the entanglement of atomic ensembles [27]. The utility of reservoir engineering has also been shown with two-level systems, with demonstrations of superconducting qubit state control [28], as well as entanglement in both trapped ion [29] and superconducting [30] systems.…”