Controlling steady-state bipartite entanglements and quadrature squeezing in a membrane-in-the-middle optomechanical system with two Bose-Einstein condensates

TL;DR

This paper theoretically investigates a hybrid optomechanical system with two Bose-Einstein condensates, demonstrating control over entanglement and squeezing via the scattering frequency and trapping parameters.

Contribution

It introduces a method to control entanglement and squeezing in a membrane-BEC system through the scattering frequency of the condensates, linking it to experimentally adjustable trapping frequencies.

Findings

Entanglement between BECs and membrane can be tuned by scattering frequencies.

Squeezing of BECs can be controlled via trapping frequency adjustments.

The system allows for external control of quantum correlations in optomechanical setups.

Abstract

We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave scattering frequency of the other one. Since the \textit{s}-wave frequency of each BEC depends on the transverse trapping frequency of the atoms which is an experimentally controllable parameter, one can control the entanglement and squeezing of each BEC through the trapping frequency of the other one.