Quantum effect in a hybrid bose-einstein condensate opto-magnomechanical system

We present a hybrid opto-magno-mechanical cavity system consisting of an optical cavity that creates an opto-mechanical cavity with a fixed mirror, a magnon mode in a ferrimagnetic crystal linked to the movable mirror and an intracavity Bose-Einstein condensate. The mechanical displacement is coupled to the magnon by the magnetostriction force and to the optical cavity by the radiation pressure, and the latter is also weakly coupled to a Bose-Einstein condensate. We provide a strategy to measure and quantify entanglement using logarithmic negativity. In addition, we study the quantum or EPR steering in order to present the stationary quantum steering. We consider that all composite modes in our model are given in a Gaussian state described by a covariance matrix. In these studies, we focus on the interaction between the Bose-Einstein condensate and the magnonic modes in a ferrimagnetic crystal. It is important to note that we use experimentally controllable realizable parameters to observe the interaction of modes at temperatures in the microkelvin range.