Gaussian geometric discord, entanglement and EPR steering of two rotational mirrors in a double-Laguerre-Gaussian cavity optomechanics in the presence of YIG sphere

Abstract

We propose a theoretical scheme to study stationary Gaussian quantum steering, entanglement, and Gaussian geometric discord (GGD) between two spatially separated rotating mirrors (RMs) in a double-Laguerre-Gaussian cavity (DLGC). Each cavity is driven by a Laguerre-Gaussian (LG) beam. A Yttrium Iron Garnet (YIG) sphere is placed at the intersection of the two cavities. Gaussian quantum steering characterizes steerability, while logarithmic negativity quantifies entanglement. Our analysis reveals that the entanglement between the two Rms is strongly influenced by temperature, magnon mode detuning, the orbital angular momentum (OAM) of the LG modes, magnon-cavity coupling strength, and the mass of the RMs. The magnon-photon coupling emerges as a key parameter for controlling and manipulating the RMs entanglement. A weak mass of the RMs serves to be an advantageous factor that improves the amount of entanglement and makes it strong in the face of thermal effects. GGD increases with rising RMs mass. Within experimentally accessible parameters, we achieve two-way steering. The GGD shows a robustness against thermal effects compared to entanglement and steering.