Steady-state entanglement in a mechanically coupled double cavity containing magnetic spheres

The article delves into the intricate world of steady-state entanglement within a mechanically coupled double cavity system featuring magnetic spheres. It begins by introducing the concept of quantum entanglement and its significance in quantum information technologies. The authors then describe the experimental advancements in preparing entangled qubits and the necessity of interfacing qubits with electromagnetic radiations of different frequencies and modes, commonly supplied by cavities. The focus shifts to cavity optomechanics and the groundbreaking work by Cohadon et al. in 1999, which sparked broad interest in the field. The article proceeds to discuss the entanglement between cavity modes and mechanical oscillators, and the subsequent exploration of macroscopic quantum entanglement in cavity magnomechanical systems. The authors present their own model, which involves two microwave cavities coupled via a movable mirror and containing magnetic YIG spheres. They study both bipartite and tripartite entanglement between photons, magnons, and phonons. The effects of various parameters, such as detunings, dissipations, coupling rates, and temperature, on the entanglement properties are meticulously analyzed. The authors conclude by highlighting the robustness of the entanglement against environmental temperature and the potential applications of their model in quantum information processing and quantum sensing. The article is rich in technical detail and offers valuable insights into the complex dynamics of entanglement in cavity magnomechanical systems.