Entangled atomic ensemble and an yttrium-iron-garnet sphere in coupled microwave cavities

We present a scheme to generate distant bipartite and tripartite entanglement between an atomic ensemble and an yttrium iron garnet (YIG) sphere in coupled microwave cavities. We consider an atomic ensemble in a single-mode microwave cavity which is coupled with a second single-mode cavity having a YIG sphere. Our system, therefore, has five excitation modes, namely, cavity-1 photons, an atomic ensemble, cavity-2 photons, a magnon and a phonon mode in the YIG sphere. We show that significant bipartite entanglement exists between indirectly coupled subsystems in the cavities which is robust against temperature. Moreover, we present suitable parameters for a significant tripartite entanglement of the ensemble, magnon, and phonon modes. We also demonstrate the existence of tripartite entanglement between the magnon and phonon modes of the YIG sphere with indirectly coupled cavity photons. Interestingly, this distant tripartite entanglement is of the same order as that previously found for a single-cavity system. We show that cavity-cavity coupling strength affects both the degree and transfer of quantum entanglement between various subsystems. Therefore, an appropriate cavity-cavity coupling optimizes the distant entanglement by increasing the entanglement strength and its robustness against temperature.