Entangling two cavity modes and squeezing magnon mode via parametric down-conversion

A scheme to entangle two cavity modes and squeeze magnon mode in a magnon-cavity QED system is presented, where the two microwave cavity modes are coupled to a massive yttrium iron garnet sphere. The nonlinearity used in our system originates from parametric down-conversion. By using the mean field approximation and employing experimentally feasible parameters, we indicate that the entanglement between squeezed cavity mode and magnon mode can be transferred to the other cavity mode and magnon mode, and then the two cavity modes get entangled. Meanwhile, the magnon mode is squeezed in our QED system. Furthermore, we show that it is a good way to enhance entanglement and squeezing by increasing the nonlinear gain. Our results denote that magnon-cavity QED system is a powerful platform for studying macroscopic quantum phenomena, which illustrates a new approach to photon-photon entanglement and magnon squeezing.