Bipartite and tripartite entanglement caused by squeezed drive in magnetic-cavity quantum electrodynamics system

Utilizing optical nonlinearity for generating the entanglement is still a most widely used approach due to its quality and simplicity. Here in this paper, we propose a theoretical scheme to generate bipartite and tripartite entanglement in a cavity quantum electrodynamics (QED) system with one Yttrium iron garnet (YIG) sphere by using a squeezed drive. In such a system, the parametric down-conversion process is used to generate the nonlinearity and further increase the coupling between cavity and YIG. Thus, the enhanced coupling between the microwave cavity photons and the ferromagnetic resonance (FMR) mode/magnetostatic (MS) mode results in bipartite entanglements. By using the mean field theory, we show that the bipartite entanglements strongly depend on the detuning of the cavity and magnon mode. When the driving field is tuned to be resonant with the FMR mode, but the MS mode is far off-resonant, the entanglement between photons and the FMR mode reaches its maximum. However, when the driving field is tuned to be resonant with the MS mode, but the FMR mode is detuned very well, the entanglement between photons and the MS mode reaches its maximum. We show that the dissipation of the FMR/MS mode affects the entanglement greatly, and the bipartite entanglement decreases as the dissipation rate of the FMR/MS mode increases. Under the steady-state approximation, we also show that the tripartite entanglement can be generated, and the minimum residual contangle increases with the enhancement of the nonlinear gain coefficient. With the nonlinearity induced by the parametric down conversion process, the interaction between the driving field and the magnetic-cavity QED system leads to the tripartite entanglement involving the cavity photons, FMR mode and the MS mode. Likewise, we show that the tripartite entanglement also strongly depends on the dissipation rate of MS mode, and the minimum residual contangle increases as the dissipation rate of the MS mode decreases. We also show that the squeezed field induced tripartite entanglement is insensitive to the temperature and has good robustness. Our results suggest that the magnetic-cavity QED system could provide a promising platform for studying the macroscopic quantum phenomena, and the squeezing field opens a new method of generating the entanglement.