  We propose a scheme to generate entanglement between two cavity modes and
squeeze magnon mode in a magnon-cavity QED system, where the two microwave
cavity modes are coupled with a massive yttrium iron garnet (YIG) sphere
through magnetic dipole interaction. The nonlinearity used in our system
originates from a squeezed driving via parametric down-conversion process,
which is the reason to cause entanglement and squeezing. By using the mean
field approximation and employing experimentally feasible parameters, we
demonstrate that the system shows zero entanglement and squeezing without
squeezed driving. Meanwhile, our QED system denotes that the entanglement
between squeezed cavity mode and magnon mode can be transferred to the other
cavity mode and magnon mode via magnon-cavity coupling interaction, and then
the two cavity modes get entangled. A genuinely tripartite entangled state is
formed. We also show that magnon mode can be prepared in a squeezed state via
magnon-cavity beam-splitter interaction, which is as a result of the squeezed
field. Moreover, we show that it is a good way to enhance entanglement and
squeezing by increasing the nonlinear gain coefficient of squeezed driving. Our
results denote that magnon-cavity QED system is a powerful platform for
studying macroscopic quantum phenomena, which illustrates a new method to
photon-photon entanglement and magnon squeezing.
