  The dynamics of arbitrary-order quantum correlations in a cavity
magnon-polariton system are investigated based on the quantum master equation
in the coherent state representation. The phenomena of Rabi-like oscillation
and level repulsion of the average cavity-photon number agree remarkably well
with existing experimental observations. The competing nature of coherent and
incoherent components in these two cases is further revealed by the
second-order quantum coherence of the cavity photons and magnons, which can be
systematically tuned by the driving microwave and thermal bath. Our results
demonstrate the rich higher-order quantum dynamics induced by magnetic
light-matter interaction, and serve as an indispensable step toward exploring
nonclassical states for cavity photons and magnons in quantum cavity magnonics.
