  We show how to entangle two cavity-magnon polaritons (CMPs) formed by two
strongly coupled microwave cavity and magnon modes. This is realized by
introducing vibration phonons, via magnetostriction, into the system that are
dispersively coupled to the magnon mode. Stationary entanglement between two
CMPs can be achieved when they are respectively resonant with the two sidebands
of the drive field scattered by the phonons, and when the proportions of the
cavity and magnon modes in the two polaritons are appropriately chosen. The
entangled CMPs can improve the detection sensitivity in the dark matter search
experiments using CMPs, and can also lead to the emission of
frequency-entangled microwave photons.
