  Cavity electromagnonics has increasingly emerged as a new platform for the
fundamental study of quantum mechanics and quantum technologies. Since the
coupling between the microwave field and magnon Kittle modes in current
experiments is much weaker than their resonant frequencies, the anti-rotating
terms in magnon-microwave-photon interaction can be neglected and only the
beam-splitter-like part takes effect. In this situation, the direct generation
of magnonic nonclassical states is impossible, unless other subsystems e.g.
phonons, squeezed photons or superconducting qubits are incorporated. In this
paper, we consider two-tone modulated cavity electromagnonics to keep the
nontrivial anti-rotating terms and obtain tunable phase factors, resulting in
an effective Hamiltonian exactly the same as that of generic linearized cavity
optomechanics. This can therefore be exploited to directly prepare macroscopic
magnonic quantum states, as detailedly exemplified by the generation of steady
and strongly squeezed and entangled states, realize ultra-sensitive
magnon-based sensing by engineering backaction-evading interaction of magnons
and photons, and develop spintronics-related quantum information processing
devices.
