  Entanglement and quantum squeezing have wide applications in quantum
technologies due to their non-classical characteristics. Here we study
entanglement and quantum squeezing in an open spin-optomechanical system, in
which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to
an ancillary cavity field via a quadratic optomechanical coupling. We find that
their performances can be significantly modulated via the photon of the
ancillary cavity, which comes from photon-dependent spin-oscillator coupling
and detuning. Specifically, a fully switchable spin-oscillator entanglement can
be achieved, meanwhile a strong mechanical squeezing is also realized.
Moreover, we study the environment-induced decoherence and dissipation, and
find that they can be mitigated by increasing the number of photons. This work
provides an effective way to manipulate entanglement and quantum squeezing and
to suppress decoherence in the cavity quantum electrodynamics with a quadratic
optomechanics.
