  We propose a theoretical project in which quantum squeezing induces quantum
entanglement and Einstein-Podolsky-Rosen steering in a coupled
whispering-gallery-mode optomechanical system. Through pumping the
$\chi^{(2)}$-nonlinear resonator with the phase matching condition, the
generated squeezed resonator mode and the mechanical mode of the optomechanical
resonator can generate strong quantum entanglement and EPR steering, where the
squeezing of the nonlinear resonator plays the vital role. The transitions from
zero entanglement to strong entanglement and one-way steering to two-way
steering can be realized by adjusting the system parameters appropriately. The
photon-photon entanglement and steering between the two resonators can also be
obtained by deducing the amplitude of the driving laser. Our project does not
need an extraordinarily squeezed field, and it is convenient to manipulate and
provides a novel and flexible avenue for diverse applications in quantum
technology dependent on both optomechanical and photon-photon entanglement and
steering.
