  Quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering are valuable
resources in quantum information processing. How to enhance the quantum
entanglement and EPR steering of coupled optomechanical systems with a weak
squeezed vacuum field are studied when the displacement of detuning induced by
the mechanical mode is considered. Compared with the condition that the system
interacts with a vacuum environment, the quantum entanglement and EPR steering
are stronger when the squeezed vacuum field is applied. A squeezed vacuum field
with a large degree is not beneficial to enhance the quantum entanglement and
EPR steering. Rather than the squeezing parameter of the squeezed vacuum field,
the reference phase plays a vital role in this model.
