  We investigate the effect of a degenerate optical parametric amplifier (OPA)
placed inside an optomechanical cavity on the steady-state entanglement of two
cavity modes, which jointly interact with a mechanical resonator. Two cavity
modes are respectively driven at the red and blue sideband associated with the
mechanical resonator, which generates entanglement between them in the limit of
resolved sideband. The OPA gives rise to single-mode squeezing of the cavity
fields, which results in significant improvement of the two-mode entanglement.
It is found that an optimal nonlinear gain of the OPA exists, depending on the
system temperatures, which yields the maximum entanglement. The improvement is
particularly remarkable for the system at cryogenic temperatures.
