  We propose an approach to generate strong quantum entanglement by the
controllable four wave mixing mechanism in a single cavity, weak coupling
optomechanical system. The optomechanical system is driven by a strong two tone
pump field and a weak signal field, simultaneously. The two tone pump field
consists of a lower and an upper sideband, which couple with the optical cavity
and mechanical resonator, and generate the beam splitter and two mode squeezing
interactions under the rotating wave approximation. This interaction mechanism
modifies the effective susceptibility of the optomechanical cavity and
optomechanically induces a four wave mixing process. Strong quantum
entanglement can be generated between the signal and four wave mixing fields
with an entangled degree over 16 dB in realistic optomechanical systems. The
generation scheme of the quantum entanglement is quite robust against thermal
mechanical noise, and entanglement above 3 dB can persist at room temperature
in the weak coupling regime.
