  We propose how to achieve significantly enhanced quantum refrigeration and
entanglement by coupling a pumped auxiliary cavity to an optomechanical cavity.
We obtain both analytical and numerical results, and find optimal-refrigeration
and -entanglement conditions under the auxiliary-cavity-assisted (ACA)
mechanism. Our method leads to a giant amplification in the net refrigeration
rate, and reveals that the ACA entanglement has a much stronger noise-tolerant
ability in comparison with the unassisted case. By appropriately designing the
ACA mechanism, an effective mechanical susceptibility can be well adjusted, and
a genuine tripartite entanglement of cooling-cavity photons, auxiliary-cavity
photons, and phonons could be generated. Specifically, we show that both
optomechanical refrigeration and entanglement can be greatly enhanced for the
blue-detuned driving of the auxiliary cavity but suppressed for the red-detuned
case. Our work paves a way towards further quantum control of macroscopic
mechanical systems and the enhancement and protection of fragile quantum
resources.
