We theoretically study the unique applications of optomechanics based ontraveling-wave microresonators, where the optomechanical coupling of degeneratemodes can be enhanced selectively by optically pumping in different directions.We show that the unique features of degenerate optical modes can be applied tothe entangled photon generation of clockwise and counter-clockwise opticalmodes, and the nonclassicality of entangled photon pair is discussed. Thecoherent coupling between the clockwise and counter-clockwise optical mods andtwo acoustic modes is also studied, in which the relative phase of theoptomechanical couplings plays a key role in the optical non-reciprocity. Theparity-time symmetry of acoustic modes can be observed in the slightly deformedmicroresonator with the interaction of forward and backward stimulatedBrillouin Scattering in the triple-resonance system. In addition, thedegenerate modes are in the decoherence-free subspace, which is robust againstenvironmental noises. Based on parameters realized in recent experiments, theseoptomechanical devices should be readily achievable.
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