We study the energy-level evolution and ground-state cooling of mechanical resonators under a synthetic phononic gauge field. The tunable gauge phase is mediated by the phase difference between the PT- and anti-PT-symmetric mechanical couplings in a multimode optomechanical system. The transmission spectrum then exhibits an asymmetric Fano line shape or a double optomechanically induced transparency by modulating the gauge phase. Moreover, the eigenvalues will collapse and become degenerate, although the mechanical coupling is continuously increased. Such counterintuitive energy-level attraction, instead of anticrossing, is attributed to destructive interferences between PT- and anti-PT-symmetric couplings. We find that the energy-level attraction, as well as the accompanying exceptional points (EPs), can be clearly observed in the cavity output power spectrum where the mechanical eigenvalues correspond to distinct peaks. For mechanical cooling, the average phonon occupation number is minimized at the EPs. Especially, phonon transport becomes nonreciprocal and even ideally unidirectional at the EPs. Finally, we propose a heating-resistant ground-state cooling based on the nonreciprocal phonon transport, which is mediated by the gauge field. Towards the quantum regime of macroscopic mechanical resonators, most optomechanical systems are ultimately limited by their intrinsic cavity or mechanical heating. Our work shows that the thermal energy transfer can be blocked by tuning the gauge phase, which suggests a promising route to bypass the heating limitations.
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