Thermal reconfiguration in optomechanical arrays via synthetic phase

Thermal management in coupled quantum systems is essential, given the inherent fragility of quantum states and correlations. In this work, we theoretically investigate thermal reconfiguration by manipulating the steady-state phonon currents and phonon numbers in an optomechanical array. The system consists of $N$ cells, each containing an optical cavity coupled to a mechanical resonator. Each resonator is coupled to an independent thermal bath, its temperature increasing with the site index. This setup creates a temperature gradient that induces a steady-state phonon current flowing from the hotter region to the colder region of the array. The direction of the phonon current can be manipulated by introducing a synthetic gauge field, which is achieved by modulating the driving laser with a site-dependent phase. This modulation results in a phase-dependent linearized optomechanical coupling. Counterintuitively, the direction of the phonon current can be reversed to flow against the tempe