  Optomechanical systems with parametric coupling between optical (photon) and
mechanical (phonon) modes provide a useful platform to realize various
magnetic-free nonreciprocal devices, such as isolators, circulators, and
directional amplifiers. However, nonreciprocal router with multiaccess channels
has not been extensively studied yet. Here, we propose a nonreciprocal router
with one transmitter, one receiver, and two output terminals, based on an
optomechanical plaquette composing of two optical modes and two mechanical
modes. The time-reversal symmetry of the system is broken via synthetic
magnetism induced by driving the two optical modes with phase-correlated laser
fields. The prerequisites for nonreciprocal routing are obtained both
analytically and numerically, and the robustness of the nonreciprocity is
demonstrated numerically. Multi-terminal nonreciprocal router in optomechanical
plaquette provides a useful quantum node for development of quantum network
information security and realization of quantum secure communication.
