  We study the quantum interference between different weak signals in a
three-port optomechanical system, which is achieved by coupling three cavity
modes to the same mechanical mode. If one cavity serves as a control port and
is perturbed continually by a control signal, nonreciprocal quantum
interference can be observed when another signal is injected upon different
target ports. In particular, we exhibit frequency-independent perfect blockade
induced by the completely destructive interference over the full frequency
domain. Moreover, coherent photon routing can be realized by perturbing all
ports simultaneously, with which the synthetic signal only outputs from the
desired port. We also reveal that the routing scheme can be extended to
more-port optomechanical systems. The results in this paper may have potential
applications for controlling light transport and quantum information
processing.
