  The transportation of photons and phonons typically obeys the principle of
reciprocity. Breaking reciprocity of these bosonic excitations will enable the
corresponding non-reciprocal devices, such as isolators and circulators. Here,
we use two optical modes and two mechanical modes in a microresonator to form a
four-mode plaquette via radiation pressure force. The phase-controlled
non-reciprocal routing between any two modes with completely different
frequencies is demonstrated, including the routing of phonon to phonon (MHz to
MHz), photon to phonon (THz to MHz), and especially photon to photon with
frequency difference of around 80 THz for the first time. In addition, one more
mechanical mode is introduced to this plaquette to realize a phononic
circulator in such single microresonator. The non-reciprocity is derived from
interference between multi-mode transfer processes involving optomechanical
interactions in an optomechanical resonator. It not only demonstrates the
non-reciprocal routing of photons and phonons in a single resonator but also
realizes the non-reciprocal frequency conversion for photons and circulation
for phonons, laying a foundation for studying directional routing and thermal
management in an optomechanical hybrid network.
