  Based on photon-phonon nonlinear interaction, a scheme is proposed to realize
a controllable multi-path photon-phonon converter at single-quantum level in a
composed quadratically coupled optomechanical system. Considering the
realization of the scheme, an associated mechanical oscillator is introduced to
enhance the effective nonlinear effect. Thus, the single-photon state can be
converted to the phonon state with high fidelity even under the current
experimental condition that the single-photon coupling rate is much smaller
than mechanical frequency ($g\ll\omega_m$). The state transfer protocols and
their transfer fidelity are discussed both analytically and numerically. A
multi-path photon-phonon converter is designed, by combining the optomechanical
system with low frequency resonators, which can be controlled by experimentally
adjustable parameters. This work provides us a potential platform for quantum
state transfer and quantum information processing.
