  A challenging task of cavity optomechanics is to observe single-photon
optomechanical effects. To explore an intrinsic nonlinear effect of
single-photon cavity optomechanics, we need to strengthen the
radiation-pressure (RP) interaction between a single photon and a finite number
of phonons. In this work, introducing the two-laser driving and considering the
second-order correction to the cavity resonance frequency beyond the RP
interaction, we realize controllable enhancement of the single-photon
optomechanical coupling in a prototypical Fabry-Perot cavity. By adjusting the
parameters of the two driving lasers and the cross-Kerr (CK) interaction so
that the effective optomechanical coupling may become a real number, we
theoretically propose effective symmetric optomechanical dynamics at the
single-photon level, in which the forms of the quantum fluctuation dynamics
satisfied by the photon and phonon are identical to each other. We study
optimal reciprocal transport in symmetric optomechanics. By observing the
critical behavior of the optimal transmission of the laser field, we identify
the boundary point of the optomechanical strong coupling. We compare the
scattering behavior of the laser field in the dissipative equilibrium and
non-equilibrium symmetric optomechanics before and after the rotating-wave
approximation (RWA). We also present a reliable experimental implementation of
the present scheme. This work may pave the way to studying the single-photon
optomechanical effects with current experimental platforms.
