  We theoretically propose a scheme to realize an all-optically controlled
quantum optomechanical transistor based on a cavity-optomechanical system,
where the cavity photons interfere with the input signal photons while the pump
field controls the transmission spectrum of the signal laser. Theoretical
analysis shows such a quantum optomechanical transistor can be switched on or
off by turning on or off the pump laser, which corresponds to amplification or
attenuation of the signal laser, respectively. The results further demonstrate
that the output signal gain is enhanced abruptly with increasing the input pump
power. The scheme proposed here will pave the way towards many important
applications such as all-optical logic circuits and quantum repeaters.
