Pulse Transmission and State Conversion in Two-mode Optomechanical Cavity Coupled with Atomic Medium

We investigate the quantum state conversion between cavity modes of distinctively different wavelengths for the two-mode optomechanical cavity coupled with the three-level lambda atom. In the frequency domain, we show that the coherence of atom medium leads to the two maximum transmissions. We also show that the injected atom can interrupt the traveling photon pulses which is transmitted between the different input and output channels. Thus, the addition of atom provides us a way to control the transmission between the quantum states of two cavity modes and the photon information storage.