Quantum optomechanical transducer with ultrashort pulses

We propose an optomechanical setup allowing quantum mechanical correlation, entanglement and steering of two ultrashort optical pulses. The protocol exploits an indirect interaction between the pulses mediated optomechanically by letting both interact twice with a highly noisy mechanical system. We prove that significant entanglement can be reached in the bad cavity limit, where the optical decay rate exceeds all other damping rates of the optomechanical system. Moreover, we demonstrate that the protocol generates a quantum non-demolition interaction between the ultrashort pulses which is the basic gate for further applications.