Optomechanically induced transparency and directional amplification in a non-Hermitian optomechanical lattice

In this paper, we propose a 1-dimensional optomechanical lattice which possesses non-Hermitian property due to its nonreciprocal couplings. We calculated the energy spectrum under periodical boundary condition and open boundary condition, respectively. To investigate the transmission property of the system, we calculate the Green function of the system using non-Bloch band theory. By analyzing the Green function and the periodical boundary condition results, we studied the directional amplification of the system and found the frequency that supports the amplification. By adding probe laser on one site and detect the output of the same site, we found that optomechanically induced transparency (OMIT) can be achieved in our system. Different from the traditional OMIT spectrum, quantum interference due to a large number of modes can be observed in our system. When varying the nonreciprocal and other parameters of the system, the OMIT peak can be effectively modulated or even turned into optomechanically induced amplification. Our system is very promising to act as a one-way signal filter. Our model can also be extended to other non-Hermitian optical systems which may possess topological features and bipolar non-Hermitian skin effect.