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

Cavity optomechanics is important in both quantum information processing and basic physics research. In this paper, we propose an optomechanical lattice which manifests non-Hermitian physics . We first use the non-Bloch band theory to investigate the energy spectrum and transmission property of an optomechanical lattice. The generalized Brillouin zone of the system is calculated with the help of the resultant. And the periodical boundary condition (PBC) and open boundary condition energy spectrum are given, subsequently. By introducing probe laser on different sites we observed the directional amplification of the system. The direction of the amplification is analyzed combined with the non-Hermitian skin effect. The frequency that supports the amplification is analyzed by considering the PBC energy spectrum. By introducing probe laser on one site we investigate the onsite transmission property. Optomechanically induced transparency (OMIT) can be achieved in our system. By varying the parameters and size of the system, the OMIT peak can be effectively modulated or even turned into optomechanically induced amplification . Our system shows its potential as the function of a single-way signal filter. And our model can be extended to other non-Hermitian Bosonic model which may possess topological features and bipolar non-Hermitian skin effect.