Optomechanically induced transparency in a multi-cavity system subjected to two-level atomic ensemble interference

We investigate a hybrid multi-cavity optomechanical system with interference from a two-level atomic ensemble. The system is composed of three optical cavities and two nanomechanical resonators, with the middle optical cavity being filled with the two-level atomic ensemble. The optical cavity located in the middle has two interaction forces with the two outermost optical cavities. What is more, the system also includes various types of interaction relations, which are the couplings of the optical cavities with the mechanical resonators and the coupling of the optical cavity with the two-level atomic ensemble. In order to study the optical response of optomechanically induced transparency, we modulate the interaction intensity within the system to achieve different electromagnetic induced transparency phenomena. It has been found that under the influence of different parameters, the number and the width of transparency windows increase with an increase in the coupling of the optical cavities with atomic ensemble. In addition, changes in system parameters lead to shifts transparency points, specifically, the distance between the two outermost transparent points also expands when the couplings between the optical cavities and the mechanical resonators increases. We further examine the slow and fast light effects related to phase and group delay in the detection field. Our approach provides great flexibility for controlling electromagnetically induced transparency, presenting substantial potential applications in quantum information processing.