Optomechanically dark state in hybrid BEC–optomechanical systems

Abstract

We study theoretically the propagation of slow light in a hybrid BEC–optomechanical system comprising a Bose–Einstein condensate (BEC) trapped inside an optical cavity with a moving end mirror. We show that when the system is driven by a weak probe in the presence of a strong laser field, there exists an analog of the electromagnetically induced transparency (EIT) in coupled BEC–optomechanical systems. When the coupling of the cavity field with a mechanical mirror and the condensate mode is considered simultaneously, three absorption peaks appear in the output spectrum of the probe field. The central absorption peak appears in the reflection spectrum of the weak probe field when the pump-probe detuning occurs at half the sum of frequencies of the two oscillators, which corresponds to the long-live dark state. Furthermore, we also study the occurrence of normal mode splitting in the output spectrum of the probe and Stokes fields.