Controllable transparency and slow–fast light in an optomechanical system with a triple quantum well

The optical response in a hybrid optomechanical system containing a triple quantum well (TQW) is investigated theoretically. The optomechanical cavity is driven by a strong pump field and a weak probe field. We show that multiple electromagnetically induced transparency windows and optomechanically induced transparency (OMIT) window exist simultaneously for the weak probe field due to the Jaynes–Cummings coupling and optomechanical coupling respectively. Furthermore, the system absorption spectra can be tuned by changing the system coupling strength. Especially, when two external control lasers are applied to the TQW with frequency detuning, multiple transparency windows can be illustrated and adjusted by the external fields. Therefore, via changing the external coupling fields, we can realize manipulating the OMIT transparency window, tunable group delay and switch from fast light to slow light. Such a system may be much practical for the flexibility of TQW in the quantum information processing.