In this article, we propose an experimentally feasible scheme for the ultraslow light realization based on the optomechanically induced transparency (OMIT) phenomenon using a hybrid optomechanical system consisting of a one-dimensional Bose–Einstein condensate trapped in a shallow optical lattice considering the nonlinear effect of atom-atom interaction. It is shown how the system can switch from the normal mode splitting to the OMIT regime by manipulation of the s-wave scattering frequency of atomic collisions when the cavity is pumped at a fixed rate. Then, it is shown that an ultraslow light with a time delay more than 150 ms corresponding to a group velocity about 1 mm/s is achievable by controlling the optical lattice depth as well as the strength of atom-atom interaction and the number of atoms. Importantly, such an ultraslow light is detectable in the output of the cavity since it occurs in the frequency region of coupling-probe detuning where the reflection coefficient of the cavity is maximum.

We investigate the realization of the phenomenon of optomechanically induced gain in a hybrid optomechanical system consisting of an interacting Bose-Einstein condensate trapped inside the optical lattice of a cavity which is generated by an external coupling laser tuned to the red sideband of the cavity. It is shown that the system behaves as an optical transistor while the cavity is exposed to a weak input optical signal which can be amplified considerably in the cavity output if the system is in the unresolved sideband regime. Interestingly, the system has the capability to switch from the resolved to unresolved sideband regime by controlling the s-wave scattering frequency of atomic collisions. We show that the system gain can be enhanced considerably by controlling the s-wave scattering frequency as well as the coupling laser intensity while the system remains in the stable regime. Based on our obtained results, the input signal can be amplified more than 100 million percent in the system output which is much larger than those already reported in the previously proposed similar schemes.