Transparency and enhancement in fast and slow light in $q$-deformed optomechanical system

Nonclassical phenomena can be enhanced by introducing $q$-deformation in optomechanical systems. This motivated us to investigate the optical response in a $q$-deformed linearly coupled optomechanical system. The system consists of two deformed cavities that are linearly coupled to the motion of mechanical mirrors, and the cavities are coupled to each other by transmission strength parameter. Our study shows that compared to non-deformed cases, the deformed system exhibits more rapid phase transition at the positions of transparency windows, causing stronger and enhanced fast and slow light phenomena. Moreover, in the region $0<q