Cavity-optomechanics, a rapidly developing area of research, has made a remarkable progress. A stunning manifestation of optomechanical phenomena is in exploiting the mechanical effects of light to couple the optical degree of freedom with mechanical degree of freedom. In this report, we investigate the controlled bistable dynamics of such hybrid optomechanical system composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside high-finesse optical cavity with one moving-end mirror and is driven by a single mode optical field. The numerical results provide evidence for controlled optical bistability in optomechanics using transverse optical field which directly interacts with atoms causing the coupling of transverse field with momentum side modes, exited by intra-cavity field. This technique of transverse field coupling is also used to control bistable dynamics of both moving-end mirror and BEC. The report provides an understanding of temporal dynamics of moving-end mirror and BEC with respect to transverse field. Moreover, dependence of effective potential of the system on transverse field has also been discussed. To observe this phenomena in laboratory, we have suggested a certain set of experimental parameters. These findings provide a platform to investigate the tunable behavior of novel phenomenon like electromagnetically induced transparency and entanglement in hybrid systems.

Cavity-optomechanics, a tool to manipulate mechanical effects of light to couple optical field with other physical objects, is the subject of increasing investigations, especially with regards to electromagnetically induced transparency (EIT). EIT, a result of Fano interference among different atomic transition levels, has acquired a significant importance in many areas of physics, such as atomic physics and quantum optics. However, controllability of such multi-dimensional systems has remained a crucial issue. In this report, we investigate the controllability of EIT and Fano resonances in hybrid optomechanical system composed of cigar-shaped Bose-Einstein condensate (BEC), trapped inside high-finesse Fabry-Pérot cavity with one vibrational mirror, driven by a single mode optical field and a transverse pump field. The transverse field is used to control the phenomenon of EIT. It is detected that the strength of transverse field is not only efficiently amplifying or attenuating out-going optical mode but also providing an opportunity to enhance the strength of Fano-interactions which leads to the amplification of EIT-window. To observe these phenomena in laboratory, we suggest a certain set of experimental parameters. The results provide a route for tunable manipulation of optical phenomena, like EIT, which could be a significant step in quantum engineering.