Tunable Optomechanically Induced Transparency and Fano Resonance in Optomechanical System with Levitated Nanosphere

We analytically investigate the phenomena of optomechanically induced transparency and Fano resonance in optomechanical system with levitated nanosphere trapped inside Fabry-Perot cavity. We report that mechanical oscillator and nanosphere play their independent role in our system. We demonstrate that, an OMIT window exists in the absence of coupling between the nanosphere and the cavity. However the interaction of nanosphere evolves to display fano profile, besides the OMIT window, in the output at the probe frequency. We also report that the Fano profile and the width of the OMIT window can be controlled simultaneously by appropriate system's parameters. Within the experimental reach, based on our analytical results, we find that the optomechanical system with levitated nanosphere provides great flexibility to tune the OMIT and the Fano resonances by controlling the system's parameters.