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We explain the phenomena of electromagnetically induced transparency (EIT) ofa weak probe field and tunable Fano resonances in hybrid optomechanics. Thesystem of study consists of a two-level atom coupled to a single-mode field ofan optomechanical resonator with a moving mirror. We show that a single EITwindow exists in the presence of optomechanical coupling or Jaynes-Cummingscoupling, whereas two distinct double EIT windows occur when both the couplingsare simultaneously present. Furthermore, based on our analytic and numericalwork, we prove the existence of tunable fano resonances in the system. Thecontrolling parameters of the system, which switch from a single EIT window todouble EIT windows and are needed to tune the fano resonances, can be realizedin present-day laboratory experiments.

Electromagnetically induced transparency and tunable fano resonances in hybrid optomechanics