We explain the phenomena of electromagnetically induced transparency (EIT) of a weak probe field and tunable Fano resonances in hybrid optomechanics. The system of study consists of a twolevel atom coupled to a single-mode field of an optomechanical resonator with a moving mirror. We show that a single EIT window exists in the presence of optomechanical coupling or JaynesCummings coupling, whereas two distinct double EIT windows occur when both the couplings are simultaneously present. Furthermore, based on our analytic and numerical work, we prove the existence of tunable Fano resonances in the system. The controlling parameters of the system, which switch from a single EIT window to double EIT windows and are needed to tune the Fano resonances, can be realized in present-day laboratory experiments.

We explain the probe field transmission spectrum under the influence of a strong pump field in a hybrid optomechanical system, composed of an optical cavity, a mechanical resonator, and a twolevel atom. We show fast (superluminal) and slow (subluminal) light effects of the transmitted probe field in the hybrid system for suitable parametric regimes. For the experimental accessible domain, we find that the fast light effect obtained for the single optomechanical coupling can further be enhanced with the additional atom-field coupling in the hybrid system. Furthermore, we report the existence of a tunable switch from fast to slow light by adjusting the atomic detuning with the antiStokes and Stokes sidebands, respectively, as ∆a = +ωm and −ωm. The reported characteristics are realizable in state-of-the-art laboratory experiments.

We study the classical and quantum dynamics of a Fermi accelerator realized by an atom bouncing off a modulated atomic mirror. We find that in a window of the modulation amplitude dynamical localization occurs in both position and momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. 74, 4972 (1995)] shows that this system can be implemented experimentally.

The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.