  In this study, a standing wave in an optical nanocavity with Bose-Einstein
condensate (BEC) constitutes a one-dimensional optical lattice potential in the
presence of a finite two bodies atomic interaction. We report that the
interaction of a BEC with a standing field in an optical cavity coherently
evolves to exhibit Fano resonances in the output field at the probe frequency.
The behavior of the reported resonance shows an excellent compatibility with
the original formulation of asymmetric resonance as discovered by Fano [U.
Fano, Phys. Rev. 124, 1866 (1961)]. Based on our analytical and numerical
results, we find that the Fano resonances and subsequently electromagnetically
induced transparency of the probe pulse can be controlled through the intensity
of the cavity standing wave field and the strength of the atom-atom interaction
in the BEC. In addition, enhancement of the slow light effect by the strength
of the atom-atom interaction and its robustness against the condensate
fluctuations are realizable using presently available technology.
