The Ettore Majorana paper "Theory of incomplete P' triplets", published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels.This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels.The Feshbach resonances and shape resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high T c superconductivity.
In this study, a standing wave in an optical nano cavity with Bose-Einstein Condensate (BEC) constitutes one dimensional optical lattice potential in the presence of finite two bodies atomic interaction. We report that interaction of a BEC with standing field in an optical cavity coherently evolve to exhibit Fano resonances in the output field at probe frequency. The behavior of the reported resonance shows an excellent compatibility with the original formulation of asymmetric resonance as discovered by Ugo Fano. 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.