Fano resonance in the strong-coupling regime

Fano resonance is a well-celebrated weak-coupling phenomenon whereby a small interaction between a discrete and a continuum of excited states leads to an interference between the respective two transition amplitudes, resulting in an asymmetric line shape in the excitation spectra. We present the strong-coupling phase of the Fano's model where the interaction is localized in a region $\ensuremath{\xi}$ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability $\ensuremath{\sigma}$ as a function of $\ensuremath{\xi}$, the ratio of the bare transition amplitudes, and the energy of the discrete state. In the strong-coupling phase, the spectral function of the discrete state splits up and produces up to three complete destructive interferences or zeros of $\ensuremath{\sigma}$ along with ultrasharp features. We also find that the discrete state does not have to lie within the continuum to produce the well-known weak-coupling profiles of $\ensuremath{\sigma}$ as long as the collective coupling is strong enough. In addition, we consider a broadened state instead of a continuum and present a method that exactly treats such cases by explicitly including the source of the broadening---a weak coupling to the continuum of environment states---in the model.