Three-channel interference interpretation of Fano profile

Fano resonance is a ubiquitous phenomenon, and it is commonly interpreted as a two-channel interference of the discrete and continuous channels. The present work investigates the Fano profile from a perspective of the temporal evolution of the wave function. By exciting the atom with a δ pulse and calculating the evolution of the wave function, the Fano formula is deduced. The results clearly show that the Fano resonance is of a three-channel interference, which is different from the traditional understanding. The three channels are revealed as the ground-continuum, ground-discrete-continuum, and a previously unmentioned third channel, i.e., ground-continuum-discrete-continuum. The present three-channel interpretation can be easily generalized to other physical systems, contributing to a deeper understanding of the Fano profile.