Non-linear Fano Interferences in Open Quantum Systems: an Exactly Solvable Model

We obtain an explicit solution for the stationary state populations of a dissipative Fano model, where a discrete excited state is coupled to a continumm set of states; both excited set of states are reachable by photo-excitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the continuum states population as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a $4\times 4$ matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic induced-transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.