Quantum theory of the nonlinear Fano effect in hybrid metal-semiconductor nanostructures: The case of strong nonlinearity

We develop a quantum theory of the field-tunable nonlinear Fano effect in the hybrid metal-semiconductor nanostructures, in which the plasmon (semicontinuous collective intraband excitation) and the exciton (discrete single-particle interband excitation) are treated on the same footing. Our quantum theory shows that the quantum interference due to the plasmon-exciton interaction leads to the nonlinear Fano effect described by a generalized complex field-tunable Fano factor for the systems with strong external field and dephasing. We establish the relation between quantum and semiclassical theories and show that the results of the quantum and semiclassical theories differ both qualitatively and quantitatively in the strongly nonlinear regime-in particular, the quantum theory predicts the absence of nonlinear instability in the hybrid systems with plasmon relaxation.