Fano Resonances in Time-Dependent Wells

Abstract: Floquet’s theorem, a temporal analogue of Bloch’s theorem, is used for studying a time-dependent potential. With applications in cold atoms on optical lattices, quantum dots and more, there is a growing interest in Floquet engineering exotic materials and phases. By solving the time-dependent Schrödinger equation scattering amplitudes are derived from which the transmission spectrum are generated. The driving field induces Floquet sidebands into which the particle can inelastically scatter. Fano resonances are observed when the incoming particle and a bound state of the staticpotential differ by some energy quanta. This process is mediated by the driving field. The scattering matrix and transmission spectra are reproduced from previous work on electron gas, graphene, and a semi-metal admitting a point of quadratic band touching (QBT). The QBT system is extended with linear tilting along the potential, which proves to be another good quantum number for tunable control.