Floquet scattering resonances in two dimensions

In this work we establish a general scattering theory for two-dimensional quantum systems with periodically modulated interactions. We show that scattering quantities, such as the scattering cross section, effective scattering length, and effective-range parameter, can be defined in a manner analogous to conventional scattering theory, even in the presence of modulation. Unlike systems with static interactions, the incident wave in our setup can be scattered inelastically into different Floquet channels, absorbing or emitting quanta from the modulation field. A family of Floquet resonances is identified, at which universal recurrence relations are derived for the Floquet scattering amplitudes. These relations are equivalent to a discrete Schr"odinger equation describing a pointlike source trapped by an effective potential. The resonance mechanism is explained as the coincidence of the point source's energy with the bound states of the effective potential. We discuss the scattering properties both at and near the resonances, finding that the resonance width and the ratio of the inelastic to elastic cross sections can be effectively controlled through the modulation of the interaction. Our results provide a pathway to precisely manipulate many-body interactions in periodically driven quantum systems.