Suppression of scattering from slow to fast subsystems and application to resonantly Floquet-driven impurities in strongly interacting systems

TL;DR

This paper investigates how a high-frequency Floquet-driven impurity can suppress excitations from a low-energy system into a high-energy band, revealing universal effects on transmission despite resonant driving.

Contribution

It introduces a universal framework for understanding suppression of scattering into high-energy bands caused by resonant Floquet impurities in strongly interacting systems.

Findings

Excitations into high-energy bands are suppressed at resonance with the impurity.

Transmission is universally affected by high-energy bands, independent of their specific details.

The results apply to systems like Fermi-Hubbard chains and optical lattices.

Abstract

We study solutions to the Lippmann-Schwinger equation in systems where a slow subsystem is coupled to a fast subsystem via an impurity. Such situations appear when a high-frequency Floquet-driven impurity is introduced into a low-energy system, but the driving frequency is at resonance with a high-energy band. In contrast to the case of resonant bulk driving, where the particles in the low-energy system are excited into the high-energy band, we surprisingly find that these excitations are suppressed for resonantly driven impurities. Still, the transmission through the impurity is strongly affected by the presence of the high-energy band in a universal way that does not depend on the details of the high-energy band. We apply our general result to two examples and show the suppression of excitations from the low-energy band into the high-energy band: a) bound pairs in a Fermi-Hubbard chain scattering at a driven impurity, which is at resonance with the Hubbard interaction and b) particles in a deep optical lattice described by the tight-binding approximation, which scatter at a driven impurity, whose driving frequency equals the band gap between the two lowest energy bands.