Singularities of Floquet Scattering and Tunneling

TL;DR

This paper investigates how periodic driving in three-dimensional scattering systems causes singularities in the S-matrix, leading to abrupt changes in quasi-bound states and enabling total absorption and wave conversion at specific drive amplitudes.

Contribution

It introduces the concept of Floquet singularities in scattering, revealing nonanalytic behavior and discontinuous state transitions absent in static approximations.

Findings

Poles of the S-matrix cross the real energy axis at certain drive amplitudes.

Discontinuous jumps in angular momentum and energy of emitted waves occur at singular points.

Total absorption of low-energy particles and conversion to high-energy waves at singular drive amplitudes.

Abstract

We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.