Absence of Floquet scattering in oscillating non-Hermitian potential wells

TL;DR

This paper introduces two families of oscillating non-Hermitian potential wells that completely suppress Floquet scattering, making the potentials fully invisible and energy-independent, using Darboux transformation techniques.

Contribution

The authors develop a method to create oscillating non-Hermitian potentials that eliminate Floquet scattering for all incident energies, advancing control over quantum scattering processes.

Findings

Floquet scattering is fully suppressed in the proposed potentials.

One family of potentials is completely invisible.

Darboux transformation is used to synthesize these potentials.

Abstract

Scattering of a quantum particle from an oscillating barrier or well does not generally conserve the particle energy owing to energy exchange with the photon field, and an incoming particle-free state is scattered into a set of outgoing (transmitted and reflected) free states according to Floquet scattering theory. Here we introduce two families of oscillating non-Hermitian potential wells in which Floquet scattering is fully suppressed for any energy of the incident particle. The scattering-free oscillating potentials are synthesized by application of the Darboux transformation to the time-dependent Schr\"{o}dinger equation. For one of the two families of scattering-free potentials, the oscillating potential turns out to be fully invisible.