Asymmetric scattering by non-hermitian potentials

TL;DR

This paper explores how non-Hermitian potentials in quantum scattering can produce asymmetric transmission and reflection, classifying device types and designing potentials for one-way quantum devices using symmetry principles.

Contribution

It introduces a classification of asymmetric scattering devices based on non-Hermitian potentials and their symmetry properties, expanding the understanding of one-way quantum transport.

Findings

Six basic device types identified with zero/one scattering coefficients

Symmetry analysis determines possible and forbidden asymmetries

Designed potentials demonstrate broad momentum range behavior

Abstract

The scattering of quantum particles by non-hermitian (generally nonlocal) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. Eight generalized symmetries based on the discrete Klein's four-group (formed by parity, time reversal, their product, and unity) are used together with generalized unitarity relations to determine the possible and/or forbidden scattering asymmetries. Six basic device types are identified when the scattering coefficients (squared moduli of scattering amplitudes) adopt zero/one values, and transmission and/or reflection are asymmetric. They can pictorially be described as a one-way mirror, a one-way barrier (a Maxwell pressure demon), one-way (transmission or reflection) filters, a mirror with unidirectional transmission, and a transparent, one-way reflector. We design potentials for these devices and also demonstrate that the behavior of the scattering coefficients can be extended to a broad range of incident momenta.