Continuum of Bound States in a Non-Hermitian Model

TL;DR

This paper explores how non-Hermitian quantum systems can host a continuum of bound states with complex energies, unlike Hermitian systems, and proposes lattice models for experimental realization of these states.

Contribution

It introduces the concept of continuum Landau modes in non-Hermitian systems and provides lattice models for their experimental study.

Findings

Eigenstates form a continuum in the complex energy plane.

Lattice models can localize and manipulate these states.

Proposed designs include rainbow traps and wave funnels.

Abstract

In a Hermitian system, bound states must have quantized energies, whereas extended states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an imaginary momentum and Landau-type vector potential. The eigenstates, which we call ``continuum Landau modes'' (CLMs), have gaussian spatial envelopes and form a continuum filling the complex energy plane. We present experimentally-realizable 1D and 2D lattice models that can be used to study CLMs; the lattice eigenstates are localized and have other features that are the same as in the continuous model. One of these lattices can serve as a rainbow trap, whereby the response to an excitation is concentrated at a position proportional to the frequency. Another lattice can act a wave funnel, concentrating an input excitation onto a boundary over a wide frequency bandwidth. Unlike recent funneling schemes based on the non-Hermitian skin effect, this requires only a simple lattice design without nonreciprocal couplings.