Continuum of Bound States in a Non-Hermitian Model

In a Hermitian system, bound states must have quantized energies, whereas free 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 host CLMs; the lattice eigenstates are localized and have other features matching 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 a simple lattice design with reciprocal couplings.

Automated summary

In a Hermitian system, bound states have quantized energies, while free states form a continuum. However, this principle fails in non-Hermitian systems, as demonstrated by analyzing imaginary momentum and Landau-type vector potential non-Hermitian continuous Hamiltonians. The eigenstates, called continuum Landau modes (CLMs), have Gaussian spatial envelopes and occupy a continuum in the complex energy plane. Realizable 1D and 2D lattice models hosting CLMs are presented, with localized lattice eigenstates that match features of the continuous model. These lattice models can function as a rainbow trap, concentrating excitation at a position proportional to the frequency, or as a wave funnel, concentrating input excitation onto a boundary over a wide frequency bandwidth. Unlike recent funneling schemes based on the non-Hermitian skin effect, these lattice designs require simple reciprocal couplings.