Continuum of bound states in a non-hermitian model

• Main Authors: Wang, Qiang, Zhu, Changyan, Zheng, Xu, Xue, Haoran, Zhang, Baile, Chong, Yi Dong
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2023
• Subjects: Science::Physics::Optics and light; 2D Lattice; Bound-States
• Online Access: https://hdl.handle.net/10356/166240
• Institution: Nanyang Technological University

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.