Electrical circuit simulation of non-Hermitian lattice models

Abstract

<sec>Quantum simulation serves as a significant tool for studying and understanding novel phenomena in the quantum world. In recent years, it has be realized that apart from quantum platforms, classical systems like photonic crystals, phononic crystals, and mechanical oscillators can also be used to simulate quantum models by analogizing the Schrödinger equation. Among these systems, electrical circuits have emerged as a promising simulation platform owing to their low cost, technological maturity, and ease of scalability, successfully simulating numerous important quantum phenomena. Meanwhile, non-Hermitian physics breaks the Hermiticity of systems’ Hamiltonians in traditional quantum mechanics, providing a fresh perspective for understanding the physics of quantum systems, particularly open quantum systems. Non-Hermitian systems, owing to their manifestation of unique phenomena absent in Hermitian systems, have become emerging research subjects in various fields of physics. However, many non-Hermitian phenomena require specialized configurations that pose relatively high technical thresholds on quantum platforms. For instance, the non-Hermitian skin effect typically requires systems to possess non-reciprocal hopping between lattice sites. Therefore, utilizing flexible electrical circuits to simulate non-Hermitian physics becomes a natural choice.</sec><sec>This paper provides a short review of the current experimental progress in simulating non-Hermitian lattice models by using electrical circuits. It offers a brief introduction to the relevant knowledge of non-Hermitian physics, including mathematical concepts and novel phenomena, as well as the simulation theory of electrical circuits, including the mapping theory of the lattice models, the introduction of non-Hermiticity, and the measurement of physical quantities. The aim is to provide readers with a reference for better understanding or engagement in related researches, thus promoting further development in this field.</sec>