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Acta Physica Sinica

Research progress of non-Hermitian dynamics in quadratic bosonic systems

Huawei ZHAO, Xinlei LIU, Xinyao HUANG, Guofeng ZHANG

Published Dec 6, 2025• 0 citations
Publisher

Abstract

非厄米物理是近年来快速发展的重要前沿研究领域,揭示了诸多新奇物理现象与功能应用.然而,当前非厄米物理的研究多集中于经典系统,非厄米特性对量子效应的影响作为亟待探索的关键科学问题,已发展为非厄米物理与量子物理交叉领域的新兴研究方向.无耗散二次型玻色系统中的压缩作用,既能使系统动力学演化呈现等效非厄米特性,又能诱导系统产生量子关联效应.因此,该系统不仅为实现量子体系中多样化的非厄米动力学提供了天然载体,更为深入探究非厄米动力学与量子关联等效应的内在联系、实现基于非厄米特性的量子调控提供了重要平台.本综述将介绍二次型玻色系统中实现非厄米动力学的物理原理,回顾非厄米动力学诱导的典型物理效应,并总结基于非厄米动力学调控系统量子关联的近期研究进展.

DOI
10.7498/aps.75.20251497

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Non-Hermitian physics has emerged as a rapidly advancing field of research, revealing a range of novel phenomena and potential applications. Traditional non-Hermitian Hamiltonians are typically simulated by constructing asymmetric couplings or by introducing dissipation and gain to realize non-Hermitian systems. The quadratic bosonic system (QBS) with squeezing interaction is intrinsically Hermitian; however, its dynamical evolution matrix in both real and momentum spaces is non-Hermitian. Based on this, applying a field-operator transformation xp to the dynamical evolution matrix yields quadrature nonreciprocal transmission between the x and p operators. This nonreciprocal characteristic can be utilized in signal amplifiers. On the other hand, within the Bogoliubov-de Gennes framework in momentum space, one can observe non-Hermitian topological phenomena such as point-gap topology and the non-Hermitian skin effect, both induced by spectra with nonzero winding numbers. Additionally, QBS can be employed to realize non-Hermitian Aharonov-Bohm cages and to extend non-Bloch band theory. Previous studies in non-Hermitian physics have largely concentrated on classical systems. The influence of non-Hermitian properties on quantum effects remains a key issue awaiting exploration and has evolved into a research direction at the interface of non-Hermitian and quantum physics.
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Hole degrees of freedom play a central role in the exact solution of quadratic (mean-field) systems. Although a variety of experiments have suggested the existence of bosonic holes, a consistent and complete theory has long been hindered by the ghost problems. Here, we resolve the ghost problem and establish a unified theoretical framework for bosonic holes by introducing the CPT\mathcal{CPT}CPT theory and bosonic particle-hole (PH) transformation. The bosonic analogs of the `Fermi surface' and `Fermi level' are proposed. Furthermore, a PH duality between Hermitian and non-Hermitian quadratic bosonic systems (QBSs) is revealed. In both distinct QBSs, the C\mathcal{C}C-parity is shown to label PH conjugate eigenspaces. Building on this duality, we demonstrate the PH Bogoliubov quasiparticles in APT\mathcal{APT}APT symmetric Hamiltonians, investigate the dynamical generation of PH entanglement, and predict Hermitian PH Aharonov-Bohm interference in non-Hermitian QBSs.
Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built in to these Hamiltonians, we show that as long as dynamical stability holds, one may always construct a non-trivial dual (unitarily equivalent) number-conserving quadratic bosonic Hamiltonian. We exemplify this construction for a gapped harmonic chain and a bosonic analogue to Kitaev's Majorana chain. Our duality may be used to identify local number-conserving models that approximate stable bosonic Hamiltonians without the need for parametric amplification and to implement non-Hermitian -symmetric dynamics in non-dissipative number-conserving bosonic systems. Implications for computing topological invariants are addressed.