非厄米线性响应理论及其应用

Non-Hermitian linear response theory and its applications

线性响应理论是现代物理实验尤其是量子物态测量实验的理论基础,其核心是将物理系统的探测信号作为微扰,利用系统在未受扰动时的关联函数来刻画物理可观测量的响应.半个多世纪以来,基于封闭量子系统的线性响应理论在量子物态测量实验上取得了巨大的成功.随着超冷原子实验在光场与系统相互作用精确操控方面的快速进展,近年来高精度的冷原子实验已经具备研究耗散量子多体系统的条件,新奇的物理现象在实验中层出不穷,这使得国内外研究者对量子开放系统及其非厄米物理的研究与日俱增.基于此,我们发展了一个量子开放系统的线性响应理论-非厄米线性响应理论.该理论将耗散带来的非厄米效应与量子噪声作为外部探测输入来探测量子系统的性质,并将实验可观测量的含时演化与系统未受扰动状态时的关联函数及其谱函数联系了起来,提供了区分正常物态和奇异物态的一种新手段,所得到的结果与最近冷原子系统实验的结果高度吻合.本文介绍了非厄米线性响应理论,并讨论该理论在量子多体系统以及具有时间反演对称性的量子系统中的应用.

Linear response theory is the theoretical foundation of modern experiments.In particular,it plays a vital role in measuring quantum matters.Its main idea is to take the external probe signal of the physical system as a perturbation and use the correlation function in the unperturbed equilibrium state to depict the response to the observable in system.In recent half century,the linear response theory for the closed quantum system has achieved great success in experiments on quantum matters.In recent years,with the tremendous progress of the precise manipulation of the light-matter interaction,the ultracold atom experiments can precisely control dissipative quantum many-body systems.With the discovery of many novel phenomena,dissipative quantum systems and non-Hermitian physics have attracted extensive attention in theory and experiment.We developed a linear response theory,named non-Hermitian linear response theory,to deal with open quantum systems.This theory takes the non-Hermitian term and quantum noise,which are induced by dissipation,as an external perturbative input,to detect the properties of the quantum system,and relates the time evolution of the observable with the correlation function in the unperturbed state of the system.The non-Hermitian linear response theory provides a new method for distinguishing the exotic quantum phase from the normal phase.The theoretical predictions are highly consistent with the recent experimental results of cold atom systems.This paper will review the non-Hermitian linear response theory and discuss its applications in quantum many-body and time-reversal symmetric quantum systems.