近日，南京大学郎利君团队报道了伪厄米系统中量子几何张量的直接测量。相关论文于2025年12月18日发表在《物理评论A》杂志上。

量子几何张量（QGT）从根本上编码了量子态在厄米与非厄米体系下的几何与拓扑性质。在厄米系统中，绝热微扰理论将其实部（量子度规）和虚部（贝里曲率）分别联系于能量涨落与广义力，然而对于由非厄米哈密顿量的左、右本征态共同定义的QGT，其直接测量仍具挑战性。

研究组针对具有实能谱的伪厄米系统，提出两种直接提取QGT所有分量的量子模拟方案。每种方案均通过设计不同的非绝热演化路径，制备两组时间演化态，并分别利用能量涨落算符或广义力算符的广义期望值独立测定完整QGT，从而建立两套自洽的测量协议。研究组在两个q形变双带模型上验证了方案的有效性：一个具有非平凡拓扑结构，另一个则具有非对角量子度规。

数值模拟表明，在适当选取非绝热调节速度时，两种方案对两个模型QGT的测量结果均与理论预测高度吻合，并成功通过贝里曲率计算的陈数捕捉到第一个模型的拓扑相变。当调节速度较大时，广义力方案对QGT实部的测量精度更高，而能量涨落方案则能更准确地捕捉其虚部。该研究为将动态测量方案从厄米体系推广至具有实能谱的伪厄米体系建立了框架。

附：英文原文

Title: Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems

Author: Ze-Hao Huang, Hai-Tao Ding, Li-Jun Lang

Issue&Volume: 2025/12/18

Abstract: The quantum geometric tensor (QGT) fundamentally encodes the geometry and topology of quantum states in both Hermitian and non-Hermitian regimes. While adiabatic perturbation theory links its real part (quantum metric) and imaginary part (Berry curvature) to energy fluctuations and generalized forces, respectively, in Hermitian systems, direct measurement of the QGT, which is defined using both left and right eigenstates of a non-Hermitian Hamiltonian, remains challenging. Here we develop two quantum simulation schemes to directly extract all components of the QGT in pseudo-Hermitian systems with real spectra. Each scheme independently determines the complete QGT using generalized expectation values of either the energy fluctuation operator or the generalized force operator with respect to two time-evolved states prepared through distinct nonadiabatic evolutions, thereby establishing two self-contained measurement protocols. We illustrate the validity of these schemes on two q-deformed two-band models: one with nontrivial topology and the other with a nonvanishing off-diagonal quantum metric. Numerical simulations demonstrate that, for suitably chosen nonadiabatic ramp velocities, both schemes achieve high-fidelity agreement with theoretical predictions for measuring the QGT in both models and successfully capture the topological phase transition of the first model using Chern numbers calculated from Berry curvatures. For larger velocities, the generalized force scheme yields greater accuracy for the real part of the QGT, while the energy fluctuation scheme better captures its imaginary part. This work establishes a framework for extending dynamical measurement schemes from Hermitian to pseudo-Hermitian systems with real spectra.

DOI: 10.1103/x8tj-bhwz

Source: https://journals.aps.org/pra/abstract/10.1103/x8tj-bhwz