近日，兰州大学物理科学与技术学院的应祖建及其研究团队取得一项新进展。经过不懈努力，他们利用量子费希尔信息和极化子图像识别量子拉比模型中的相变耦合。相关研究成果已于2024年9月19日在国际知名学术期刊《物理评论A》上发表。

在本研究中，研究人员反其道而行之，利用临界量子度量学（CQM）中的量子费希尔信息（QFI）来识别相变耦合，结果揭示了一旦开启有限频率，相变耦合与传统耦合将存在显著偏差。研究人员采用极化子图像来解析地重现数值QFI。受极化子频率重整化所揭示的分数幂律效应的启发，研究人员得到了相变耦合的精确表达式。从极化子图像中的QFI他们发现，相变发生在有效速度和模式正交分量期望值的磁化率达到最大值的点附近。

这项研究结果为非零频率下的量子度量学提供了精确的相变耦合参考。此外，极化子图像中QFI的表述还为数值上难以触及的参数区域提供了一种具有精确补偿的解析方法。除了通过整数/分数幂律分析来提炼相变的潜在物理机制外，QFI与速度的关系也可能为连接QFI和相变可观测量提供新的见解。

据悉，量子拉比模型（QRM）是描述光与物质相互作用的一个基本模型。QRM的一个迷人之处在于它展现了一种适用于临界量子度量学（CQM）的量子相变。CQM的有效应用需要精确确定相变点的位置，然而传统的相变耦合表达式仅在极低频率极限下有效，而在非零频率下，准确的位置仍然缺乏。

附：英文原文

Title: Quantum Fisher information and polaron picture for the identification of transition coupling in the quantum Rabi model

Author: Zu-Jian Ying, Wen-Long Wang, Bo-Jian Li

Issue&Volume: 2024/09/19

Abstract: The quantum Rabi model (QRM) is a fundamental model for light-matter interactions. A fascinating feature of the QRM is that it manifests a quantum phase transition which is applicable for critical quantum metrology (CQM). Effective application for CQM needs the exact location of the transition point, however the conventional expression for transition coupling is only valid in the extreme limit of low frequency, while apart from zero frequency an accurate location is still lacking. In the present work we conversely use the quantum Fisher information (QFI) in the CQM to identify the transition coupling, which reveals that transition coupling indeed deviates greatly from the conventional one once a finite frequency is turned on. Polaron picture is applied to analytically reproduce the numeric QFI. An accurate expression for the transition coupling is obtained by inspiration from the revealed fractional-power-law effect of polaron frequency renormalization. From the QFI in the polaron picture we find that the transition occurs around a point where the effective velocity and the susceptibility of the expected value of mode quadrature reach maximum. Our result provides an accurate reference of transition couplings for quantum metrology at nonzero frequencies. The formulation of the QFI in the polaron picture also prepares an analytic method with an accurate compensation for the parameter regime difficult to access for the numerics. Besides the integer/fractional-power-law analysis to extract the underlying physics of transition, the QFI/velocity relation may also add some insight in bridging the QFI and transition observables.

DOI: 10.1103/PhysRevA.110.033715

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.033715