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Chinese Science Bulletin (Chinese Version)

Non-Abelian adiabatic evolution and shortcuts to adiabaticity in non-Hermitian systems

Zihan Zhou, Xin Wang, Haodi Liu, Xuexi Yi

Published Mar 26, 2026• 0 citations

Abstract

本文以具有非互易耦合的三脚架系统为研究对象，系统探讨了非厄米系统中的非阿贝尔绝热演化、几何相位及其绝热捷径实现。我们首先建立了赝厄米哈密顿量下的非阿贝尔绝热演化理论框架，并通过数值方法求解了双正交本征态的演化过程。研究发现，系统非简并本征态上的布居数在绝热过程中强烈依赖于非厄米参数和初始态的选择。而对于简并子空间中的非阿贝尔绝热演化，其布居数和相位呈现类似厄米体系的特性；也就是说，非厄米性对非简并本征态布居有较大影响，而不会影响简并本征态。基于这些发现，我们进一步推广了适用于该系统的绝热捷径方案并用数值模拟加以验证，该方案在保持简并子空间内厄米特性的同时，实现了演化速度的有效提升。本文的研究不仅拓展了非阿贝尔绝热捷径在非厄米系统中的适用性，也为发展非厄米量子调控技术提供了新的理论工具。

DOI: 10.1360/csb-2025-5932

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本文以具有非互易耦合的三脚架系统为研究对象，系统探讨了非厄米系统中的非阿贝尔绝热演化、几何相位及其绝热捷径实现。我们首先建立了赝厄米哈密顿量下的非阿贝尔绝热演化理论框架，并通过数值方法求解了双正交本征态的演化过程。研究发现，系统非简并本征态上的布居数在绝热过程中强烈依赖于非厄米参数和初始态的选择。而对于简并子空间中的非阿贝尔绝热演化，其布居数和相位呈现类似厄米体系的特性；也就是说，非厄米性对非简并本征态布居有较大影响，而不会影响简并本征态。基于这些发现，我们进一步推广了适用于该系统的绝热捷径方案并用数值模拟加以验证，该方案在保持简并子空间内厄米特性的同时，实现了演化速度的有效提升。本文的研究不仅拓展了非阿贝尔绝热捷径在非厄米系统中的适用性，也为发展非厄米量子调控技术提供了新的理论工具。

The existence of exceptional points (EPs) in the spectrum of non-Hermitian Hamiltonians leads to a nontrivial spectral topology that can be exploited to generate topological operations. However, their implementation has remained elusive due to the difficulty of generating a true adiabatic evolution. Here, we develop fast, robust control protocols that generate a desired topological operation. Our strategy relies on shortcuts to adiabaticity, but is not a trivial extension. The presence of EPs renders the strategy developed for Hermitian Hamiltonians impractical as it will lead to faulty control protocols. Moreover, due to the dynamics sensitivity to parameter uncertainties, not all shortcuts to adiabaticity can be used in a realistic setting. We illustrate our method in the context of a two-mode non-Hermitian Hamiltonian and discuss why in general celebrated shortcuts to adiabaticity like transitionless driving and superadiabatic transitionless are not appropriate control protocols for non-Hermitian systems.

The technique of shortcuts to adiabaticity (STA) has attracted broad attention due to their possible applications in quantum information processing and quantum control. However, most studies published so far have been only focused on Hermitian systems under the rotating-wave approximation (RWA). In this paper, we propose a modified shortcuts to adiabaticity technique to realize population transfer for a non-Hermitian system without RWA. We work out an exact expression for the control function and present examples consisting of two-and three-level systems with decay to show the theory. The results suggest that the shortcuts to adiabaticity technique presented here is robust for fast passages. We also find that the decay has small effect on the population transfer in the three-level system. To shed more light on the physics behind this result, we reduce the quantum three-level system to an effective two-level one with large detunings. The shortcuts to adiabaticity technique of effective two-level system is studied. Thereby the high-fidelity population transfer can be implemented in non-Hermitian systems by our method, and it works even without RWA.