近日，浙江大学景俊团队研究了非厄米哈密顿量的通用量子控制。2025年9月4日，《物理评论A》杂志发表了这一成果。

对量子系统的传统操作，如相干种群捕获和单向转移，集中在哈密顿工程上，而将系统的流形几何和约束方程作为次要主题。

研究组在非厄米哈密顿量下控制有限维量子系统时，将它们等同对待，这是受D' Alembert原理的启发，即以无偏的方式看待主动力、约束力和惯性力。在双正交条件下，非厄米哈密顿量可以在由一组完整和正交基态跨越的约束图中进行三角化，这被发现是在bra和ket空间中构造至少一个通用非绝热通道的充分条件。该通道最终得到一个理想的目标状态，该状态在非厄米量子系统的现有处理中无需人工归一化即可自动归一化。

此外，当其全局相位的实部随时间快速变化时，该通道对参数偏差具有较强的抵抗能力。对两级系统的完美种群转移和三级系统的手性种群转移进行了明确的验证。将该通用量子控制框架推广到双正交量子力学领域。

附：英文原文

Title: Universal quantum control by non-Hermitian Hamiltonian

Author: Zhu-yao Jin, Jun Jing

Issue&Volume: 2025/09/04

Abstract: Conventional manipulations over quantum systems for, such as coherent population trapping and unidirectional transfer, focus on Hamiltonian engineering while regarding the system's manifold geometry and constraint equation as secondary causes. Here, we treat them on equal footing in controlling a finite-dimensional quantum system under a time-dependent non-Hermitian Hamiltonian, which is inspired by the D'Alembert principle of regarding active force, constraint force, and inertial force in an unbiased way. Under the biorthogonal condition, the non-Hermitian Hamiltonian could be triangularized in a constraint picture spanned by a set of completed and orthonormal basis states, which is found to be a sufficient condition to construct at least one universal nonadiabatic passage in both bra and ket spaces. The passage ends up with a desired target state that is automatically normalized without artificial normalization in the existing treatments for non-Hermitian quantum systems. Moreover, the passage is found to be robust against the parametric deviation when the real part of its global phase is rapidly varying with time. Our protocol is explicitly verified for the perfect population transfer in the two-level system and the chiral population transfer in the three-level system. It generalizes our framework of universal quantum control to the field of the biorthogonal quantum mechanics.

DOI: 10.1103/7h6g-1z57

Source: https://journals.aps.org/pra/abstract/10.1103/7h6g-1z57