日本中央大学Shion Yamashika团队研究了二维超流体到自由玻色子的淬灭：纠缠、对称性和量子Mpemba效应。2025年4月9日，《物理评论A》杂志发表了这一成果。

课题组研究了二维光学晶格中玻色子从超流相突然猝灭到自由玻色子状态后的非平衡动力学。初始超流体状态用Bogoliubov理论和高斯变分原理近似描述。随后的时间演化仍然是高斯的，通过检查动力学的不同方面来比较初始状态的每个近似值的结果。

首先，他们分析了纠缠熵，并观察到，在这两种情况下，纠缠熵在达到饱和点之前都随时间线性增加。这种行为归因于超流态中量子耗尽纠缠对的传播。接下来，又探索粒子数对称性的命运，它在超流体相中自发地被打破。为此，研究组使用纠缠不对称性，这是一种最近引入的可观测性，能够跟踪子系统内的对称性破坏。研究组观察到，它的演变在性质上取决于用于描述初始状态的理论。然而，在这两种情况下，对称性仍然被破坏，永远不会恢复到静止状态。

最后，研究组通过评估稳态约化密度矩阵和时间演化矩阵之间的量子保真度来评估达到稳态所需的时间。有趣的是，在高斯变分原理中，他们发现离静止态更远的初始态比离它更近的初始态弛豫得更快，这表明最近发现的量子Mpemba效应的存在。研究组推导出了这种效应发生所需的微观条件，并证明这些条件在Bogoliubov理论中从未得到满足。

附：英文原文

Title: Quenching from superfluid to free bosons in two dimensions: Entanglement, symmetries, and the quantum Mpemba effect

Author: Shion Yamashika, Pasquale Calabrese, Filiberto Ares

Issue&Volume: 2025/04/09

Abstract: We study the nonequilibrium dynamics of bosons in a two-dimensional optical lattice after a sudden quench from the superfluid phase to the free-boson regime. The initial superfluid state is described approximately using both the Bogoliubov theory and the Gaussian variational principle. The subsequent time evolution remains Gaussian, and we compare the results from each approximation of the initial state by examining different aspects of the dynamics. First, we analyze the entanglement entropy and observe that, in both cases, it increases linearly with time before reaching a saturation point. This behavior is attributed to the propagation of entangled pairs of quantum depletions in the superfluid state. Next, we explore the fate of particle-number symmetry, which is spontaneously broken in the superfluid phase. To do so, we use the entanglement asymmetry, a recently introduced observable that enables us to track symmetry breaking within a subsystem. We observe that its evolution varies qualitatively depending on the theory used to describe the initial state. However, in both cases, the symmetry remains broken and is never restored in the stationary state. Finally, we assess the time it takes to reach the stationary state by evaluating the quantum fidelity between the stationary reduced density matrix and the time-evolved one. Interestingly, within the Gaussian variational principle, we find that an initial state further from the stationary state can relax more quickly than one closer to it, indicating the presence of the recently discovered quantum Mpemba effect. We derive the microscopic conditions necessary for this effect to occur and demonstrate that these conditions are never met in the Bogoliubov theory.

DOI: 10.1103/PhysRevA.111.043304

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.043304