量子自旋在Heisenberg相互作用下的自由感应衰减中相同步与对齐的观测
Observation of phase synchronization and alignment during free induction decay of quantum spins with Heisenberg interactions
AI总结：
本研究观测到量子自旋在Heisenberg相互作用下的相同步与对齐现象，揭示了封闭系统中自旋方向的同步机制，与经典自旋动力学存在显著差异。
摘要：
在由幺正时间演化描述的封闭量子系统中，可观测量的平衡是一个同时已被充分确立的现象，除了少数同样已被充分确立的例外。在这里，我们报告了一个令人惊讶的理论观测结果：可积和不可积的自旋环，无论具有最近邻还是长程各向同性Heisenberg相互作用，不仅达到平衡，而且还会同步单个自旋期望值的方向。我们强调，这与量子耗散系统中的自发同步不同。在这里，我们观察到在幺正时间演化下封闭系统中局部自旋方向的相互同步。与耗散系统不同，这种同步不依赖于相互作用是铁磁还是反铁磁的。在我们的数值模拟中，我们通过数值精确求解时间依赖的Schrödinger方程，研究了最多包含N=25个自旋为1/2的量子自旋集合的自由感应衰减（FID）。我们的发现与系统的守恒定律有关，但并未完全由这些守恒定律解释。同步对例如Heisenberg耦合的随机波动和不均匀磁场具有很强的鲁棒性。在强对称破缺相互作用（如偶极相互作用）下，同步现象并未被观测到。我们还将我们的结果与封闭系统经典自旋动力学进行了比较，后者由于缺乏纠缠而不表现出相同步。对于经典自旋系统，单个自旋的固定幅度实际上起到了额外的N个守恒定律的作用。
英文摘要：
Equilibration of observables in closed quantum systems that are described by a unitary time evolution is a meanwhile well-established phenomenon apart from a few equally well-established exceptions. Here we report the surprising theoretical observation that integrable as well as non-integrable spin rings with nearest-neighbor or long-range isotropic Heisenberg interaction not only equilibrate but moreover also synchronize the directions of the expectation values of the individual spins. We highlight that this differs from spontaneous synchronization in quantum dissipative systems. Here, we observe mutual synchronization of local spin directions in closed systems under unitary time evolution. Contrary to dissipative systems, this synchronization is independent of whether the interaction is ferro- or antiferromagnetic. In our numerical simulations, we investigate the free induction decay (FID) of an ensemble of up to $N = 25$ quantum spins with $s = 1/2$ each by solving the time-dependent Schrödinger equation numerically exactly. Our findings are related to, but not fully explained by conservation laws of the system. The synchronization is very robust against for instance random fluctuations of the Heisenberg couplings and inhomogeneous magnetic fields. Synchronization is not observed with strong enough symmetry-breaking interactions such as the dipolar interaction. We also compare our results to closed-system classical spin dynamics which does not exhibit phase synchronization due to the lack of entanglement. For classical spin systems the fixed magnitude of individual spins effectively acts like additional $N$ conservation laws.
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