Zhou Xu, Wan Qing-Kun, Wang Xiao-Hui
School of Physics, Northwest University, Xi'an 710127, China.
Institute of Modern Physics, Northwest University, Xi'an 710127, China.
Entropy (Basel). 2019 Dec 23;22(1):23. doi: 10.3390/e22010023.
The many-body dynamics of an electron spin-1/2 qubit coupled to a bath of nuclear spins by hyperfine interactions, as described by the central spin model in two kinds of external field, are studied in this paper. In a completely polarized bath, we use the state recurrence method to obtain the exact solution of the X X Z central spin model in a constant magnetic field and numerically analyze the influence of the disorder strength of the magnetic field on fidelity and entanglement entropy. For a constant magnetic field, the fidelity presents non-attenuating oscillations. The anisotropic parameter λ and the magnetic field strength significantly affect the dynamic behaviour of the central spin. Unlike the periodic oscillation in the constant magnetic field, the decoherence dynamics of the central spin act like a damping oscillation in a disordered field, where the central spin undergoes a relaxation process and eventually reaches a stable state. The relaxation time of this process is affected by the disorder strength and the anisotropic parameter, where a larger anisotropic parameter or disorder strength can speed up the relaxation process. Compared with the constant magnetic field, the disordered field can regulate the decoherence over a large range, independent of the anisotropic parameter.
本文研究了通过超精细相互作用与核自旋浴耦合的电子自旋 1/2 量子比特在两种外场下的多体动力学，这由中心自旋模型描述。在完全极化的浴中，我们使用状态递归方法得到了恒定磁场下 XXZ 中心自旋模型的精确解，并数值分析了磁场无序强度对保真度和纠缠熵的影响。对于恒定磁场，保真度呈现非衰减振荡。各向异性参数λ和磁场强度显著影响中心自旋的动力学行为。与恒定磁场中的周期性振荡不同，中心自旋在无序场中的退相干动力学表现为阻尼振荡，其中中心自旋经历弛豫过程并最终达到稳定状态。该过程的弛豫时间受无序强度和各向异性参数的影响，较大的各向异性参数或无序强度可以加速弛豫过程。与恒定磁场相比，无序场可以在很大范围内调节退相干，且与各向异性参数无关。
