Quantum decoherence of the central spin in a sparse system of dipolar coupled spins
Quantum decoherence of the central spin in a sparse system of dipolar coupled spins
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DOI：
10.1103/physrevb.86.035452
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发表时间：
2012-07-30
影响因子：
3.7
通讯作者：
Das Sarma, S.
中科院分区：
文献类型：
--
作者：
Witzel, Wayne M.;Carroll, Malcolm S.;Das Sarma, S.
在核磁共振和电子自旋共振的背景下，中心自旋退相干问题已经研究了50多年。直到最近，理论模型一直采用现象学的随机描述浴缸诱导的噪声。在过去的几年里，团簇展开方法提供了一种微观的量子理论来研究中心自旋的光谱扩散。这些方法已经被证明是非常准确和有效的核诱导的电子自旋退相干问题，其中与中心电子自旋的超精细相互作用比原子核之间的偶极相互作用强得多。我们深入研究了正则标度不变全偶极自旋系统的中心自旋退相干。我们展示了如何采用团簇方法来处理中心自旋相互作用和浴场自旋相互作用具有相当强度的问题。我们广泛的数值工作表明，一个适当修正的团簇理论在这个问题上是收敛的，即使简单的微扰论点开始崩溃。通过处理由于周围环境的长程(对角)偶极相互作用而存在能量失谐的团簇，并仔细平均不同自旋态的影响，我们发现自旋之间的非平凡触发动力学被自旋能量分裂中的无序有效地局域化。这种局部化效应允许在考虑不超过6个自旋的簇的情况下，在相同类型的自旋的偶极耦合的浴池中稳健地计算自旋回波信号。我们将这些微观计算结果与现有的随机模型联系起来。此外，我们还对候选固态量子比特的一系列相关问题进行了计算，包括硅中的施主和量子点以及钻石中的氮空位中心。
The central spin decoherence problem has been researched for over 50 years in the context of both nuclear magnetic resonance and electron spin resonance. Until recently, theoretical models have employed phenomenological stochastic descriptions of the bath-induced noise. During the last few years, cluster expansion methods have provided a microscopic, quantum theory to study the spectral diffusion of a central spin. These methods have proven to be very accurate and efficient for problems of nuclear-induced electron spin decoherence in which hyperfine interactions with the central electron spin are much stronger than dipolar interactions among the nuclei. We provide an in-depth study of central spin decoherence for a canonical scale-invariant all-dipolar spin system. We show how cluster methods may be adapted to treat this problem in which central and bath spin interactions are of comparable strength. Our extensive numerical work shows that a properly modified cluster theory is convergent for this problem even as simple perturbative arguments begin to break down. By treating clusters in the presence of energy detunings due to the long-range (diagonal) dipolar interactions of the surrounding environment and carefully averaging the effects over different spin states, we find that the nontrivial flip-flop dynamics among the spins becomes effectively localized by disorder in the energy splittings of the spins. This localization effect allows for a robust calculation of the spin echo signal in a dipolarly coupled bath of spins of the same kind, while considering clusters of no more than six spins. We connect these microscopic calculation results to the existing stochastic models. We, furthermore, present calculations for a series of related problems of interest for candidate solid state quantum bits including donors and quantum dots in silicon as well as nitrogen-vacancy centers in diamond.