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首页> 外文期刊>Physical review >Quantum many-body theory of qubit decoherence in a finite-size spin bath
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Quantum many-body theory of qubit decoherence in a finite-size spin bath

机译：有限尺寸自旋浴中量子位退相干的量子多体理论

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摘要

Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin-bath dynamics relevant to the qubit decoherence problem. A cluster-correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. This correlation accounts for the authentic (nonfactorizable) collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in the qubit decoherence problem, a convergent result can be obtained by truncating the expansion up to a certain cluster size. The two-spin cluster truncation of the CCE corresponds to the pair-correlation approximation developed previously [W. Yao et al, Phys. Rev. B 74, 195301 (2006)]. In terms of the standard linked cluster expansion, a cluster-correlation term is the infinite summation of all the connected diagrams with all and only the spins in the group flip-flopped, and thus the expansion is exact whenever convergence occurs. When the individual contribution of each higher-order correlation term to the decoherence is small (while all the terms combined in product could still contribute substantially), as the usual case for relatively large baths, where the decoherence could complete well within the bath spin flip-flop time, the CCE coincides with the cluster expansion [W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006)]. For small baths, however, the qubit decoherence may not complete within the bath spin flip-flop time scale and thus individual higher-order cluster correlations could become significant. In such cases, only the CCE converges to the exact coherent dynamics of multispin clusters. We check the accuracy of the CCE in an exactly solvable spin-chain model.
机译：自旋浴中中心自旋或量子位的去相干性基本上由多体浴的演化决定。我们针对与量子位退相干问题有关的自旋浴动力学发展了一种簇相关展开（CCE）理论。聚类相关项递归定义为一组浴旋转的演化除以所有子组的聚类相关性。这种相关性说明了给定组内真实的（不可分解的）集体激发。浴传播者是所有可能的簇相关项的乘积。对于像量子位去相干问题中的有限时间演化，可以通过将扩展截断到一定的簇大小来获得收敛结果。 CCE的两自旋簇截短对应于先前发展的成对相关近似[W。姚等人，物理学。 B 74，195301（2006）。就标准链接簇展开而言，簇相关项是所有连通图的无限求和，其中只有组中的所有自旋被触发器翻转，因此只要发生收敛，扩展就是精确的。当每个高阶相关项对退相干的单独贡献很小时（尽管产品中组合的所有项仍然可以做出实质性贡献），这是相对较大浴池的通常情况，其中退相干可以在浴池旋转翻转中很好地完成触发器时间，CCE与集群扩展一致。 M. Witzel和S. Das Sarma，物理学。 B 74，035322（2006）。然而，对于小浴场，在浴场旋转触发器的时间尺度内，量子位去相干性可能无法完成，因此各个高阶簇相关性可能变得很重要。在这种情况下，只有CCE会收敛到多纺丝簇的精确相干动力学。我们在完全可解的自旋链模型中检查CCE的准确性。

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