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首页> 外文期刊>Physical review >Master equation approach to the central spin decoherence problem: Uniform coupling model and role of projection operators
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Master equation approach to the central spin decoherence problem: Uniform coupling model and role of projection operators

机译：中心自旋退相干问题的主方程方法：统一耦合模型和投影算子的作用

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摘要

The generalized master equation of Nakajima-Zwanzig (NZ) type has been used extensively to investigate the coherence dynamics of the central spin model with a nuclear bath in a narrowed state characterized by a well-defined value of the Overhauser field. We reconsider the perturbative NZ approach and apply it to the exactly solvable case of a system with uniform hyperfine couplings. This is motivated by the fact that the effective-Hamiltonian-based theory suggests that the dynamics of the realistic system at low magnetic fields and short times can be mapped onto the uniform coupling model. We show that the standard NZ approach fails to reproduce the exact solution of this model beyond very short times, while the effective-Hamiltonian calculation agrees very well with the exact result on time scales during which most of the coherence is lost. Our key finding is that, in order to extend the time scale of applicability of the NZ approach in this case, instead of using a single projection operator one has to use a set of correlated projection operators which properly reflect the symmetries of the problem and greatly improve the convergence of the theory. This suggests that the correlated projection operators are crucial for a proper description of narrowed-state free-induction decay at short times and low magnetic fields. Our results thus provide important insights toward the development of a more complete theory of central spin decoherence applicable in a broader regime of time scales and magnetic fields.
机译：Nakajima-Zwanzig（NZ）类型的广义主方程已被广泛用于研究具有狭窄浴场的中心自旋模型的相干动力学，该浴场处于狭窄状态，其特征是Overhauser场的定义明确。我们重新考虑了扰动NZ方法，并将其应用于具有均匀超精细耦合的系统的完全可解决的情况。这是由于基于有效哈密顿理论的事实表明，可以将低磁场和短时间的真实系统的动力学映射到均匀耦合模型上。我们表明，标准的NZ方法无法在很短的时间内重现此模型的精确解，而有效的哈密顿量计算与损失大部分相干性的时间尺度上的精确结果非常吻合。我们的主要发现是，在这种情况下，为了扩展NZ方法的适用时间尺度，必须使用一组相关的投影算子来正确地反映问题的对称性，并且在很大程度上避免使用单个投影算子。改善理论的融合。这表明相关的投影算子对于正确描述在短时间和低磁场下的窄态自由感应衰减至关重要。因此，我们的结果为更完整的中心自旋退相干理论的发展提供了重要见识，该理论适用于更广泛的时标和磁场。

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