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Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins the nuclear solid-state environment

机译:半导体量子计算机体系结构中由核自旋动力学引起的电子自旋退相干的量子理论:局部电子的光谱扩散使核固态环境自旋

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We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, which is of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is developed, motivated, and tested for the problem of localized electron spin decoherence due to dipolar fluctuations of lattice nuclear spins. The method is presented with enough generality for possible application to other types of spin decoherence problems. We present numerical results which are in quantitative agreement with electron spin echo measurements in phosphorus doped silicon. We also present spin echo decay results for quantum dots in GaAs which differ qualitatively from that of the phosphorus doped silicon system. Our theoretical results provide the ultimate limit on the spin coherence (at least, as characterized by Hahn spin echo measurements) of localized electrons in semiconductors in the low temperature and the moderate to high magnetic field regime of interest in scalable semiconductor quantum computer architectures.
机译:我们考虑到单个局部电子自旋的退相干性,这是由于其与半导体量子计算机体系结构中的晶格核自旋浴耦合。在存在外部磁场且处于低温的情况下,主要的退相干机制是电子自旋共振频率的频谱扩散,这归因于与偶极相互作用引起的核自旋对触发器相关的随时间波动的随机磁场。由于该随机磁场而引起的电子自旋移相复杂地取决于核自旋浴的量子动力学,这使得耦合去相干问题难以解决。我们提供了此非马尔可夫量子退相干问题的形式精确解决方案,该问题可以在短时间内通过数值计算出精确的自旋退相干,这在固态自旋量子计算机体系结构中特别重要。针对由于晶格核自旋的偶极波动而引起的局部电子自旋退相干问题,开发了一种量子簇扩展方法,并对其进行了测试。该方法具有足够的通用性,可以应用于其他类型的自旋退相干问题。我们提出的数值结果与掺磷硅中电子自旋回波的测量结果定量吻合。我们还给出了GaAs中量子点的自旋回波衰减结果,该结果在质量上与磷掺杂硅系统不同。我们的理论结果为可扩展半导体量子计算机体系结构中感兴趣的低温和中高磁场机制下的半导体局部电子的自旋相干性(至少以哈恩自旋回波测量为特征)提供了最终极限。

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