发表机构
Jožef Stefan Institute; Faculty of Mathematics and Physics, University of Ljubljana（约泽夫·斯特凡研究所; 卢布尔雅那大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出安德烈夫自旋量子比特的连续变分理论，揭示双准粒子构型对自旋依赖约瑟夫森耦合的关键贡献，并建立强关联模型与有效哈密顿量的联系。
AI 中文摘要
安德烈夫自旋量子比特存储一个未配对的单自旋，但其与超导相的耦合可能由相干的虚准粒子对主导。我们开发了一个连续变分描述，用于具有库仑相互作用和自旋依赖背景隧穿的量子点约瑟夫森结中的奇宇称二重态。保留最多包含两个博戈柳博夫准粒子的构型，为能量和波函数提供了紧凑的解析表达式。我们将结果与数值重整化群计算进行基准比较，并识别误差来源。我们获得了常规和自旋依赖约瑟夫森耦合的闭式表达式。尽管两个准粒子构型的概率很小，但通过与零准粒子分量的相干性，即使在无库仑排斥的情况下，它们也提供了领先的自旋依赖约瑟夫森耦合的一半，并随着排斥的增长而主导该耦合。自旋轨道诱导的点与引线之间的自旋转移产生了一个约瑟夫森电流贡献，该贡献对两种量子比特态都是共同的，并且在点与引线的塞曼能量不同时，在零相位偏置下是有限的。我们还映射了虚准粒子的局域化和引线中的自旋密度。这些结果将强关联量子点模型与用于安德烈夫自旋量子比特电路的有效哈密顿量联系起来，并阐明了波函数结构如何决定它们的耦合。
英文摘要
An Andreev spin qubit stores a single unpaired spin, yet its coupling to the superconducting phase can be dominated by coherent virtual quasiparticle pairs. We develop a continuum variational description of the odd-parity doublet in a quantum-dot Josephson junction with Coulomb interaction and spin-dependent background tunneling. Retaining configurations with up to two Bogoliubov quasiparticles provides compact analytical expressions for energies and wavefunctions. We benchmark the results against numerical renormalization group calculations and identify sources of error. We obtain closed-form expressions for the conventional and spin-dependent Josephson couplings. Despite their small probability, two-quasiparticle configurations, through coherence with the zero-quasiparticle component, supply exactly half of the leading spin-dependent Josephson coupling even without Coulomb repulsion and dominate it as the repulsion grows. Spin-orbit-induced spin transfer between the dot and the leads produces a Josephson-current contribution that is common to both qubit states and finite at zero phase bias when the dot and lead Zeeman energies differ. We also map the localization of the virtual quasiparticles and the spin density in the leads. The results connect strongly correlated quantum-dot models to effective Hamiltonians used for Andreev-spin-qubit circuits and clarify how the wavefunction structure determines their couplings.
Comments21 pages, 14 figures (+10 pages of Supplemental Material with 3 figures)
