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理论物理通讯：英文版

Berry Phase of Composite System Induced by Time-Dependent Interaction

杨林广, 邵彬, 邹健

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

在时间依赖者相互作用导致的一个合成系统的果浆阶段被讨论。我们作为合成系统选二为联合 spin-1/2 系统：分系统之一受到一个静态的磁场，并且在二旋转之间的联合参数及时是可控制的。我们证明时间依赖者相互作用能作为那以一个类似的方法导致果浆阶段一个 spin-1/2 系统(qubit ) 被一个有效时间依赖者磁场驾驶。而且，与静态的磁场以及反面的相反的方向使用二个连续周期联合参数签名，重要 two-qubit 单一的转变基于完全，果浆阶段能被构造。

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The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.

Communications in Theoretical Physics•Apr 1, 2010•1 citation
在时间依赖者相互作用导致的一个合成系统的果浆阶段被讨论。我们作为合成系统选二为联合 spin-1/2 系统：分系统之一受到一个静态的磁场，并且在二旋转之间的联合参数及时是可控制的。我们证明时间依赖者相互作用能作为那以一个类似的方法导致果浆阶段一个 spin-1/2 系统(qubit ) 被一个有效时间依赖者磁场驾驶。而且，与静态的磁场以及反面的相反的方向使用二个连续周期联合参数签名，重要 two-qubit 单一的转变基于完全，果浆阶段能被构造。
本文研究了由SU(1,1)和SU(2)李代数生成元所构成的含时非厄米系统的Berry相位, 其分别对应于周期驱动外场下的一维谐振子及任意参数下的单个自旋粒子模型. 具体来说, 基于广义规范变换方法,通过引入含时厄米的且非幺正的变换算符, 系统可变换为不显含时间的形式, 并可导出系统的精确解及其对应的非绝热Berry相位. 结果表明, 对于SU(2)系统, 存在奇异点Gc (ω) = Ω+ω/2, 在该点处等效本征值发散, Berry相位从实数变为复数, 对应赝厄米相的自发破缺. 而SU(1,1)系统的能谱始终保持实数,Berry相位为纯实数, 无奇异点出现. 该对比揭示了SU(1,1)非紧致群与SU(2) 紧致群结构对非厄米系统几何相位的根本性影响. 该研究结果为非厄米系统中Berry相位的理论分析提供了新的视角和理解.
The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field.Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.
The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.