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Chinese Physics Letters

Cooper-Pair Number-Phase Quantization for a Mesoscopic LC Circuit Including a Josephson Junction

梁宝龙, 王继锁, 范洪义

Published Jan 1, 2007• 0 citations
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Abstract

由介绍纠缠的州的表示和 Feynman 假设“电子对是波色子，...，界限对充当一个 Bose 粒子”，我们为一个 mesoscopic 电感电容( LC )构造操作员 Hamiltonian 包括一个 Josephson 连接的电路，然后，我们使用运动的海森堡方程越过电感以及越过 Josephson 连接导出当前的方程和电压方程。结果明白地显示出连接电压怎么被联合的电容影响。这样，为这个系统的库柏对数字阶段量子化被完成。

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由介绍纠缠的州的表示和 Feynman 假设“电子对是波色子，...，界限对充当一个 Bose 粒子”，我们为一个 mesoscopic 电感电容( LC )构造操作员 Hamiltonian 包括一个 Josephson 连接的电路，然后，我们使用运动的海森堡方程越过电感以及越过 Josephson 连接导出当前的方程和电压方程。结果明白地显示出连接电压怎么被联合的电容影响。这样，为这个系统的库柏对数字阶段量子化被完成。
By introducing the entangled state representation and Feynman assumption that `electron pairs are bosons, ..., a bound pair acts as a Bose particle', we construct an operator Hamiltonian for a mesoscopic inductance-capacitance (LC) circuit including a Josephson junction, then we use the Heisenberg equation of motion to derive the current equation and the voltage equation across the inductance as well as across the Josephson junction. The result manifestly shows how the junction voltage is affected by the capacitance coupling. In this way the Cooper-pair number-phase quantization for this system is completed.
为二个 LC 电路与相互电感，我们通过标准 Lagrangian 形式主义在数字阶段量子化的上下文介绍一个新量子化计划。在费用操作员和磁性的流动操作员之间的可交换的关系被导出。然后，我们使用运动的海森堡方程越过电感和电容获得电流和电压方程。结果清楚地显示出在一个单个 LC 电路的电流和电压怎么被电路参数和电感联合系数影响。另外，采用不变的 eigen 操作员方法描述二个 LC 电路与的动态 Hamiltonian 的精力级的差距相互电感被获得。
Based on the entangled state representation and Feynman's idea that ‘electron pairs are bosons, …, a bound pair acts as a Bose particle’, we present a cooper-pair number-phase quantization scheme for the mesoscopic LC circuit including two coupled Josephson junctions (JJs). Then we use the Heisenberg equation of motion to obtain the modified current equation and voltage equation across each JJ, as well as the equation for realizing quantum control. Besides, we investigate how the phases in two JJs are affected mutually through the capacitor coupling and the coupled JJs.