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Chinese Physics Letters

Cooper-Pair Number-Phase Quantization for Inductance Coupling Circuit Including Josephson Junctions

孟祥国, 王继锁, 梁宝龙

Published Jan 1, 2008• 0 citations
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Abstract

基于纠缠的州的表示和一个 bosonic 阶段操作员形式体系，我们为包括 Josephson 连接联合电路的电感与库柏对号码阶段量子化处理，然后调查 Josephson 当前的方程怎么由于联合电感的存在变化并且获得 bosonic 操作员法拉第公式，象相应数字阶段不确定性关系一样。

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基于纠缠的州的表示和一个 bosonic 阶段操作员形式体系，我们为包括 Josephson 连接联合电路的电感与库柏对号码阶段量子化处理，然后调查 Josephson 当前的方程怎么由于联合电感的存在变化并且获得 bosonic 操作员法拉第公式，象相应数字阶段不确定性关系一样。
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.
For a mesoscopic L-C circuit, besides the Louisell's quantization scheme in which electric charge q and electric current I are respectively quantized as the coordinate operator Q and momentum operator P , in this paper we propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.