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International Journal of Theoretical Physics

Entangled States in the Capacitance Coupling Double Josephson Junction Mesoscopic Circuit

Bao‐Long Liang, Ji‐Suo Wang, Xiang‐Guo Meng

Published May 14, 2007• 3 citations
Publisher
DOI
10.1007/s10773-007-9401-7

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This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman's assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.
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.
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.