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International Journal of Modern Physics B

QUANTUM STATE OF JOSEPHSON JUNCTION AS COOPER PAIR NUMBER-PHASE ENTANGLED STATE IN THE BOSONIC OPERATOR JOSEPHSON MODEL

Hong-Yi Fan, Ji‐Suo Wang, Xiang‐Guo Meng

Published Aug 20, 2007• 7 citations
Publisher

Abstract

Based on Feynman's explanation about Cooper pair that "a bound pair acts as a Bose particle" and the bosonic operator Hamiltonian of the Josephson junction, we realize that the quantum state of the Josephson junction is a Cooper pair number-phase entangled state constructed by the phase operator across the junction. Its Schmidt decomposition is derived. The Cooper pair number-phase squeezed state's projection onto this entangled state leads to a geometric distribution.

DOI
10.1142/s0217979207037697

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Based on Feynman's explanation about Cooper pair that "a bound pair acts as a Bose particle" and the bosonic operator Hamiltonian of the Josephson junction, we realize that the quantum state of the Josephson junction is a Cooper pair number-phase entangled state constructed by the phase operator across the junction. Its Schmidt decomposition is derived. The Cooper pair number-phase squeezed state's projection onto this entangled state leads to a geometric distribution.
Based on Feynman's explanation about the Cooper pair that "a bound pairs act as a Bose particle" and the bosonic operator Hamiltonian of Josephson junction (H.-Y. Fan, Int. J. Mod. Phys. B17 (2003) 2599) as well as the entangled state representation, we establish a possible number–phase squeezing mechanism for the Cooper-pair and the phase difference between the two sides of the junction. We find that when an extra energy (e.g. microwave radiation) is provided to the junction, then this squeezing mechanism can happen.
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.