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Communications in Theoretical Physics

On Bosonic Magnetic Flux Operator and Bosonic Faraday Operator Formula

Fan Hong-Yi, Wang Tong-Tong, Ji‐Suo Wang

Published Jun 1, 2007• 1 citation
Publisher

Abstract

In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators' commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.

DOI
10.1088/0253-6102/47/6/008

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In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators' commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.
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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.