Modified Josephson equations for the mesoscopic LC circuit including two coupled Josephson junctions**Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation of Liaocheng University under Grant X071049.

Abstract

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.