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

Based on the entangled state representation and a bosonic phase operator formalism, we tackle with Cooper-pair number--phase quantization for the inductance coupling circuit including Josephson junctions, and then investigate how Josephson current equations change due to the presence of the coupling inductance and obtain bosonic operator Faraday formula, as well as the corresponding number--phase uncertainty relation.