BOSONIC OPERATOR HAMILTONIAN MODELS OF JOSEPHSON JUNCTIONS IN SERIES AND IN PARALLEL AND THEIR PROJECTIONS ONTO ENTANGLED STATE REPRESENTATIONS

摘要

We present the bosonic operator Hamiltonian models of two Josephson junctions which are connected in series and in parallel, respectively. By introducing the entangled state representations (|η? representation and Cooper pairs representation) and projecting the operator Hamiltonian onto the |η? representation we obtain the correct Josephson current and phase equations consistent with the classical Hamiltonian cases.