Self-consistent Microscopic Description of Charging Effect on Phase Coherence in Ultrasmall Josephson Tunnel Junctions

We discuss the effect of charging energy on phase coherence from a microscopic point of view. Physics is characterized by single electron charging energy Ec and Josephson coupling energy Ey It is shown that currents due to Cooper pair tunneling from partially phase-coherent regime (E_j/E_c Lt1) to phase-incoherent regime (E_j/E_c rarr0) can be seamlessly described up to higher order tunneling processes, provided that generalized charged states of the island is introduced.