JOSEPHSON CURRENT OF INTERACTING ELECTRONS

We study the Josephson current through a one-dimensional quantum wire or a ring connected to two superconductors by tunnel junctions (S-Sc-S system). The Coulomb interaction is treated by means of the Luttinger model and Haldane's concept of topological excitations. The Josephson current I-c is found to be exponentially suppressed by the Coulomb in teraction, I-c proportional to d(-2/gp), where d is the distance betwe en the junctions and g(p) is the usual parameter for the interaction s trength in the Luttinger model. If the Luttinger liquid has a ring geo metry, the Josephson current is sensitive to the number of electrons N module 4. The number of electrons can be controlled by a gate voltage and by a magnetic flux threading the ring. The Josephson current show s a periodic, quasicontinuous dependence on the gate voltage. The peri od corresponds to the addition of four electrons to the system. The fl ux dependence of the Josephson current has a stepwise form and shows h /e periodicity. The jumps are associated with the change in electron n umber. For strong interaction the number of electrons in the ring and consequently the Josephson current do not depend on the flux for virtu ally all values of the gate voltage.