DC AND AC JOSEPHSON EFFECT IN A SUPERCONDUCTOR LUTTINGER-LIQUID SUPERCONDUCTOR SYSTEM

We calculate both the dc and the ac Josephson current through a one-di mensional system of interacting electrons, connected to two supercondu ctors by tunnel junctions. We treat the (repulsive) Coulomb interactio n in the framework of the one-channel, spin-1/2 Luttinger model. The J osephson current is obtained for two geometries of experimental releva nce: a quantum wire and a ring. At zero temperature, the critical curr ent is found to decay algebraically with increasing distance d between the junctions. The decay is characterized by an exponent which depend s on the strength of the interaction. At finite temperatures T, lower than the superconducting transition temperature T-c, there is a crosso ver from algebraic to exponential decay of the critical current as a f unction of d, at a distance of the order of HBARv(F)/k(B)T. Moreover, the dependence of critical current on temperature shows nonmonotonic b ehavior. If the Luttinger liquid is confined to a ring of circumferenc e L, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage an d applied flux, the ring acts as a pi junction. These features an robu st against thermal fluctuations up to temperatures on the order of HBA Rv(F)/k(B)L. For the wire geometry, we have also studied the ac-Joseph son effect. The amplitude and the phase of the time-dependent Josephso n current are affected by electron-electron interactions. Specifically , the amplitude shows pronounced oscillations as a function of the bia s voltage due to the difference between the velocities of spin and cha rge excitations in the Luttinger liquid. Therefore, the ac-Josephson e ffect can be used as a tool for the observation of spin-charge separat ion.