Parity-induced suppression of the Coulomb blockade of Josephson tunneling

We study the Josephson current through a superconducting grain coupled by two tunnel junctions to macroscopic superconducting leads. As a result of the Coulomb blockade we predict the critical Josephson current to have a threshold behavior when the superconducting gap is suppressed below the charging energy by a magnetic field. This effect is a direct consequence of a discrimination by the superconducting ground state between odd and even number of electrons on the grain. The critical current is periodically modulated by the voltage of a gate electrostatically coupled to the grain. We find a characteristic change in this modulation at the threshold.