Andreev-level spectroscopy and Josephson-current switching in a three-terminal Josephson junction

We calculate the electrical currents through a superconductor-insulator-sup erconductor junction which is also weakly coupled to a normal-metal side pr obe. The voltage V applied to the normal-metal terminal controls the occupa tion of Andreev energy levels E-n, and therefore controls the Josephson cur rent flowing through these levels. Whenever the probe voltage crosses an An dreev level, the Josephson current changes abruptly by an amount equal to t he current flowing through the Andreev level. The differential conductance along the normal-metal terminal permits spectroscopy of the Andreev levels. In a short junction (L much less than xi(0)), the critical current switche s abruptly from the Ambegaokar-Baratoff value to zero when the probe voltag e is approximately equal to the superconducting energy gap (\eV\similar or equal to Delta). The magnitude of the Josephson-current switching in a long junction (L much greater than xi(0)), and the range of probe voltages over which the Josephson current differs from its equilibrium value, are much s maller than for three-terminal ballistic superconductor-normal-metal-superc onductor junctions. [S0163-1829(98)00738-3].