Control of Andreev-level occupation in a Josephson junction by a normal-metal probe

We calculate the electrical current flowing through a mesoscopic superconductor-normal-metal-superconductor (SNS) junction coupled to a normal-metal probe. This additional normal terminal models either a scanning tunneling microscope probe or the gate electrode of a three-terminal SNS junction. We find the Josephson current switches between two different values as the probe voltage V is varied. This switching occurs because the Andreev energy levels are populated with an effective electrochemical potential eV. When the probe voltage \eV\ > Delta, so that all of the Andreev levels are either filled or emptied, we show it is possible to directly measure the ''continuum'' contribution to the Josephson current. The differential conductance dI/dV at the normal probe can also be used to detect the density of Andreev levels.