Supercurrent in Atomic Point Contacts and Andreev States

We have measured the supercurrent in aluminum atomic point contacts containing a small number of well characterized conduction channels. For most contacts, the measured supercurrent is adequately described by the opposite contributions of two thermally populated Andreev bound states per conduction channel. However, for contacts containing an almost perfectly transmitted channel $0.9\le \tau \le 1$ the measured supercurrent is higher than expected, a fact that we attribute to nonadiabatic transitions between bound states.