Josephson current through a superconducting quantum point contact shorter than the coherence length

It is shown theoretically that the critical current of a smooth and impurity-free superconducting constriction increases stepwise as a function of its width. The step height at zero temperature is e${\mathrm{\Delta }}_0$/ħ, dependent on the energy gap ${\mathrm{\Delta }}_0$ of the bulk superconductor but not on the junction parameters. This is the analog of the quantized conductance of a point contact in the normal state. It is essential that the constriction is short compared to the superconducting coherence length.