Supercurrent noise in quantum point contacts

Spectral density of current fluctuations in a short ballistic superconducting quantum point contact is calculated for arbitrary bias voltages $V$. Contrary to a common opinion that the supercurrent flow in Josephson junctions is coherent process with no fluctuations, we find extremely large current noise that is {\em caused} by the supercurrent coherence. An unusual feature of the noise, besides its magnitude, is its voltage dependence: the noise decreases with increasing $V$, despite the fact that the dc current grows steadily with $V$. At finite voltages the noise can be qualitatively understood as the shot noise of the large charge quanta of magnitude $2\Delta /V$ equal to the charge transferred during one period of Josephson oscillations.