Onset of the Critical Velocity Regime in SuperfluidHe4at Low Temperature

We have measured the critical velocity of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ flow through a submicron orifice from 1.2 K down to 5 mK. The velocity for the onset of phase-slip events is found to be independent of pressure, to be strongly altered by minute traces of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ impurities, and to vary with temperature as $1-\frac{T}{T_0}$ with $T_0=2.46\mathrm{}$ K. These results imply the existence at $T=0\mathrm{}$ of a hydrodynamic instability which is thermally activated at finite temperature and takes place in a very small volume.