Variation of the critical order-parameter phase difference with temperature from 0.4 to 1.9 K in the flow of superfluidHe4through a tiny orifice

The temperature dependence of the order-parameter phase difference at the critical rate of flow of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ through a tiny orifice has been studied between 0.4 and 1.9 K. Use was made of a low-frequency two-chamber acoustic resonator at frequencies between 400 and 2900 Hz. The orifice consisted of a hole ∼170 nm in diameter in a free-standing foil ∼100 nm thick. The critical phase difference was found in four runs to equal 31×2π rad and in two later runs to equal 16×2π rad at 0.95 K. In all cases the critical phase difference decreased linearly with increasing temperature between 0.4 and 1.9 K. The lines which fit the data extrapolate to zero at 2.45±0.1 K.