Analog of the ac Josephson Effect in Superfluid Helium

When a chemical potential difference exists between the superfluid helium on two sides of an orifice, superfluid flow takes place at a critical velocity accompanied by the creation of quantized vortices. The frequency with which vortices are created is expected to be equal to the chemical potential difference (the analog of the ac Josephson frequency in superconducting tunneling). An experiment is described in which this frequency condition is verified by a method analogous to that used in superconductors. Experimental conditions were selected such that the gravitational head difference $\mathrm{mgZ}$ was the dominant contribution to the chemical potential difference. $Z$ was measured by a capacitance technique. An ultrasonic transducer was used to modulate the flow through the orifice at the frequency $\omega$ so that the rate of creation of vortices was synchronized with the modulation frequency. The system was observed to exhibit dynamic stability at values of head difference $Z=\frac{n\hslash \omega }{n^{\prime }\mathrm{mg}}$ corresponding to $n$ quantized vortices created every $n^{\prime }$ cycles of the modulation. The correspondence between theory and experiment is most convincing under experimental conditions such that the strength of the stability decreases rapidly with increasing values of the integer $n^{\prime }$. This was found to occur with small orifices and with moderate modulation amplitude, in agreement with the results of the analogous experiments in superconductors.