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Physical Review Letters

Probable Observation of the Two-Orifice Macroscopic Interference Effect in Superfluid Helium

George Gamota

Published Dec 9, 1974• 9 citations
Publisher

Abstract

I have observed level differences between two baths of superfluid helium which are multiply connected by two orifices whenever the flow velocity past the orifices was of such value as to cause the quantum-mechanical phase difference between them to be an odd multiple of $\ensuremath{\pi}$.

DOI
10.1103/physrevlett.33.1428

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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 $\ensuremath{\omega}$ 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 $Z=\frac{n\ensuremath{\hbar}\ensuremath{\omega}}{{n}^{\ensuremath{'}}\mathrm{mg}}$ corresponding to $n$ quantized vortices created every ${n}^{\ensuremath{'}}$ 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 ${n}^{\ensuremath{'}}$. This was found to occur with small orifices and with moderate modulation amplitude, in agreement with the results of the analogous experiments in superconductors.

Physical Review A•Oct 1, 1970•26 citations
I have observed level differences between two baths of superfluid helium which are multiply connected by two orifices whenever the flow velocity past the orifices was of such value as to cause the quantum-mechanical phase difference between them to be an odd multiple of \ensuremathπ\ensuremath{\pi}\ensuremathπ.
Striking observations of quantised events in superfluid flow through a microscopic orifice have been made recently at Orsay, France. Sudden, stepwise reductions of the flow velocity at the critical velocity threshold, seen both in superfluid 3 He and 4 He, are interpreted as slips by 2π of the phase of the quantum mechanical wavefunction that describes the condensate of the superfluid. Moreover, in superfluid 3 He slightly below the superfluid transition, at low pressure and at a temperature of 0.9 mK, the mass flow through the orifice becomes fully dominated by quantum mechanics.
Two chambers filled with superfluid helium to different levels were connected by a small orifice (10-15 \ensuremath{\mu}m). The flow of the liquid through the orifice was modulated by a sound field. With one experimental apparatus only a continuous flow was observed. With a modified apparatus it was possible to obtain stable states with no net flow at finite level differences between the baths. The spacing between these states is inversely proportional to the sound frequency. It depends on the total height of the liquid in one of the baths and not on the level difference between them. We conclude that the stable states of zero flow result from ultrasonic standing waves of the superfluid in one of the chambers. A phase coupling or Josephson effect can be excluded as an explanation for these states.
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 mgZ\mathrm{mgZ}mgZ was the dominant contribution to the chemical potential difference. ZZZ was measured by a capacitance technique. An ultrasonic transducer was used to modulate the flow through the orifice at the frequency $\ensuremath{\omega}$ 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 $Z=\frac{n\ensuremath{\hbar}\ensuremath{\omega}}{{n}^{\ensuremath{'}}\mathrm{mg}}$ corresponding to nnn quantized vortices created every ${n}^{\ensuremath{'}}$ 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 ${n}^{\ensuremath{'}}$. This was found to occur with small orifices and with moderate modulation amplitude, in agreement with the results of the analogous experiments in superconductors.