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Physical Review A

Acoustic Resonance Effects in the Richards-Anderson Experiment on the Josephson Effect in Superfluid Helium

I. Rudnick

Published Oct 1, 1973• 10 citations
Publisher

Abstract

It is shown that first- and second-sound resonance can lead to the appearance of spurious stable states and pumping phenomena in the Richards-Anderson experiment on the Josephson effect in superfluid helium, and proposals are made for their elimination.
DOI
10.1103/physreva.8.1969

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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.
A microscopic theory of the ac Josephson effect in superfluid helium is proposed on the basis of the Heisenberg equation of the dressed-boson operators. The equation is solved exactly. The interference of the two eigen-oscillations in the exact solution produces the Josephson oscillation. It is verified that the oscillation occurs even when the quantum fluctuation of the relative phase is infinitely large. On the basis of these results, we propose an experiment to detect the tunnelling effect of the dressed-bosons. The formulation of this paper can be applied to the Josephson effect in superconductor.
At the Symposium on Quantum Fluids and Solids in Paris this past July, Richard Packard of the University of California, Berkeley, entertained the audience by playing a brief recording: The sound on the tape began as a high-pitched whistle and slid down the frequency scale over a period of a few seconds. What people were hearing was the sound of a superfluid surging rapidly back and forth through the holes in a membrane1 in response to a pressure difference applied across the membrane. This phenomenon is the superfluid analog of the AC Josephson effect for superconductors, according to which a supercurrent will oscillate across a thin tunnel junction under an applied voltage. (A French group had earlier reported evidence of this phenomenon.) In addition to recording the sounds of the mass oscillations, Packard and Seamus Davis and their respective groups at Berkeley found that the measured frequencies agreed with those predicted by the Josephson equations.