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Physical Review A

Quantization of Circulation in Superfluid Helium

J. C. Garrison, Jack Wong, Harry L. Morrison

Published Aug 1, 1970• 3 citations
Publisher

Abstract

It is shown that the quantization of circulation in superfluid helium can be understood in a fundamental way by an argument analogous to that used by Byers and Yang for flux quantization in superconductors. The ac Josephson effect in helium also follows simply from this argument.
DOI
10.1103/physreva.2.491

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Physical Review A•Dec 1, 1970•5 citations
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.
When liquid helium-4 is cooled to 2.17 K it changes from an ordinary fluid to a superfluid somewhat similar in nature to superfluid helium-3 and to the electron fluid in superconductors. Extensive investigation over the last five decades has given us a highly refined phenomenological description of how superfluid He4 behaves, even though the underlying quantum theory is only partially understood. Much of the current research on superfluid He4 is part of a continuing effort to work out the implications of this phenomenological description, in the same way as classical fluid dynamicists are still working out the implications of the Navier-Stokes equations.
Quantization of superflow circulation and of magnetic flux are considered for systems, such as superfluid 3A^{3}\mathit{A}3A and unconventional superconductors, having nonscalar order parameters. The circulation is shown to be the anholonomy in the parallel transport of the order parameter. For multiply-connected samples free of distributed vorticity, circulation and flux are predicted to be quantized, but generically to nonintegral values that are tunably offset from integers. This amounts to a version of Aharonov-Bohm physics. Experimental settings for testing these issues are discussed. \textcopyright{} 1996 The American Physical Society.
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.