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Physical Review Letters

Vortex-Free Landau State in Rotating Superfluid Helium

Harry Kojima, W. Veith, Seth Putterman, E. Guyon, I. Rudnick

Published Sep 13, 1971• 46 citations
Publisher

Abstract

Evidence is presented that below a rather large angular velocity, ${\ensuremath{\omega}}_{c1}$, there is a vortex-free state in rotating locked helium, which we call the Landau state. This is similar to the Meissner state in superconductors. We further show that all the properties of the rotating helium have counterparts in irreversible type-II superconductors and find that ${\ensuremath{\omega}}_{c2}$ (analogous to ${H}_{c2}$) greatly exceeds our high speeds of rotation.

DOI
10.1103/physrevlett.27.714

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Evidence is presented that below a rather large angular velocity, \ensuremathωc1{\ensuremath{\omega}}_{c1}\ensuremathωc1​, there is a vortex-free state in rotating locked helium, which we call the Landau state. This is similar to the Meissner state in superconductors. We further show that all the properties of the rotating helium have counterparts in irreversible type-II superconductors and find that \ensuremathωc2{\ensuremath{\omega}}_{c2}\ensuremathωc2​ (analogous to Hc2{H}_{c2}Hc2​) greatly exceeds our high speeds of rotation.
In the previous chapter we described quantized vortex lines, which are one of the characteristic features of superfluids. In a classical fluid, the circulation of vortex lines is not quantized and, in addition, vortex lines decay because of viscous processes. Another feature of a superfluid, the lack of response to rotation for a small enough angular velocity, was also demonstrated. This is analogous to the Meissner effect for superconductors. One characteristic common to superfluids and superconductors is the ability to carry currents without dissipation. Such current-carrying states are not the lowest-energy state of the system. They are metastable states, the existence of which is intimately connected to the nature of the low-lying elementary excitations. The word ‘superfluidity’ does not refer to a single property of the system, but it is used to describe a variety of different phenomena (see Ref. [1]). Historically, the connection between superfluidity and the existence of a condensate, a macroscopically occupied quantum state, dates back to Fritz London's suggestion in 1938, as we have described in Chapter 1. However, the connection between Bose–Einstein condensation and superfluidity is a subtle one. A Bose–Einstein condensed system does not necessarily exhibit superfluidity, an example being the ideal Bose gas for which the critical velocity vanishes, as demonstrated in Sec. 10.1 below. Also lower-dimensional systems may exhibit superfluid behaviour in the absence of a true condensate, as we shall see in Chapter 15.
In superconductors, as in Helium II (He II), the holes round which quantisation occurs can be either physical boundaries, or the cores of quantised vortex lines. For convenience we summarise here the resemblances and differences between vortex lines and vortex states in He II and in superconductors. In contrast, states in which a whole vortex is attached to the wire should be comparatively stable. The rotation of the superfluid can be satisfactorily explained by assuming that it is threaded by a series of parallel straight vortex lines. Consider a single straight vortex line in the superfluid. The energy associated with a single vortex line is mainly the kinetic energy of the circulating superfluid. The number and separation of vortex lines present for a given angular velocity clearly depends on their individual circulations. Two rival models for the ion-vortex transition have been proposed, generally known as the peeling model and the quantum transition model.
When a vessel containing a superfluid is set in rotational motion, the superfluid does not rotate uniformly with it; instead, quantized vortices develop. Vortices have been observed in a range of superfluids, including helium, atomic Bose-Einstein condensates, and type II superconductors in a magnetic field. Freilich et al. (p. [1182][1]) visualized real-time vortex dynamics in the most tunable of superfluid systems, an atomic Bose-Einstein condensate. A small section of condensate was displaced from the trap and imaged as it fell in the gravitational field. The technique is applicable to exploring other complex dynamic systems, such as vortex reconnections and the role of vortices in quantum turbulence. [1]: /lookup/doi/10.1126/science.1191224