Visualization of quantized vortices

Abstract

When liquid helium is cooled to below its phase transition at 2.172 K, vortices appear with cores that are only ångströms in diameter, about which the fluid circulates with quantized angular momentum¹. Here we generate small particles of solid hydrogen that can be used to image the cores of quantized vortices in their three-dimensional environment of liquid helium. This technique enables the geometry and interactions of these vortices to be observed directly.

Main

Since the discovery of quantized vortices², attempts have been made to visualize them. Although the ends of parallel vortices in an array could be located³, there has been no successful imaging of vortices in arbitrary three-dimensional configurations. Suspended particles can trace fluid motions, and the velocities of frozen particles in superfluid helium have been measured since hydrogen was first condensed for the purpose⁴. These particles usually have diameters larger than 10 μm^5,6, although smaller polymer particles have been used⁷.

Our technique generates smaller hydrogen particles by injecting a premixed gaseous solution of hydrogen, greatly diluted with helium, into liquid helium in its normal phase above the transition temperature (for details of methods, see supplementary information). This procedure yields a mist of randomly distributed hydrogen particles (Fig. 1a) that are smaller than the 2.7-μm resolution of our long-range microscope. The suspension so prepared is then cooled to below the transition temperature.

Figure 1: Quantized vortex cores in liquid helium.

a–d, Images of particles (light against dark background) obtained with a camera and 105-mm lens under different conditions: a, just above the transition temperature, when they are uniformly dispersed; b, c, on branching filaments at tens of millikelvin below the transition temperature; and d, regrouping along vertical lines for steady rotation about the vertical axis. In b and c, the particles on lines are evenly separated in small regions. Scale bar, 1 mm.

Images taken with a digital camera focused on a thin laser-illuminated sheet show that not only do the particles trace fluid motions, but a fraction of them also collect on slender filaments, which are often several millimetres long (Fig. 1b, c).

Particles respond in a complicated way to superfluid flows⁸ and can be trapped in vortex cores⁹. The following evidence suggests that the observed filaments are particles collected on such cores. First, these filaments appear only below the transition temperature. Second, when the liquid-helium cell is set in steady rotation, the particles arrange themselves along uniformly spaced lines (Fig. 1d). The lines are parallel to the axis of rotation, which is in the image plane. This observation agrees with the expectation that quantized vortices form a rectilinear array aligned with the axis¹. Third, if we assume that our sheet illuminates a slice of such an array, we find that the number density of lines per unit area normal to the axis of rotation, for a series of rotation rates, is consistent with Feynman's rule¹⁰, which predicts about 2,000σ lines per cm², where V is the angular velocity of the container in radians per second.

The filaments are complex: for example, they may give rise to branched networks and to particles evenly spaced along lines. Others have speculated how particles could act as passive tracers of the flow^7,8; our images indicate that the presence of particles in the superfluid may transform the topology of vortex tangles by stabilizing forks in the vortices. This technique offers a tantalizing glimpse of new phenomena for future investigation.