The two-dimensional point vortex model was first introduced in the nineteenth century by Helmholtz and Kirchhoff.  The methods of statistical physics were used to apply it to the problem of two-dimensional fluid flow and turbulence by Onsager in the 1940s, and it has provided many qualitative insights into the emergence of large scale vortices from turbulence.  However, until recently there has been no quantitative comparison of its predictions with experimental measurements.

Here we present the results of two sets of superfluid dynamics experiments for which the point vortex model provides quantitative insights.  The first is in a planar quasi-two-dimensional atomic gas Bose-Einstein condensate cooled to nanokelvin temperatures [1].  The superfluid is confined and manipulated in a potential formed by laser light reflected from a Digital Micromirror Device (DMD) identical to those found in digital video projectors.   Two different stirring procedures inject vortices into the gas.  For the first stirring method the vortex number decays relatively quickly.  However, the second stirring method leads to the formation of two macroscopic vortex clusters of opposite signs.  The system quickly relaxes into a deeply negative temperature Onsager vortex state that persists in quasi-equilibrium for more than fifty cluster turnover times.

The second experiment is in a superfluid helium thin film [2].  Optical stirring generates a macroscopic superfluid flow in the system that lifts the degeneracy in frequency of a number of third sound modes.  These frequency splitting are subsequently observed to decay.  Modelling the system using the point vortex model with a small amount of dissipation leads to a consistent interpretation of the measurements.  We infer that a pinned persistent current slowly decays as a cluster of opposite sign vortices slowly annihilate the central charge.  Improvements in the experimental apparatus are expected to lead to the capability of tracking the dynamics of a single vortex in real time.

[1] Negative-Temperature Onsager Vortex Clusters in a Quantum Fluid,
G. Gauthier, M. T. Reeves, X. Yu, A. S. Bradley, M. Baker, T. A. Bell, H. Rubinsztein-Dunlop, M. J. Davis, T. W. Neely, to appear in Science (2019).
arXiv:1801.06951

[2] Coherent vortex dynamics in a strongly-interacting superfluid on a silicon chip,
Yauhen P. Sachkou, Christopher G. Baker, Glen I. Harris, Oliver R. Stockdale, Stefan Forstner, Matthew T. Reeves, Xin He, David L. McAuslan, Ashton S. Bradley, Matthew J. Davis, Warwick P. Bowen.
arXiv:1902.04409