Observing the dance of a vortex−antivortex pair, step by step

Abstract

The investigation of vortices in superfluids is a fascinating and active line of research that, by now, has a history spanning over half a century. Starting from the first observations of quantized circulation in liquid helium in the 1950s [1], the field has undergone tremendous progress. Nowadays, dilute-gas Bose-Einstein condensates (BECs) provide a powerful tool with which vortex research can be pushed into new regimes, and several hallmark results have been obtained, reaching from interferometric measurements of the quantum mechanical phase of individual vortices to the direct imaging of large vortex lattices containing over 300 vortices in a regular array [2]. Now Tyler Neely and collaborators at the University of Arizona in the US, the Jack Dodd Center for Quantum Technology in New Zealand, and the University of Queensland in Australia [3] are adding another chapter to the story of vortices in superfluids. They have succeeded in creating vortex dipoles, consisting of a vortex paired with an antivortex, in such a controlled way that the dynamics can be studied in detail. An antivortex differs from a vortex only in the orientation of the circular fluid flow. When a vortex and an antivortex meet in a harmonic trap (such as the one holding the BEC in the Neely experiment), they can pair up to form a vortex dipole and then perform an enchanting dance that has now been imaged for the first time. The long lifetime of the vortex dipole and the stability of the observed dynamics are quite intriguing, indicating that such dynamics may also play a key role in other situations where vortices and antivortices emerge, e.g., superfluid turbulence. In another recent paper, periodic streets of vortex pairs in BECs have been studied numerically by Sasaki et al. [4]. Vortex physics also exists in systems as diverse as superfluid Fermi systems, magnetic flux lines in superconductors, and neutron stars. Thus a precise understanding of vortex dynamics is highly desirable, and BECs can lead the way in elucidating the physics of vortices in a well-controlled environment. Vortices emerge when a superfluid is subjected to rotation. At first sight, it may seem surprising that something as apparently simple as inducing rotation would lead to interesting dynamics. To see why this is the case, recall that the velocity of a superfluid is proportional to the gradient of the phase of the underlying macroscopic wave function. The curl of a gradient field is generally zero and thus the flow is irrotational. Consequently, interesting dynamics are bound to occur when the irrotational fluid is subjected to rotation. The outcome is best understood by first considering the flow of water in a sink after the drain plug has been pulled. The water starts rushing down the drain and after a short while forms a rather stable vortex above the drain. If a little paper boat is placed into the swirling water, the boat spirals around the drain in such a way that its bow always points into the same direction. This is due to the fact that conservation of angular momentum of the water spiraling towards the drain leads to a 1/r dependence of the fluid velocity on the distance r from the drain, “compensating” for the rotation of the fluid around the drain. So the flow is irrotational, even though the stream is clearly curved. If, on the other hand, the boat is placed such that it stretches across the central eddy, then it is found to rapidly spin around its vertical axis. For a rotating superfluid, the situation is quite similar: based on the requirement of a uniquely valued wave function, similar 1/r dependence can be derived. Vorticity, defined as the curl of the velocity field, is concentrated in the vortex core where the superfluid density goes to zero. Everywhere else the fluid is irrotational, as expected for a superfluid. Over the past decade, many experimental techniques have been devised and implemented to generate vorticity in BECs [2]. Most of these techniques either create vortices that all spin in the same way (i.e., no antivortices), or offer little to no control over the vor-