Session K1: Visualization of Vorticity in Quantum Fluids

Three-dimensional nanoparticle dynamics in superfluid helium

Quantized vortices have been observed in superfluid $^4$He and AMO trapped atom systems, and have been infered in superfluid $^3$He and neutron stars. The dynamics of quantum fluids is substantially controlled by the motion of quantized vortices, which are topological phase defects analogous to crystalline dislocations. Long-range quantum order underlies a number of related physical phenomena, including superfluidity, trapped-atom Bose-Einstein condensates, superconductivity, ferromagnetism, antiferromagnetism, lasers, and the Higgs mechanism. While superfluidity in $^4$He is one of the first discovered of these, it is one of the least understood, given that the strongly interacting nature of helium makes theory difficult, and that development of local experimental probes is lagging. The advent of three-dimensional flow visualization of particles that trace quantized vortices provides new oportunities to investigate their creation and dynamics. We work to address the following questions using flow visualization in this system: What are field equations that express the coupling of the ordered and disordered parts of the flow? How does vortex reconnection lead to dissipation and breaking of time-reversal invariance? What are the similarities and differences between quantum and classical turbulence at small and large scales? How do quantized vortices form through the lambda transition?   

Imaging of quantum vortices in superfluid helium droplets

Helium nanodroplets are especially promising for exploring quantum hydrodynamics in self-contained, isolated superfluids. However, until very recently, the dynamic properties of individual droplets, such as vorticity, could not be assessed experimentally. Here we investigate the rotation of single superfluid 4-He droplets ranging from 200 to 2000 nm in diameter at T $=$ 0.4 K via single-shot femtosecond X-ray coherent diffractive imaging. The droplets were produced by free jet expansion of liquid helium into vacuum. The angular velocities of the droplets were estimated from the centrifugal distortion and span a range from vanishing to those close to the disintegration limit. For visualization of vortices, Xe atoms were added to the droplets where they gather in cores forming nm-thin filaments. A newly developed phase retrieval technique enables the reconstruction of the instantaneous positions and shapes of the vortices from the diffraction images with about 20 nm resolution. The vorticity attainable in the nano-droplets was found to be about six orders of magnitude larger than achieved in previous experiments in the bulk. Stationary configurations of vortices are represented by triangular lattice in large (2 $\mu $m) droplets and symmetric arrangements of few vortices in smaller (200 nm) droplets. Evidence for non-stationary vortex dynamics comes from observation of asymmetric formations of vortices in some droplets. This collaborative work was performed at Linac Coherent Light Source, the free electron laser within SLAC National Accelerator Laboratory. The experiments and the full list of collaborators are reported in: L. F. Gomez et. al. Science, 345 (2014) 906.   

Numerical simulation of quantum turbulence

Turbulence in quantum fluids has been studied for more than half century, and the recent developments of visualization experiments are so remarkable that they have made significant contributions for understanding the topics. Numerical simulation is also indispensable for this field. Two kinds of formulation are generally available. One is the vortex filament model useful for simulation of dynamics of quantized vortices in superfluid helium. The other is the Gross-Pitaevskii model that addresses the order parameters in Bose-Einstein condensation and is applicable for atomic condensates. We discuss some novel important topics of both simulations. One is inhomogeneous turbulence in superfluid helium, which was recently revealed by the visualization experiments. Another is quantum turbulence in atomic Bose condensates addressing multi-component order parameters.   

Turbulent flows of superfluid helium visualized by particle dynamics

The motions of relatively small particles in quantum flows of superfluid helium (He II) are visualized in order to reveal the underlying flow-induced physics. It is specifically shown how the derived flow properties - such as the particle velocity distribution - depend on the length scale probed by the particles, for both thermally and mechanically driven flows of He II. Quantum features may indeed appear at small enough length scales, smaller than the quantum scale of the flow, the average distance between quantized vortices, while, at larger length scales, a classical (viscous-like) picture emerges, reinforcing the idea that quantum turbulence is not only interesting in its own right but may also lead to the deeper understanding of fluid turbulence in general, an open problem of classical physics relevant to many research fields, ranging from fluid dynamics to cosmology.   

Flow visualization in superfluid helium-4 using He2 molecular tracers

Flow visualization in superfluid helium is challenging, yet crucial for attaining a detailed understanding of quantum turbulence. Two problems have impeded progress: finding and introducing suitable tracers that are small yet visible; and unambiguous interpretation of the tracer motion. We show that metastable He$_{\mathrm{2}}$ triplet molecules are outstanding tracers compared with other particles used in helium. These molecular tracers have small size and relatively simple behavior in superfluid helium: they follow the normal fluid motion at above 1 K and will bind to quantized vortex lines below about 0.6 K. A laser-induced fluorescence technique has been developed for imaging the He$_{\mathrm{2}}$ tracers. We will present our recent experimental work on studying the normal-fluid motion by tracking thin lines of He$_{\mathrm{2}}$ tracers created via femtosecond laser-field ionization in helium. We will also discuss a newly launched experiment on visualizing vortex lines in a magnetically levitated superfluid helium drop by imaging the He$_{\mathrm{2}}$ tracers trapped on the vortex cores. This experiment will enable unprecedented insight into the behavior of a rotating superfluid drop and will untangle several key issues in quantum turbulence research.