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Kristina T. Gaff - Department of Physics, University of Maryland, College Park, MD, USA
Enrico Fonda - Department of Physics, University of Maryland, College Park, MD, USA; and, University of Trieste, Trieste, Italy
Matthew S. Paoletti - Department of Physics, University of Maryland, College Park, MD, USA
Katepalli R. Sreenivasan - Department of Physics, University of Maryland, College Park, MD, USA; and New York University, New York, NY, USA
Daniel P. Lathrop - Department of Physics, University of Maryland, College Park, MD, USA
For more than fifty years, scientists have worked to observe and understand the dynamics of lattices of quantized vortices, which may be best thought of as long, skinny quantum tornadoes. Armed with real-time videos of solid hydrogen particles trapped on quantum vortices in superfluid helium, the Maryland group has been able to observe the lattice motions and capture what may be the first movies of waves in the vortex lattice.
Figure 1: A sheet of laser light illuminates frozen hydrogen particles trapped on vortex cores, which are then captured on video.
While it is easy to visualize tornadoes whipping across the Midwest or mini water spouts spiraling down the bathtub drain, the vortices we are pursuing are of a special ilk. Called quantized vortices, they exist only in superfluids or superfluid-like systems such as liquid helium, type-II superconductors, liquid crystals, Bose-Einstein condensates, the inner cores of neutron stars, and perhaps cosmic strings in the early universe. But even with this prevalence, their dynamics remain only partially understood. For example, in type-II superconductors, the creation and dynamics of the vortices can lead to the breakdown of superconductivity; yet the opacity of solid superconductors hampers direct observation of these effects except at the edges of the material. Liquid helium, though, is much easier to observe, and when it is cooled below 2.17 Kelvin (colder than deep space), it undergoes a phase transition to a “superfluid” state. This state exhibits special properties, such as quantized vortices, which allow one to witness quantum mechanics with the naked eye. In particular, when spun, a lattice of quantized vortices develops in response to the rotation of the container.
Since the vortices are only the width of a helium atom and are therefore nominally invisible, we inject hydrogen gas into the rotating liquid helium. The gas molecules immediately freeze to form solid particles, which are about one-tenth the size of a red blood cell. Then, like Indiana Jones throwing dust onto the invisible bridge to the Holy Grail, the miniature particles are pulled onto the cores of the vortices, which we can illuminate using a sheet of laser light and track with an extremely sensitive video camera (see Fig. 1). We find that these quantized vortices look like strings of spaghetti that begin and end on the walls of the cryostat, the thermos-like vessel that contains our liquid helium. When stirred, these strings get tangled up, exchanging tails with their neighbors and “reconnecting” or ending on themselves to form rings.
Figure 2: Quantized vortices arrange themselves in a triangular lattice pattern.
Feynman predicted in 1955 that when undisturbed the quantized vortices in uniformly rotating superfluid helium would align themselves with the axis of rotation in a triangular lattice pattern, similar to that of a honeycomb (see Fig. 2). Twenty-four years later, Yarmchuk et al. first observed a small lattice of up to eleven vortices using clusters of ions. Still, those observations were restricted to observing where the vortices ended on the container walls. More than a quarter-century after that, in 2006, Bewley et al. at the University of Maryland captured the first real-time videos of the lattice in superfluid helium from the side—perpendicular to the axis of rotation—using frozen hydrogen particles. Yet, a view parallel to the axis of rotation, which is far more elucidating, has remained elusive until now. Figure 3 is a still image of the direct observation of the vortex lattice along the axis of rotation. Our photos and videos of the lattice enable us to analyze its evolution, structure, and to understand how small oscillations can affect its stability.
Figure 3: A still image captures the vortex lattice along the axis of rotation in a vat of superfluid helium. A perfect lattice is not observed due to waves and other boundary effects.
Given the relevance to superconductors and other superfluid systems, understanding these oscillations is of utmost interest. In 1966, Russian scientist V.K. Tkachenko predicted that small perturbations of the lattice would result in wave-like oscillations that propagate perpendicular to the axis of rotation. From the side, these oscillations, later dubbed “Tkachenko waves,” make the vortex lines look like swaying seaweed, but underneath, they look more like an agitating washing machine. We have captured videos of what may be the first direct observation of Tkachenko waves in superfluid helium along the axis of rotation. Still unpublished, these videos will be shown for the first time at the 2009 APS/DFD Conference. With further analysis, we hope that this information will help us better understand why extraordinary substances like superfluids, superconductors, Bose-Einstein condensates, liquid crystals, and the cores of neutron stars behave the way they do.
R.P. Feynman, in Progress in Low Temperature Physics, edited by C.J. Groter (North-Holland, Amsterdam, 1955), Vol. 1, p. 17.
E.J. Yarmchuk, M.J.V. Gordon, and R.E. Packard, Phys. Rev. Lett. 43, 214 (1979).
Gregory P. Bewley, Daniel P. Lathrop, and Katepalli R. Sreenivasan, Nature 441 588 (2006).