Just as storm chasers track down and study tornadoes across the Great Plains, scientists around the world chase much smaller tornadoes that appear in a unique state of matter called a superfluid. Everyday fluids have some internal friction among molecules that gives the fluid a thick or sticky quality called viscosity. Some fluids, like water, have relatively low viscosity, while others, like honey, have high viscosity. Imagine what would happen if you were to stir a container of water continuously and then suddenly stopped stirring; now imagine doing the same thing with a container of honey. As you might expect, the fluid with the lower viscosity will continue to rotate longer after you stop stirring. A superfluid, which has zero viscosity, will continue to rotate indefinitely without losing energy!
The “tornadoes” that form in superfluids are called quantum vortices. In a droplet of superfluid helium, the quantum vortices dictate the rotation of the droplet; the more vortices are present in the droplet, the less spherical its shape. Imaging the vortices themselves is very difficult, however. Just as tornadoes are invisible air currents that become visible when they suck debris into their cores, quantum vortices capture atoms or molecules that allow us to visualize the vortices. But the diameter of each vortex is less than 0.2 nanometers, or a hundredth of a millionth of an inch, and the wavelength of visible light is many times larger, as shown in Fig. 1. You can think of each wavelength as a pixel; if the size of one pixel is larger than the entire object to be imaged, it will be impossible to obtain an image of the object. Because of their small size, quantum vortices can only be imaged using very short x-ray waves, which are produced from a free electron laser.
Experiments spanning several decades have succeeded in imaging quantum vortices in bulk superfluid helium. (You can learn more about this process and see video images of the vortices in Daniel Lathrop’s post, “The Turbulent Tangle of Quantum Vortices”!) However, the problem of imaging quantum vortices in helium droplets was not solved until recently. An international collaboration of scientists used the scattering of x-rays from xenon atoms trapped along the vortex cores to visualize vortices in superfluid helium droplets for the first time. As you can see in Fig. 2, however, the images produced in these experiments are diffraction or scattering patterns, which do not resemble the physical droplets at all. In order to reconstruct the actual structure of quantum vortices in a helium droplet, we must perform a repeated mathematical operation on the x-ray diffraction data shown in Fig. 2. The various methods available to reconstruct images from the data could take weeks to complete, without any guarantee that a solution will be found.
This problem was solved with the invention of a new method we call Droplet Coherent Diffractive Imaging (DCDI), which can produce a meaningful image in just a few minutes. The method works by separating the diffraction pattern into two components: the concentric ring patterns close to the center correspond to the helium droplet, and the speckle patterns farther from the center come from quantum vortices. By analyzing only the speckle patterns, we are able to quickly solve for the structures of vortices inside the helium droplet, as shown in Fig. 3. We have collected thousands of such images from our x-ray imaging experiments.
These images can serve as stepping stones for us to describe how vortices evolve in superfluid droplets, and to help us understand the nature of quantum turbulence. Because of their small size, vortices inside quantum droplets could be used in the fabrication of nanowires and other nanostructures. In addition, the DCDI technique we developed can be used for imaging other objects, such as viruses and bacteria encapsulated in a droplet. Quantum vortices also play a role in superconductivity at very low temperatures, as described by three scientists who won the 2016 Nobel Prize in Physics, discussed in the video below.
This research is led by scientists from the University of Southern California, Lawrence Berkeley National Laboratory, and Stanford’s SLAC National Accelerator Laboratory, with collaborators at the Max Planck Institute, the Center for Free Electron Laser at DESY and PNSensor GmbH.
Fig. 1 (Click to enlarge) Visible light has too long a wavelength to image quantum vortices, while x-rays have much shorter wavelengths. This diagram only begins to tell the tale, however: x-rays have wavelengths between one-hundredth of a nanometer and 10 nanometers, so the x-rays shown here are more or less to scale when compared with the diameter of the quantum vortex depicted alongside them. The wavelengths of visible light are so much larger, however—on the order of 500 nanometers—that if the entire diagram were drawn to scale, around 2,500 quantum vortices would fit within a single wavelength of visible light!
Fig. 2 (Click to enlarge) Experimental diffraction image of xenon-doped superfluid helium droplets (radius 100-300 nm).