Classical liquids achieve co-rotation in a rotating container through the force of the walls on the fluid and viscous forces in the fluid. Quantum liquids, like Helium, are fundamentally different. They obey the laws of quantum mechanics in aggregate, with the collective motion of all the atoms described by a single wavefunction. Thus, at the lowest temperatures, the Helium liquids are superfluids, a state of matter in which the fluid velocity is irrotational. Indeed at low rotation speeds superfluid Helium remains at rest even as the walls of the container rotate! However, as the angular speed of rotation increases above a critical value superfluids are able to mimic classical fluid rotation. Two 20th century giants of quantum theory of matter, Richard Feynman and Lars Onsager, showed how superfluid 4He confined in such a container can mimic classical fluid rotation by nucleating quantized vortices, tiny “tornadoes” in the superfluid, each with a quantum of fluid circulation given by Planck’s constant divided by the mass of the superfluid particles.
For the light isotope of Helium, 3He, the superfluid state allows for fundamentally different types of quantized vortices depending on pressure, temperature and magnetic field. For this reason there are multiple phases of rotating Helium-three. The differences between these phases is manifest in the core of the quantized vortices, the “eyes of the tiny tornadoes”. As we describe in a new report to appear in Physical Review B, quantum theory predicts new states of matter confined in the vortex cores, i.e. new quantum phases of matter embedded in rotating 3He. These quantum phases are detected using nuclear magnetic resonance (NMR) spectroscopy. The research we report is a new theory predicting quantum phases confined in quantized vortices with accounts for the pressure-temperature-magnetic field phase diagram of the experimentally observed superfluid phases of rotating 3He. The computational and theoretical tools developed in our study open the door for wide ranging studies of superfluids, cold atomic gases and superconductors.