RUI: Topological Excitations in Spin-1 and Spin-2 Bose-Einstein Condensates

Symmetry is one of the central organizing principles in the natural world. It applies to the most energetic system we can contemplate - the early universe - as well as to some of the least energetic, such as a dilute gas cooled to only tens of billionths of a degree above absolute zero. This tabletop experimental project uses the theme of symmetry to focus on the highly-controllable, low-energy environment of an ultracold gas where direct experimental investigation is possible.

Although we often think of symmetry in terms of spatial patterns, such as the regular structure of a crystal, symmetries can also be internal and hidden from view. Their influence in such cases manifests itself in the type and behavior of the particle-like (or "quasi-particle") excitations that can exist within the medium. Examples of quasi-particles that can be observed in an ultracold gas include monopoles, knots, skyrmions, and vortices, each of which has an (as-yet unobserved) analogue in the cosmos.

The project will study the creation and time evolution of such quasi-particles in a medium with a broader range of internal symmetries than in previous experiments. The resulting quasi-particle behavior is expected to be more exotic: an ordinary collision between two vortices, for instance, can become one in which connecting filaments develop in the region between them, leaving behind a permanent physical record of the encounter.

The program provides opportunities for cutting-edge scientific and technological training for undergraduate students, thereby contributing to the education of the next generation of citizen-scientists.

This experimental research program explores the creation and time evolution of topological excitations in optically trapped rubidium-87 Bose-Einstein condensates. The spin degree of freedom in these superfluids leads to a variety of magnetic phases with different internal symmetries. Each phase can host specific topological excitations.

The Rb-87 condensate is especially interesting because it has both spin-1 and spin-2 ground state hyperfine manifolds. The spin-1 system is relatively simple, with only two magnetic phases. It provides a convenient springboard from which to understand the spin-2 system, which has five magnetic phases, two of which have entirely discrete symmetries: cyclic-tetrahedral, and biaxial nematic.

The spin-2 Rb-87 system is not fully characterized, and immediate experimental goals include (i) determining the ground state magnetic phase, and (ii) understanding the baseline time-evolution of each magnetic phase. Topological excitations in the biaxial nematic and cyclic-tetrahedral phases are of considerable interest as the discrete symmetries permit vortices with fractional circulation.

Moreover, collisions between vortices in these phases are expected to yield "rung vortices," which are permanent filaments that bridge the departing vortices. Beyond vortices, the experiments will examine the creation and time evolution of monopoles in the uniaxial nematic phase, which are expected to decay into vortex rings, as well as of exotic skyrmions in the discrete-symmetry magnetic phases.

The different excitations will be generated by exposing the condensate to carefully tailored time-dependent magnetic and optical fields, and will be characterized using established imaging techniques. The results, obtained by the PI and his undergraduate collaborators, are expected to contribute directly to our scientific understanding of topological excitations across many branches of physics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.