Topological Nodal Rings in a Bose-Einstein Condensate

Nodal structures are topological defects that play important roles in topological matter. While zero-dimensional nodal points such as Dirac points have been studied extensively, higher-dimensional nodal lines or surfaces further enrich topological physics but require more research. Here we experimentally probe a topological nodal ring in a Bose-Einstein condensate, whose four hyperfine spin states are cyclically coupled by microwaves and radio-frequency waves. The ring emerges in a parameter space constituted by the light fields’ coupling strengths, phases, and detunings. When tuning the parameters, this ring can expand or shrink to a point but can never be gapped out. Such stability corresponds to a unique second topological invariant and can be understood from a high-dimensional perspective, a nodal hyperboloid or cone in the parameter space. Moreover, the projection of the hyperboloid or cone into low dimensions also sheds light on the evolution of two nodal lines when tuning the parameters. Our study may provide insights into exploring high-dimensional topological defects and the evolution of their projections in synthetic quantum matter.