Universality class of a spinor Bose-Einstein condensate far from equilibrium

Scale invariance and self-similarity in physics provide a unified framework to classify phases of matter and dynamical properties near equilibrium in both classical and quantum systems. This paradigm has been further extended to isolated many-body quantum systems driven far from equilibrium, where physical observables exhibit dynamical scaling with universal scaling exponents. Universal dynamics appear in a wide range of scenarios, including cosmology, quark-gluon matter, ultracold atoms, and quantum spin magnets. However, how universal dynamics depend on the symmetry of the underlying Hamiltonian in nonequilibrium systems remain an outstanding challenge. Here, we report on the classification of universal coarsening dynamics in a quenched two-dimensional ferromagnetic spinor Bose gas. We observe spatiotemporal scaling of spin correlation functions with distinguishable scaling exponents that characterize binary and diffusive fluids. The universality class of the coarsening dynamics is determined by the symmetry of the order parameter and the dynamics of the topological defects, such as domain walls and vortices. Our results provide a categorization of the universality classes of far from equilibrium quantum dynamics based on symmetry properties of the system.