Classifying the universal dynamics of a quenched two-dimensional ferromagnetic superfluid*

Scale invariance and self-similarity in physics provide a unified framework to classify phases of matter and dynamical properties of near- and far-from-equilibrium many-body systems. To address universality, we monitor the non equilibrium dynamics of a two-dimensional ferromagnetic spinor gas subjected to quenches of the quadratic Zeeman and thus dynamically crossing the underlying phase boundaries triggering spin-mixing. Within the short time evolution we observe the spontaneous nucleation of topological defects (gauge or spin vortices) which annihilate through their interaction giving rise to magnetic domains for longer timescales where the gas enters the universal coarsening regime. This is characterized by the spatiotemporal scaling of the spin correlation functions and structure factor allowing to measure corresponding scaling exponents which depend on the symmetry of the order parameter and belong to distinct universality classes. These experimental observations are in excellent agreement with the predictions of the truncated Wigner method accounting both for quantum and thermal fluctuations in the initial state. Our results represent a paradigmatic example of categorizing far-from-equilibrium dynamics in quantum many-body systems.