“Phases and dynamics of dipolar gases and universality of ferromagnetic superfluids” 

This presentation consists of two separate parts. In the first, we will discuss the static properties and the dynamics of dipolar Dysprosium Bose-Einstein condensates subjected to a fastly rotating external magnetic field. The underlying phase diagram with respect to the atom number and relative interaction strengths for various field orientations is mapped out. Transitions  from a superfluid to a supersolid and then to arrays of dipolar droplets characterized by a non-vanishing global phase coherence will be elucidated. Following quenches, across the aforementioned phase transitions, we observe the dynamical nucleation of supersolids or droplet lattices. Three-body losses lead to self-evaporation of the ensuing structures, while the rotating magnetic field enables, for fixed values of the relative interactions, an enhancement of the droplet lifetimes. The second part will be devoted to  address universality in the non equilibrium dynamics of a two-dimensional ferromagnetic spinor gas subjected to modulations of the quadratic Zeeman coefficient. For short timescales we observe the spontaneous nucleation of topological defects (spin-vortices) which annihilate through their interaction giving rise to magnetic domains deeper in the evolution where the gas enters the universal coarsening regime. This is characterized by the spatiotemporal scaling of the spin correlation functions and the structure factor allowing to measure corresponding scaling exponents which depend on the symmetry of the order parameter and belong to distinct universality classes. These results represent a paradigmatic example of categorizing far-from-equilibrium dynamics in quantum many-body systems and reveal the interplay of topological defects for the emergent universality class.