Ferromagnetism in an Extended Coherently Coupled Atomic Superfluid

Ferromagnetism is an iconic example of a first-order phase transition taking place in spatially extendedsystems and is characterized by hysteresis and the formation of domain walls. We demonstrate that anextended atomic superfluid in the presence of a coherent coupling between two internal states exhibits aquantum phase transition from a paramagnetic to a ferromagnetic state. The nature of the transition isexperimentally assessed by looking at the phase diagram as a function of the control parameters, athysteresis phenomena, and at the magnetic susceptibility and the magnetization fluctuations around thecritical point. We show that the observed features are in good agreement with mean-field calculations.Additionally, we develop experimental protocols to deterministically generate domain walls that separatespatial regions of opposite magnetization in the ferromagnetic state. Thanks to the enhanced coherenceproperties of our atomic superfluid system compared to standard condensed matter systems, our resultsopen the way toward the study of different aspects of the relaxation dynamics in isolated coherent manybodyquantum systems.