Observation of a Dynamical Phase Transition in a Quantum Simulation of the Collective Heisenberg Model

We engineer a quantum simulator of the collective Heisenberg model with a local longitudinal field. The model is implemented using the two lowest hyperfine states of a Fermi-degenerate gas of Potassium (40K) atoms, in a weakly interacting regime with motion frozen in single-particle eigenstates. We initialize a coherent superposition with maximal transverse magnetization, and measure magnetization dynamics using a Ramsey sequence. We observe a dynamical phase transition between two steady states: an ordered ferromagnetic state, where the transverse magnetization is stabilized by a large energy gap, and a demagnetized state. We explore the dynamical phase diagram of the model by tuning both interaction strength (with a Feshbach resonance) and inhomogeneity variance (with vector light shifts). We also validate experimentally the spin model description of the dynamics. We find excellent agreement with theoretical calculations based on a mean-field treatment of the Heisenberg model. The observed stabilization of many-body coherence over long times opens a new window for the generation of correlated quantum states in fermions, with applications to enhanced metrology and advanced materials.