Probing the Lipkin-Meshkov-Glick model with ultracold Dysprosium atoms

In this talk, we will report the study of the Lipkin-Meshkov-Glick model, induced by near-resonant light coupling to the J$=$8 ground state of an ultracold cloud of Dysprosium. We investigate the paramagnetic to ferromagnetic phase transition expected from this model, making a full characterisation of the ground state properties as well as a quantitative study of the dynamics of the quantum critical regime. Due to the large value of J, a good qualitative agreement is found, away from the phase transition, with mean-field predictions.