Simulation of XXZ Spin Models using Sideband Transitions in Trapped Bosonic Gases

We theoretically propose and experimentally demonstrate the use of motional sidebands in a trapped ensemble of $^{87}$Rb atoms as a way to engineer tunable long-range XXZ spin models. We benchmark our simulator by probing a ferromagnetic to paramagnetic dynamical phase transition in the collective XXZ model plus additional transverse and longitudinal fields via Rabi spectroscopy. Based on experimental observations, we reconstruct the boundary of the dynamical phases and show good agreement with mean-field theoretical predictions. We also theoretically analyze the achievable spin squeezing in our XXZ simulator, opening the possibilities of using motional sidebands to push the frontiers of metrology via quantum entanglement.