We theoretically propose and experimentally demonstrate the use of motional sidebands in a trapped ensemble of $^{87}$Rb atoms to engineer tunable long-range XXZ spin models. We benchmark our simulator by probing a ferromagnetic to paramagnetic dynamical phase transition in the Lipkin-Meshkov-Glick (LMG) model, a collective XXZ model plus additional transverse and longitudinal fields, via Rabi spectroscopy. We experimentally reconstruct the boundary between the dynamical phases, which is in good agreement with mean-field theoretical predictions. Our work introduces new possibilities in quantum simulation of anisotropic spin-spin interactions and quantum metrology enhanced by many-body entanglement.
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