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We theoretically propose and experimentally demonstrate the use of motionalsidebands in a trapped ensemble of $^{87}$Rb atoms to engineer tunablelong-range XXZ spin models. We benchmark our simulator by probing aferromagnetic to paramagnetic dynamical phase transition in theLipkin-Meshkov-Glick (LMG) model, a collective XXZ model plus additionaltransverse and longitudinal fields, via Rabi spectroscopy. We experimentallyreconstruct the boundary between the dynamical phases, which is in goodagreement with mean-field theoretical predictions. Our work introduces newpossibilities in quantum simulation of anisotropic spin-spin interactions andquantum metrology enhanced by many-body entanglement.

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