Quantum Simulator for Massive Relativistic Fields in Two Spatial Dimensions

We report on the experimental demonstration of an analog quantum simulator for massive relativistic fields in two spatial dimensions (2D). Our quantum simulator is based on a coherently coupled two-component spin mixture of bosonic ³⁹K atoms in a uniform 2D box trap. We prepare the system at a special spin imbalance that decouples the spin and density degrees of freedom and operate in the Josephson regime where the coherent coupling strength is much weaker than the spin chemical potential. The spin dynamics in our system encode the sine-Gordon model, which is a prototypical example of massive relativistic fields. To benchmark our simulator, we examine perturbative excitations of the system at both zero and finite momenta and demonstrate the tuning of the effective mass by varying the coherent coupling strength.