Quantum simulation of lattice spin models can provide new fundamental insights into quantum magnetism. State-of-the-art quantum simulators can probe how interacting Hamiltonians stabilize highly correlated states at low energy, and how they can drive the spreading of correlations away from equilibrium. In this context, Rydberg atoms with resonant interactions play a special role, given the full flexibility of the lattice geometry they can realize, as well as the dipolar nature of the spin-spin interactions. These unscreened power-law interactions are generally not realized in the solid state, and they can stabilize new regimes characterized either by the cooperative nature of the interactions when ferromagnetic or by their frustrated nature when antiferromagnetic. In this talk, we will present recent experiments probing the low-energy physics and excitation spectrum of one-dimensional and two-dimensional dipolar spins. We prepared low-energy states close to the absolute ground state for both ferromagnetic and antiferromagnetic Hamiltonians on one-dimensional chains [1] and on two-dimensional square lattices [2], thereby reconstructing how dimensionality and frustration fundamentally influence the spatial decay of correlations. Moreover, we studied the non-equilibrium quench dynamics of correlations starting from a low-energy fiducial state, which allowed us to reconstruct the spectrum of elementary excitations and their nature (stable vs. unstable quasiparticles) [3]. This new form of “quench spectroscopy” can be extended to one-dimensional systems and to non-local correlation functions, thereby revealing the fermionic nature of their quasi-particle excitations [4].
