Rydberg atoms in arrays of optical tweezers offer new perspectives for applications in
quantum simulation, quantum computation, and quantum metrology. In this talk, I will
describe our recent efforts to control dipolar interactions between Rydberg states to
engineer a 2D XY spin Hamiltonian. In this model, we adiabatically prepare low-
temperature states of both the XY ferro- and antiferromagnet. In the ferromagnetic
case, we observe the presence of long-range order enabled by long-range interactions
. I will further show that by performing quantum quenches we can probe the
dispersion relation of the excitations in the system . Finally, I will illustrate that by
carefully steering the out-of-equilibrium dynamics we can generate sizable spin
squeezing, which could be used for metrological applications .
 Chen et al., Nature 616, 691 (2023).
 Chen et al., in preparation.
 Bornet et al., arXiv:2303.0053.