Controllable, coherent quantum many-body systems can provide insights into fundamental properties of quantum matter, enable the realization of exotic quantum phases, and ultimately offer a platform for quantum information processing that could surpass any classical approach. Recently, reconfigurable arrays of neutral atoms with programmable Rydberg interactions have become promising systems to study such quantum many-body phenomena, due to their isolation from the environment, and high degree of control. Using this approach, we demonstrate high fidelity manipulation of individual atoms and entangled atomic states. Furthermore, we realize a programmable Ising-type quantum spin model with tunable interactions and system sizes up to 51 qubits. Within this model, we observe transitions into ordered states that break various discrete symmetries. Varying the rate at which the quantum phase transition is crossed allows us to observe the power-law scaling of the correlation length, as predicted by the Kibble-Zurek mechanism. The scaling exponent observed is consistent with theoretical predictions for the Ising universality class when sweeping into a Z2-ordered phase, and with the 3-state Chiral Clock Model for transitions into the Z3-ordered phase.
An alternative, hybrid approach for engineering interactions is the coupling of atoms to nanophotonic structures in which guided photons mediate interactions between atoms. I will discuss our progress towards entangling two atoms that are coupled to a photonic crystal cavity and outline the exciting prospects of scaling these systems to many qubits and to quantum networks over large distances.