Quantum simulation in and out of equilibrium on a Lieb lattice of Rydberg atoms

We explore the ground state phases and dynamics under strong constraints of Rydberg atoms on the Lieb lattice, with both homogeneous and inhomogeneous detuning. We study the equilibrium physics of the lattice numerically via DMRG simulations on the NERSC Perlmutter supercomputer and experimentally via Aquila, the Rydberg atom quantum simulator from QuEra Computing, observing good agreement between theory and simulations. The homogeneous detuning phase diagram hosts a zoo of quantum phases and provides an interesting playground for exploring multicritical phenomena. With inhomogeneous detuning, we find that the systems exhibits an analog of the liquid-vapor phase transition that is driven by quantum fluctuations and probe it by engineering adiabatic paths. Out-of-equilibrium experimental quenches in the regime with strong kinetic constraints reveal emergent glassy dynamics. Our work highlights the rich equilibrium and non-equilibrium physics that can be probed in analog quantum simulators.