Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays

Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge-invariant plaquette interactions involve at least four-body interactions that are challenging to realize. In this talk I will show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian—a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, the plaquette interactions are implemented as Rabi oscillations subject to Rydberg blockade [1]. Remarkably, I will show that controlling the atom arrangement in the array is sufficient to engineer the required anisotropic interactions and the generalized blockade conditions for spins built of atom pairs. I will describe how to adiabatically prepare the resonating valence bond and crystal phases of the Rokhsar-Kivelson Hamiltonian, and probe them and their quench dynamics by on-site measurements of their quantum correlations. To conclude, I will discuss the prospects and open challenges for simulating lattice gauge theories with Rydberg atoms.

[1] A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M.D. Lukin, and P. Zoller, Phys. Rev. X 10, 021057 (2020)