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arXiv:1907.03311 · Physical Review X

Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays

Alessio Celi, Benoît Vermersch, Oscar Viyuela, Hannes Pichler, Mikhail D. Lukin, P. Zoller

Published Jun 16, 2020• 122 citations
arXivHTMLPDF

Abstract

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.Here, we 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, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade.Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs.We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations.We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.

DOI
10.1103/physrevx.10.021057

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Quantum spin-ice represents a paradigmatic example of how the physics of frustrated magnets is related to gauge theories. In the present work, we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly laser-admixing Rydberg states to the atomic ground-states, exploiting the strong angular dependence of van der Waals interactions between Rydberg p states together with the possibility of designing steplike potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state-of-the-art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g., on a 4-8 lattice.
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