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.Received 25 July 2019Revised 20 February 2020Accepted 20 April 2020DOI:https://doi.org/10.1103/PhysRevX.10.021057Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoherent controlExotic phases of matterLattice gauge theoryQuantum simulationSpin icePhysical SystemsQuantum spin modelsRydberg atoms & moleculesTechniquesDualityOptical tweezersGeneral PhysicsInterdisciplinary PhysicsCondensed Matter & Materials PhysicsAtomic, Molecular & Optical
Highlights
Atoms trapped in tweezer arrays and interacting via van der Waals interactions of laser-excited Rydberg states have recently emerged as one of the most promising platforms for quantum simulation of spin models
Only single atomic Rydberg excitations within a given blockade radius Rc are allowed, with double excitations strongly suppressed by large energy shifts from Rydberg van der Waals interactions. We show that such an experimental setting provides a natural framework for implementing 2D U(1) lattice gauge models for spin 1=2 and, in particular, the RokhsarKivelson Hamiltonian [11]
We have shown that we can perform scalable quantum simulation of 2D lattice gauge theories with reconfigurable Rydberg arrays in current experiments
Summary
Atoms trapped in tweezer arrays and interacting via van der Waals interactions of laser-excited Rydberg states have recently emerged as one of the most promising platforms for quantum simulation of spin models. We show that such an experimental setting provides a natural framework for implementing 2D U(1) lattice gauge models for spin 1=2 and, in particular, (a variant of) the RokhsarKivelson Hamiltonian [11]. A difficulty in implementing lattice gauge theories in higher spatial dimensions is that gauge invariance (Gauss law) and gauge-invariant magnetic interactions, plaquette terms, typically translate into four-body (or higher-order) interactions This difficulty applies when gauge field excitations are represented as finite dimensional, such as in lattice gauge spin models [22,23,24,25]. IV, we summarize our results and discuss future steps and potential applications of our simulator based on controllable Rydberg arrays to gauge theories and beyond
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