Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation

TL;DR

This paper introduces a novel method for quantum simulation of lattice gauge theories using ultracold atoms, leveraging atomic interactions and conservation laws to naturally incorporate local gauge invariance, enabling more realistic high energy physics simulations.

Contribution

The authors present a new approach that embeds local gauge invariance into the atomic Hamiltonian, simplifying the simulation of gauge theories without relying on constraints like Gauss's law.

Findings

Implemented gauge invariant interactions for U(1), SU(N), Z_N theories

Proposed a loop method for higher-dimensional theories

Numerical proof of principle for 2+1D compact QED

Abstract

Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge and Lorentz invariance. In this paper we discuss these special requirements, and present a new method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: compact QED (U(1)), SU(N) and Z_N, which can be used to build quantum simulators in 1+1 dimensions. We also present a new loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for d+1 dimensional lattice gauge theories (d>1), without having to use Gauss's law as a constraint, as in previous proposals. We discuss in detail the quantum simulation of 2+1 dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge invariant elementary interactions of this model suggests it may be useful for future experimental realizations.