Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices

TL;DR

This paper explores how ultracold atoms in optical lattices can be configured to simulate lattice gauge theories, potentially enabling experimental studies of high-energy physics phenomena like confinement and phase transitions.

Contribution

It demonstrates the construction of quantum simulators for Abelian and non-Abelian lattice gauge theories using ultracold atoms, bridging low-energy atomic systems with high-energy physics models.

Findings

Successfully simulated Abelian lattice gauge theories in 1+1 dimensions.

Extended simulation methods to non-Abelian gauge theories in 2+1 dimensions.

Proposed experimental setups for observing QCD phenomena in tabletop experiments.

Abstract

Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective, low energy, symmetry, or as an "exact" symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to new type of (table-top) experiments, that shall be used to study various QCD phenomena, as the confinement of dynamical quarks, phase transitions, and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing quantum simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1 dimensions using ultracold atoms in optical lattices.