Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate

TL;DR

This paper proposes a method to realize a one-dimensional topological gauge theory, specifically the chiral BF theory, using Raman-coupled Bose-Einstein condensates, enabling exploration of exotic topological phenomena in controlled quantum systems.

Contribution

It introduces a scheme to encode the chiral BF topological gauge theory into ultracold atoms with chiral interactions, building on previous proposals and recent experimental realizations.

Findings

Theoretical framework for encoding the gauge theory in BECs.

Numerical simulations validating the effective quantum description.

Discussion of properties and potential for higher-dimensional realizations.

Abstract

Topological gauge theories provide powerful effective descriptions of certain strongly correlated systems, a prime example being the Chern-Simons gauge theory of fractional quantum Hall states. Engineering topological gauge theories in controlled quantum systems is of both conceptual and practical importance, as it would provide access to systems with exotic excitations such as anyons without the need for strong correlations. Here, we discuss a scheme to engineer the chiral BF theory, a minimal model of a topological gauge theory corresponding to a one-dimensional reduction of the Chern-Simons theory, with ultracold atoms. Using the local conservation laws of the theory, we encode its quantum Hamitonian into an ultracold quantum gas with chiral interactions. Building on a seminal proposal by Edmonds et al. (Phys. Rev. Lett. 110, 085301 (2013)), we show how to implement it in a Raman-coupled Bose-Einstein condensate with imbalanced scattering lengths, as we have recently realized experimentally (Fr\"olian et al., Nature 608, 293 (2022)). We discuss the properties of the chiral condensate from a gauge theory perspective, and assess the validity of the effective quantum description for accessible experimental parameters via numerical simulations. Our approach lays the foundation for realizing topological gauge theories in higher dimensions with Bose-Einstein condensates.