# Coupled Atomic Wires in a Synthetic Magnetic Field

## TL;DR

This paper proposes coupled atomic wire systems in synthetic magnetic fields to realize exotic quantum phases, including fractional quantum Hall states, with detailed theoretical analysis and experimental proposals for cold atom setups.

## Contribution

It introduces a novel coupled wire platform combining continuous and discrete dimensions to explore topological and many-body quantum phenomena.

## Key findings

- Enhanced energy scales via sub-wavelength wire spacing enable observation of Lifshitz transitions.
- Emergence of Chern bands with tunable flatness in many-wire arrays.
- Feasible realization of complex geometries like cylinders and tori using Laguerre-Gauss beams.

## Abstract

We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as well as Meissner phases and Vortex phases in double-wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e. the Harper-Hofstadter model and the two leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semi-continuous Harper-Hofstadter model accessible with cold atom experiments. For the minimal setup of a double-wire, we explore how a sub-wavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in non-planar geometries such as cylinders, discs, and tori.