Devil's staircases in synthetic dimensions and gauge fields

TL;DR

This paper explores the emergence of devil's staircase phenomena in a synthetic dimension system of cold atoms under high synthetic magnetic fields, revealing complex crystal ground states due to long-range interactions.

Contribution

It introduces an effective one-dimensional lattice model for atoms in synthetic dimensions, demonstrating the occurrence of devil's staircase in this novel setting.

Findings

Identification of a cascade of crystal ground states

Demonstration of long-range interactions dominating in the synthetic dimension

Establishment of analogy with quantum Hall systems in the thin-torus limit

Abstract

We study interacting bosonic or fermionic atoms in a high synthetic magnetic field in two dimensions spanned by continuous real space and a synthetic dimension. Here, the synthetic dimension is provided by hyperfine spin states, and the synthetic field is created by laser-induced transitions between them. While the interaction is short-range in real space, it is long-range in the synthetic dimension in sharp contrast with fractional quantum Hall systems. Introducing an analog of the lowest-Landau-level approximation valid for large transition amplitudes, we derive an effective one-dimensional lattice model, in which density-density interactions turn out to play a dominant role. We show that in the limit of a large number of internal states, the system exhibits a cascade of crystal ground states, which is known as devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.