Devil's staircases in synthetic dimensions and gauge fields

Takeshi Y. Saito, Shunsuke Furukawa

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16 Citations (Scopus)


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 the devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.

Original languageEnglish
Article number043613
JournalPhysical Review A
Issue number4
Publication statusPublished - 2017 Apr 12
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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