Devil's staircases in synthetic dimensions and gauge fields

Takeshi Y. Saito, Shunsuke Furukawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

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

Original languageEnglish
Article number043613
JournalPhysical Review A
Volume95
Issue number4
DOIs
Publication statusPublished - 2017 Apr 12
Externally publishedYes

Fingerprint

stairways
cascades
interactions
analogs
ground state
approximation
magnetic fields
crystals
lasers
atoms

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Devil's staircases in synthetic dimensions and gauge fields. / Saito, Takeshi Y.; Furukawa, Shunsuke.

In: Physical Review A, Vol. 95, No. 4, 043613, 12.04.2017.

Research output: Contribution to journalArticle

@article{c2cd4999562c4da589a12e56e93f7e92,
title = "Devil's staircases in synthetic dimensions and gauge fields",
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 the devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.",
author = "Saito, {Takeshi Y.} and Shunsuke Furukawa",
year = "2017",
month = "4",
day = "12",
doi = "10.1103/PhysRevA.95.043613",
language = "English",
volume = "95",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "4",

}

TY - JOUR

T1 - Devil's staircases in synthetic dimensions and gauge fields

AU - Saito, Takeshi Y.

AU - Furukawa, Shunsuke

PY - 2017/4/12

Y1 - 2017/4/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85017603014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017603014&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.95.043613

DO - 10.1103/PhysRevA.95.043613

M3 - Article

VL - 95

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 043613

ER -