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 language | English |
|---|---|
| Article number | 043613 |
| Journal | Physical Review A |
| Volume | 95 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2017 Apr 12 |
| Externally published | Yes |
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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 journal › Article
}
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 -