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

9 pages, 4 figures

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• Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation
• Microscopic theory of the quantum Hall hierarchy
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• Observation of Devil's Staircase in the Novel Spin Valve System SrCo${}_6$O${}_{11}$
• Real space mean-field theory of a spin-1 Bose gas in synthetic dimensions
• Bosonic integer quantum Hall effect as topological pumping

Cited by in corpus (15)

• Topological quantum matter in synthetic dimensions
• Roadmap on Atomtronics: State of the art and perspective
• Experimental band structure spectroscopy along a synthetic dimension
• Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux
• Quantum phase transitions of a two-leg bosonic ladder in an artificial gauge field
• Coupled Atomic Wires in a Synthetic Magnetic Field
• Measuring Chern numbers in Hofstadter strips
• Different models of gravitating Dirac fermions in optical lattices
• Bosonic integer quantum Hall effect as topological pumping
• Topological chiral currents in the Gross-Neveu model extension
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Synthetic Hall tube of interacting fermions
• Devil's staircases without particle-hole symmetry
• Advances in Synthetic Gauge Fields for Light Through Dynamic Modulation