Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles

Abstract

Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this work, we numerically analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model in a box potential. By monitoring the Hall drift upon release, for a wide range of magnetic flux values, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the extracted Hall conductivity approaches a fractional value determined by the many-body Chern number, while the width of the plateau agrees with the spectral and topological properties of the prepared ground state. Besides, a direct application of Streda's formula indicates that such Hall plateaus can also be directly obtained from static density-profile measurements. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods.

13 pages, 11 figures; extended version accepted for publication

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• Recent Developments in Fractional Chern Insulators
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• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
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• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Topological pumping induced by spatiotemporal modulation of interaction
• Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations
• Floquet engineering flat bands for bosonic fractional quantum Hall in small lattices
• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Uncover band topology via quantized drift in two-dimensional Bloch oscillations
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Interaction dependence of the Hall response for the Bose-Hubbard triangular ladder
• Measurable fractional spin for quantum Hall quasiparticles on the disk
• Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements
• Bulk density signatures of a lattice quasihole with very few particles
• Quantized valley Hall response from local bulk density variations
• Absence of gapless Majorana edge modes in few-leg bosonic flux ladders
• Chiral Edge Excitations of $\nu =1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model
• Emergent topological properties in spatially modulated sub-wavelength barrier lattices