Measuring Chern numbers in Hofstadter strips

Abstract

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wavepacket exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

v1: 17 pages, 10 figures; v2: minor changes, reference added, SciPost style, 26 pages, 10 figures; v3: published version

References in corpus (25)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Spin-orbit coupled fermions in an optical lattice clock
• Spin pumping and measurement of spin currents in optical superlattices
• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Laughlin-like states in bosonic and fermionic atomic synthetic ladders
• Direct measurement of topological invariants in optical lattices
• Semi-synthetic zigzag optical lattice for ultracold bosons
• Quantum simulation of non-trivial topology
• Precursor of Laughlin state of hard core bosons on a two leg ladder
• Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
• Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
• Double transfer through Dirac points in a tunable honeycomb optical lattice
• Vortex lattice melting in a boson-ladder in artificial gauge field
• Metallic phase of the quantum Hall effect in four-dimensional space
• Majorana Quasi-Particles Protected by ${\mathbb{Z}}_2$ Angular Momentum Conservation
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Devil's staircases in synthetic dimensions and gauge fields
• Generalized Bloch theorem and topological characterization
• Different models of gravitating Dirac fermions in optical lattices
• Synthetic-gauge-field-induced resonances and Fulde-Ferrell-Larkin-Ovchinnikov states in a one-dimensional optical lattice

Cited by in corpus (15)

• Topological quantum matter in synthetic dimensions
• Synthetic dimensions for topological and quantum phases: Perspective
• Imaging topology of Hofstadter ribbons
• Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Topological phases in odd-legs frustrated synthetic ladders
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics
• Finite-temperature properties of interacting bosons on a two-leg flux ladder
• Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices
• The Coming Decades of Quantum Simulation
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field
• Determination of Chern numbers with a phase retrieval algorithm
• Dynamics of weakly interacting bosons in optical lattices with flux
• Few-particle dynamics of fractional quantum Hall lattice models