Coherence and decoherence in the Harper-Hofstadter model

Abstract

We quantum-simulated the 2D Harper-Hofstadter (HH) lattice model in a highly elongated tube geometry -- three sites in circumference -- using an atomic Bose-Einstein condensate. In addition to the usual transverse (out-of-plane) magnetic flux, piercing the surface of the tube, we threaded a longitudinal flux ${\Phi }_{\mathrm{L}}$ down the axis of the tube This geometry evokes an Aharonov-Bohm interferometer, where noise in ${\Phi }_{\mathrm{L}}$ would readily decohere the interference present in trajectories encircling the tube. We observe this behavior only when transverse flux is a rational fraction of the flux-quantum, and remarkably find that for irrational fractions the decoherence is absent. Furthermore, at rational values of transverse flux, we show that the time evolution averaged over the noisy longitudinal flux matches the time evolution at nearby irrational fluxes. Thus, the appealing intuitive picture of an Aharonov-Bohm interferometer is insufficient. Instead, we quantitatively explain our observations by transforming the HH model into a collection of momentum-space Aubry-André models.

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Cited by in corpus (13)

• Thouless pumping and topology
• A comprehensive review on developments of synthetic dimensions
• Laughlin's topological charge pump in an atomic Hall cylinder
• Bose-Einstein Condensate on a Synthetic Topological Hall Cylinder
• Manipulating synthetic gauge fluxes via multicolor dressing of Rydberg-atom arrays
• Resonant dynamics of strongly interacting SU($n$) fermionic atoms in a synthetic flux ladder
• Experimental realization of a fermionic spin-momentum lattice
• Synthetic Hall ladder with tunable magnetic flux
• Localization on a synthetic Hall cylinder
• Simulating two-dimensional dynamics within a large-size atomic spin
• Many-body phases from effective geometrical frustration and long-range interactions in a subwavelength lattice
• Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions
• Quantum States and Spectra of Small Cylindrical and Toroidal Lattices