Quantum particle in a parabolic lattice in the presence of a gauge field

Abstract

We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult, the interplay of harmonic potential and lattice leads to a different classification of states in three energy regions: In the low-energy regime, where lattice effects are small, all states are transporting topologically non-trivial states. For large energies above a certain critical value, the periodic lattice causes localization of all states through a mechanism similar to Wannier-Stark localization. In the intermediate energy regime transporting, topologically non- trivial states coexist with topologically trivial counter-transporting chaotic states. The character of the eigenstates, in particular their transport properties are studied numerically and are explained using a semiclassical analysis.

10 pages, 16 figures

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• Direct imaging of topological edge states in cold-atom systems
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Cited by in corpus (13)

• Quantum Mechanics with a Momentum-Space Artificial Magnetic Field
• Topological growing of Laughlin states in synthetic gauge fields
• Bose-Hubbard Hamiltonian: Quantum Chaos approach
• Reversal of quantised Hall drifts at non-interacting and interacting topological boundaries
• Generation of uniform synthetic magnetic fields by split driving of an optical lattice
• Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap
• Local Chern marker of smoothly confined Hofstadter fermions
• Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice
• Growing quantum states with topological order
• Wavepacket dynamics on Chern band lattices in a trap
• Response of fermions in Chern bands to spatially local quenches
• Few-particle dynamics of fractional quantum Hall lattice models
• Determination of electron-hole correlation length in CdSe quantum dots using explicitly correlated two-particle cumulant