Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices

Abstract

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically non-trivial phases of matter with ultracold atoms has become a major focus of cold atom experiments. However, several obvious differences exist between cold atom and solid state systems, for instance the finite size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states which belong to a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.

12 pages, 10 figures, updated figures and minor text corrections

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• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
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• Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
• Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons
• Quantum simulation of non-trivial topology
• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Real-space detection and manipulation of topological edge modes with ultracold atoms
• Modification and Control of Topological Insulator Surface States Using Surface Disorder
• Reversal of quantised Hall drifts at non-interacting and interacting topological boundaries
• Identifying topological edge states in 2D optical lattices using light scattering
• Multiplicative topological phases
• Topological flat bands in optical checkerboard-like lattices
• Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice
• Realization and detection of Kitaev quantum spin liquid with Rydberg atoms
• Preparation and observation of anomalous counterpropagating edge states in a periodically driven optical Raman lattice
• Detecting degenerate bands topological invariants in optical lattice