Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice

Abstract

We propose a feasible scheme to realize a four-band Stiefel-Whitney insultor (SWI) with spin-orbit coupled ultracold atoms in an optical Raman lattice. Four selected spin states are coupled by carefully designed Raman lasers, to generate the desired spin-orbit interactions with spacetime inversion symmetry. We map out a phase diagram with respect to the experimental parameters, where a large topological phase region exists. We further present two distinct detection methods to resolve the non-abelian band topology, in both equilibrium and dynamical ways. The detection relies on the spin textures extracted from the time-of-flight imaging, showing the tomographic signatures in the ground states and long-time averaged patterns on certain submanifold via a bulk-surface duality. Our work paves a realistic way to explore novel real topology with quantum matters.

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• Topologically nontrivial and trivial flat bands via weak and strong interlayer coupling in twisted bilayer honeycomb optical lattices for ultracold atoms
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc
• Ultracold atomic lattice systems for simulating topological phases: A review
• Preparation and observation of anomalous counterpropagating edge states in a periodically driven optical Raman lattice
• Detecting degenerate bands topological invariants in optical lattice