Direct Geometric Probe of Singularities in Band Structure

Abstract

The band structure of a crystal may have points where two or more bands are degenerate in energy and where the geometry of the Bloch state manifold is singular, with consequences for material and transport properties. Ultracold atoms in optical lattices have been used to characterize such points only indirectly, e.g., by detection of an Abelian Berry phase, and only at singularities with linear dispersion (Dirac points). Here, we probe band-structure singularities through the non-Abelian transformation produced by transport directly through the singular points. We prepare atoms in one Bloch band, accelerate them along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic touching points of a honeycomb lattice. Measurements of the band populations after transport identify the winding numbers of these singularities to be 1 and 2, respectively. Our work opens the study of quadratic band touching points in ultracold-atom quantum simulators, and also provides a novel method for probing other band geometry singularities.

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• Direct Geometric Probe of Singularities in Band Structure

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• Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Direct Geometric Probe of Singularities in Band Structure
• Cubic singularities in binary linear electromechanical oscillators
• Instantaneous response and quantum geometry of insulators
• Experimental demonstration of topological bounds in quantum metrology
• Frustrated extended Bose-Hubbard model and deconfined quantum critical points with optical lattices at the anti-magic wavelength
• Interferometry of non-Abelian band singularities and Euler class topology
• Multi-frequency optical lattice for dynamic lattice-geometry control
• Engineering Higgs dynamics by spectral singularities
• Transport of ultracold atoms in superpositions of S- and D-band states in a moving optical lattice
• Topologically nontrivial and trivial flat bands via weak and strong interlayer coupling in twisted bilayer honeycomb optical lattices for ultracold atoms
• Many-body phases from effective geometrical frustration and long-range interactions in a subwavelength lattice
• Unconventional transport properties in systems with triply degenerate quadratic band crossings
• Spin Phonon Relaxation Dynamics from a Conical Intersection of Trapped Rydberg Ions