Interferometry of non-Abelian band singularities and Euler class topology
arxiv(2024)
摘要
In systems with a real Bloch Hamiltonian band nodes can be characterised by a
non-Abelian frame-rotation charge. The ability of these band nodes to
annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps
the sign of their charges can be changed. Here, we theoretically construct and
numerically confirm two concrete methods to experimentally probe these
non-Abelian braiding processes and charges in ultracold atomic systems. We
consider a coherent superposition of two bands that can be created by moving
atoms through the band singularities at some angle in momentum space. Analyzing
the dependency on the frame charges, we demonstrate an interferometry scheme
passing through two band nodes, which reveals the relative frame charges and
allows for measuring the multi-gap topological invariant. The second method
relies on a single wavepacket probing two nodes sequentially, where the frame
charges can be determined from the band populations. Our results present a
feasible avenue for measuring non-Abelian charges of band nodes and the
experimental verification of braiding procedures directly, which can be applied
in a variety of settings including the recently discovered anomalous
non-Abelian phases arising under periodic driving.
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