Freiburg 2024 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 28: Fermionic Quantum Gases I (joint session Q/A)
Q 28.1: Talk
Wednesday, March 13, 2024, 11:00–11:15, HS 1199
Bulk-boundary correspondence for anomalous Floquet topological insulators: winding number and micromotion area — •Luca Asteria1,2, Klaus Sengstock1,2,3, and Christof Weitenberg1,2 — 1Institut for Quantum Physics, Hamburg University — 2Hamburg Centre for Ultrafast Imaging — 3Center for Optical Quantum Technologies, Hamburg University
Driven Floquet systems can realize topological phases with no static counterparts. So-called anomalous Floquet topological insulators (AFTIs) break the bulk-boundary correspondence based on the Chern number. The winding number, which predicts the number of edge modes instead, is calculated from the time evolution operator of the bulk states within one driving period. While in non-driven system the Chern number also predicts the quantization of the transversal Hall conductance in the systems bulk, for AFTIs so far, no dynamical bulk observable directly connected to the winding number was identified. Here we show that the winding number is directly connected to such an observable, namely the area enclosed by an initially localized particle during a Floquet period. In particular, in the associated fine-tuning limit of the Floquet protocol, we show that the winding number is exactly given by this area in units of half the unit cell area. Such a direct real-space detection of anomalous topology could be realized in several quantum simulation platforms. We also show how, by choice of the associated fine-tuning protocol, the number and the speed of coexisting edge modes could be arbitrarily tuned, which may be of relevance for quantum information and communication applications.
Keywords: Anomalous Topological Insulators; Floquet Driven Systems; Optical lattice