How to Directly Measure Floquet Topological Invariants in Optical Lattices

F. Nur Ünal; Babak Seradjeh; André Eckardt

doi:10.1103/physrevlett.122.253601

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arXiv · 1812.04636

How to Directly Measure Floquet Topological Invariants in Optical Lattices

F. Nur Ünal·Babak Seradjeh·André Eckardt

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Abstract

The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the quasienergy gaps. We propose a scheme for measuring these winding numbers in a system of fermionic cold atoms in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of experimentally feasible drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a byproduct, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.

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F. Nur Ünal, Babak Seradjeh, André Eckardt. 2018-12-11. How to Directly Measure Floquet Topological Invariants in Optical Lattices. https://doi.org/10.1103/physrevlett.122.253601

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