# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 9: Many-body Systems: Equilibration, Chaos and Localization I (joint session DY/TT)

### TT 9.1: Hauptvortrag

### Montag, 16. März 2020, 10:00–10:30, HÜL 186

**Dynamically probing winding numbers of Floquet toplogical insulators in optical lattices** — •André Eckardt — Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden

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 [Phys. Rev. X 3, 031005 (2013)]. I will present two schemes for probing these winding numbers in experiments with ultracold atoms in driven optical lattices. The first one relies on the quench-based tomography [PRL 113, 045303 (2014), Science 352, 1091 (2016)] of band-touching singularities occurring, when adiabatically connecting the driven system to a trivial high-frequency regime [PRL 122, 253601 (2019)]. The second one is based on observing the far-from equilibrium micromotion of the driven system within two driving periods after a sudden quench into the target Hamiltonian and relies on the identification of the winding numbers with an Hopf invariant characterizing the micromotion operator [Phys. Rev. Research 1, 022003(R) (2019)]. Together with the measurement of Chern numbers from the far-from equilibrium dynamics monitored in stroboscopic steps of the driving period [Nat. Comms. 10, 1728 (2019)], it provides a full characterization of the system.