Ultracold atoms in optical lattices have proven to be a powerful platform to simulate and engineer out-of-equilibrium phenomena of isolated quantum many-body systems. Here, I will report on two recent research directions: Floquet engineering of topological systems and non-ergodic behavior in tilted Fermi-Hubbard models.
A widespread technique for generating topological band structures in synthetic systems is Floquet engineering, i.e., the periodic modulation of the system’s parameters to emulate the properties of a non-trivial static system. This facilitated the realization of paradigmatic topological lattice models and recently inspired ideas for implementing Z2 lattice gauge theories . The rich properties of Floquet systems, however, transcend those of their static counterparts, resulting in a generalized bulk-edge correspondence. As a consequence, topological edge modes can exist even in situations where the bulk bands have zero Chern numbers. The novel properties of such anomalous Floquet systems open the door to exciting new non-equilibrium phases without any static analogue. In our work, we have realized anomalous Floquet systems with bosonic atoms in a periodically-modulated honeycomb lattice. Moreover, we have determined the full set of topological invariants via energy-gap and local Hall-deflection measurements .
Thermalization of isolated quantum many-body systems is a fundamental problem that has important connections to quantum information theory. While generic models are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), violation of ETH is believed to occur mainly in two types of systems: integrable models and many-body localized systems. In contrast, recent studies have predicted non-ergodic dynamics in disorder-free lattice models, due to an emergent fragmentation of the Hilbert space into many dynamically disconnected subspaces. Here, we realize such a model by implementing the 1D Fermi-Hubbard model with a strong linear potential (“tilt”). Starting from an initial charge-density wave (quarter filling), we find a robust memory of the initial state up to about 700 tunneling times, signaling non-ergodic behavior . While in the strong-tilt regime we expect Hilbert-space fragmentation to inhibit thermalization due to dipole conservation, this is not expected to hold in the parameter regime studied here. We interpret the robustness of our observations by the presence of additional energy penalties, which significantly slow down the dynamics and result in approximately disconnected subspaces that we identify numerically.
 C. Schweizer et al., Nat. Phys. 15, 1168-1173 (2019)
 K. Wintersperger et al., Nature Physics 16, 1058-1063 (2020)
 S. Scherg et al., arXiv:2010.12965 (2020)
Panopto recording: GMT20201207-201710_UW-Physics_1760x900