Floquet-engineering topological and spin-dependent bands with interacting ultracold fermions

Periodically driven quantum systems, when observed on time-scales longer than one modulation period, can be described by effective Floquet Hamiltonians that show qualitatively new features. Using a magnetic field gradient, we apply an oscillating force to ultracold fermions in an optical lattice. The resulting effective energy bands then become spin dependent, allowing for a tunable ratio of the effective mass for each internal state, also giving access to the regime where one spin is completely localized whilst the other remains itinerant. In a honeycomb lattice, circular modulation leads to the appearance of complex next-nearest neighbour tunnelling. This corresponds to a staggered magnetic flux in the lattice, allowing for the realisation of Haldane's model of a topological Chern insulator. When spin dependence is included, time-reversal symmetry can be restored giving rise to the Kane-Mele model. A crucial question is whether Floquet engineering can be extended to interacting systems, how the resulting Hamiltonians are modified, and whether the system thermalizes to a steady state. In particular, we study how heating in the system depends on the modulation and interaction parameters and identify regimes where it becomes negligible.