Interacting bosons in periodically modulated optical lattices: realization of a moat band and pre-thermal relaxation in effective Hamiltonians

We experimentally realize two different effective Hamiltonians for weakly interacting bosons held in periodically modulated optical lattices, both of which are proposed platforms for generating correlated topological states. Since the interactions required for many interesting Floquet-engineered states often lead to heating, we also study heating and equilibration in the modulated lattices. First, by modulating the amplitude of a checkerboard optical lattice, we generate an effective single particle Hamiltonian where the energy displays a continuum of nearly degenerate minima that lie along a circle in reciprocal space. We measure the condensate lifetime and argue that the observed dynamical instability is characteristic of condensates in any moatlike dispersion, including spin-orbit coupled systems. In separate experiments we shake the checkerboard lattice to engineer single particle Hamiltonians with dynamically tunable effective magnetic fields. By quenching the system between different Floquet-induced fields with different equilibrium ground states, we observe Bose re-condensation of quench-excited atoms on time scales faster than global heating due to the drive. These results are promising steps toward generation of correlated states by Hamiltonian modulation, but drive-induced heating (observed here in the weakly interacting limit) is poorly understood in the highly correlated limit and needs to be further studied to determine if such correlates states are realizable.