Non-ergodic dynamics in tunable Bose-Hubbard models

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Within this project, we are going to complete the development and construction of a tunable experimental platform based on the unique properties of ultracold Cs atoms, which combines bichromatic superlattices, state-dependent lattices, Feshbach resonances and quantum-gas microscopy in order to study non-ergodic dynamics beyond conventional many-body localization and standard Bose-Hubbard models. Recently, novel forms of localization have been predicted in homogeneous translationally-invariant systems without disorder. One example are so-called fragmented models, where the many-body Hilbert-space fragments into exponentially many disconnected subspaces or fragments that are not related to any obvious symmetry of the underlying Hamiltonian. Within this project, we are going to investigate the rich relaxation dynamics of tilted Bose-Hubbard models in one- and two-dimensions. Tilted Hubbard models are expected to perturbatively exhibit fragmentation in the limit of large tilts. One of the most striking signatures of fragmentation is the strong initial-state dependence of the relaxation dynamics, which can be directly observed using quantum gas microscopes. Due to the fragmented nature of the many-body spectrum, thermalization needs to be defined with respect to individual fragments. This results in characteristic behavior, e.g., for initial states that thermalize within a fragment the entanglement entropy quickly saturates to a value that is determined by the dimension of the fragment it lives in. This is in stark contrast to the behavior of conventional many-body-localized systems that exhibit a logarithmic growth. We are going to reveal this difference by measuring local observables, such as two-point correlations and local currents, facilitated by quantum gas microscopy and optical superlattices. Intriguingly, fragmentation paves the way towards stable non-ergodic phases in more than one dimension. As an extension, we are going to develop state-dependent optical lattices with sizable nearest-neighbor interactions and next-nearest-neighbor hopping. These terms offer additional tunability of the microscopic parameters, which will be extremely valuable for the engineering of novel constrained dynamics in optical lattices to explore different forms of disorder-free ergodicity breaking.