Abstract: Dynamical measurements of ultra-cold Fermi gases confined to optical potentials can be used to probe features of quantum matter. Control of external parameters like tunneling strengths, lattice geometries and interactions enables investigations of topology and non-equilibrium particle transport. Optical lattice geometry, created by counter propagating laser beams, can be engineered to optimize matter-wave propagation along patterned paths difficult to access in the solid-state. We investigate 2D ladder systems with a particle number bias on one half the lattice and provide a mechanism for controlling the group velocity of fermions as they propagate to the opposite boundary. Transport behavior in the presence of a flat energy band is also elucidated. Furthermore, we propose protocols to probe topological features of the one-dimensional Su-Schrieffer-Heeger model using an ultracold Fermi gas confined to an optical ring potential, cut by an off-resonant laser sheet. Single-particle injection and atomic depletion are implemented to detect edge-states dynamically for non-interacting fermions. Signatures of topology in the presence of contact interactions can be found in selected correlations as the system boundary suddenly changes from periodic to open and exhibit memory effects of the initial state, distinguishing different configurations.
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