Generating gauge fields in optical Kagome and dice lattices
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Flat energy bands are suitable for observing the Fractional Quantum Hall Effect. We propose an optical setup that can be used for probing flat bands of the Kagome and dice lattice structures dressed by a gauge field. For the Kagome lattice we show that these bands are indeed topologically nontrivial. We suggest using an optical potential that generates the Kagome and dice structures simultaneously. We propose a lattice shaking-scheme to induce a gauge field that is equivalent to a magnetic field, resulting in the desired energy spectrum. Combining the shaking with resonant driving and a site-dependent phase shift, we present a construction for the Kagome lattice that generates flat bands that can be probed experimentally. Implementing interactions in this setup immediately corresponds to being in the strongly correlated regime.