Abstract
Description of periodically and resonantly driven quantum systems can lead to solid state models where condensed matter phenomena can be investigated in time lattices formed by periodically evolving Wannier-like states. Here, we show that inseparable two-dimensional time lattices with the Möbius strip geometry can be realized for ultracold atoms bouncing between two periodically oscillating mirrors. Effective interactions between atoms loaded to a lattice can be long-ranged and can be controlled experimentally. As a specific example, we show how to realize a Lieb lattice model with a flat band and how to control long-range hopping of pairs of atoms in the model.
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