LAUSR

Description of periodically and resonantly driven 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 different two-dimensional time lattices with the Möbius strip geometry can be realized for ultra-cold 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.