Deep strong coupling of quantum mechanical motional modes with ultracold atoms in an optical lattice potential

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Ultracold atoms in optical lattice potentials represent an excellent system both for the physical implementation and for the quantum simulation of effects from different physical domains. Examples include the demonstration of phenomena known from solid-state physics, as the Mott-Isolator transition, or predictions of relativistic wave equations. In preparatory work, our group succeeded in demonstrating relativistic Klein tunneling with ultracold atoms in an optical lattice of variable dispersion, atomic quantum ratchets, and recently the spatial resolving of a topologically protected edge state with atoms in an optical lattice. Central to these experiments was the development of variable optical multi-photon lattices in our research group.Based on these preliminary works, we plan to exploit the regime of extremely strong coupling of quantum mechanical modes, in which the coupling strength between the modes exceeds their eigenfrequencies, using ultracold atoms in optical lattice potentials. On the theoretical side our experimental work is supported by the theory group of Prof. E. Solano, University of the Basque Country in Bilbao, with which the theoretical concept for the planned experimental procedure was jointly developed. With the ultracold atom system, we plan to experimentally demonstrate novel physics effects of the deep strong coupling regime.