Quantum states in ultracold fermionic gases in optical lattices:Supersolid and dynamically generated antiferromagnetic states

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In recent years the fields of condensed matter physics and ultracold atomic gas physics have developed a fruitful interplay. The former has a long history of describing quantum states of matter based on simplified models, such as the Hubbard model, whilst the latter now manages to simulate these models and generate exciting quantum states. The twofold objective of the research project is to better understand the stability of the supersolid quantum state and the dynamic generation of antiferromagnetic (AF) quantum states. The supersolid state of matter, a peculiar state with simultaneous crystalline order and superfluid properties, has been proposed to be realizable in a gas of attractive fermions confined to an optical lattice. The research project will theoretically model such a state and analyze its stability. This will be achieved by real space dynamical mean field calculations utilizing the numerical renormalization group as an impurity solver. The second part deals with a correlated fermionic system, which by an interaction quench is driven into situation where a strong AF instability is present. Using the Hubbard model, we will develop and apply non-equilibrium techniques to understand the resulting behavior. A realization of this non-equilibrium situation is possible for an ultracold gas of fermions in an optical lattice with commensurate filling, which is tuned suddenly to the strongly repulsive side of a Feshbach resonance. There, the AF instability competes with processes of molecule formation, which can also occur on this side of the Feshbach resonance. By taking into account both processes we will investigate theoretically the time-dependent response of the system and predict its dominant behavior. Current experiments are performed in regimes very close to the situations described here. The expected experimental realizations within the next years make it a timely and highly relevant research project.