SUPERSOLDYNAF · Quantum states in ultracold fermionic gases in optical lattices:Supersolid and dynamic antiferromagnetic states

In recent years the fields of condensed matter physics and ultracold atomicgas physics have developed a fruitful interplay. The former has a long historyof describing quantum states of matter based on simplified models,such as the Hubbard model, whilst the latter now manages tosimulate these models and generate exciting quantum states. Thetwofold objective of the research project is to betterunderstand the stability of the supersolid quantum state and thenon-adiabatic dynamic generation of antiferromagnetic (AF) quantumstates. The supersolid state of matter, a peculiar state withsimultaneous crystalline order and superfluid properties, hasbeen proposed to be realizable in a gas of attractive fermionsconfined to an optical lattice. The research project willtheoretically model such a state and analyze its stability. This will beachieved by real space dynamical mean field calculations utilizing thenumerical renormalization group as an impurity solver.The second part deals with a correlated fermionic system whichby an interaction quench is driven into a situation where a strong AFinstability is present. Using the Hubbardmodel, we will develop and apply non-equilibriumtechniques to understand the resulting behavior.A realization of this non-equilibrium situation is possible foran ultracold gas of fermions in an optical lattice with commensuratefilling, which is tuned suddenly to the stronglyrepulsive side of a Feshbach resonance. There, the AF instabilitycompetes with processes of molecule formation, whichcan also occur on this side of the Feshbach resonance. By taking intoaccount both processes we will investigate theoretically thetime-dependent response of the system and predict itsdominant behavior.Current experiments are performed in regimes very close to the situationsdescribed here. The expected experimental realizations within the next yearsmake it a timely and highly relevant research project.