Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases [Elektronische Ressource] / Tobias Gottwald

Superfluid and Antiferromagneticphases in Ultracold FermionicQuantum GasesD I S S E R T A T I O Nzur Erlangung des Grades“Doktor der Naturwissenschaften”am Fachbereich Physik, Mathematik und Informatikder Johannes Gutenberg-Universitat¨in MainzTobias Gottwaldgeb. in MainzMainz, den 27.08.2010(D77)AbstractIn this thesis several models are treated, which are relevant for ultracold fermionic quantumgasesloadedontoopticallattices. Inparticular,imbalancedsuperfluidFermimixtures,whichare considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) statesexperimentally, and antiferromagnetic states, whose experimental realization is one of thenext major goals, are examined analytically and numerically with the use of appropriateversions of the Hubbard model.The usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in amagnetic fieldwithastrengthexceedingthesizeof thesuperfluidgap. Aspatially inhomoge-neousspin-imbalancedsuperconductorwithacomplexorderparameterknownasFFLO-stateis predicted to occur in translationally invariant systems. Since in ultracold quantum gasesthe experimental setups have a limited size and a trapping potential, we analyze the realisticsituation of a non-translationally invariant finite sized Hubbard model for this purpose.