Non-equilibrium dynamics and quantum magnetism in 1D optical lattices [Elektronische Ressource] / Karen Rodríguez

Non-equilibrium Dynamics andQuantum Magnetism in1D Optical LatticesVon der Fakult¨at fu¨r Mathematik und Physik derGottfried Wilhelm Leibniz Universit¨at Hannoverzur Erlangung des GradesDoktorin der NaturwissenschaftenDr. rer. nat.genehmigte Dissertation vonM.Sc. Karen Rodr´ıguezgeboren am 01. November 1980 in Bogot´a, Kolumbien2011Referent : Prof. Dr. Luis SantosKorreferent : Prof. Dr. Temo VekuaTag der Promotion : 25.01.2011To ArturoAbstractIn this Thesis we examine the properties of ultra-cold strongly-correlatedquantum gases in optical lattices. Nowadays, spectacular progresses allow foran unprecedented degree of control of interparticle interactions, dimensional-ity, doping, disorder, etc., which permit the detailed analysis of many-bodyphenomena as e.g. the realization of the superfluid to Mott insulator transi-tion in bosonic lattice gases [1], the 3D fermionic Mott insulator [2, 3] or theTonks gas [4]. These advances make strongly-correlated gases an extraordi-nary scenario for the study of condensed matter physics, quantum optics, andquantum information. Cold lattice gases are often proposed as quantum sim-ulators mimicking, for instance, the Hubbard and Heisenberg models. In thisThesis, we analyze, by means of numerical and analytical methods, relevanttopics related to the dynamics and ground-state properties of lattice gases.This Thesis can be divided in two parts.