Dynamics of quantum statistical correlations in ultracold Bose gases [Elektronische Ressource] / put forward by Cédric Daniel Ghislain Bodet

DISSERTATIONsubmitted to theCombined Faculties of theNatural Sciences and Mathematicsof theRuperto-Carola-Universityof Heidelberg, Germanyfor the degree ofDoctor of Natural SciencesPut forward byCEDRIC DANIEL GHISLAIN BODETborn in Charleroi (D1), BelgiumOral examination:January 19, 2011DYNAMICS OF QUANTUMSTATISTICAL CORRELATIONSIN ULTRACOLD BOSE GASESReferees: Prof. Dr. Thomas GasenzerPD Dr. J org EversAbstractThe dynamical evolution of an ultracold Bose gas distributed across the sites ofan optical lattice is investigated theoretically in the framework of the Bose-Hubbardmodel. First, the focus is set on the evolution of squeezing correlations in the two modesystem. It is shown that the eigenstates of the Hamiltonian do not exploit the fullregion of possible squeezing allowed by Heisenbergs uncertainty relation for number andphase uctuations. The development of nonclassical correlations and relative numbersqueezing is studied at the transition from the Josephson to the Fock regime. Comparingthe full quantum evolution with classical statistical simulations allows us to identifyquantum aspects of the squeezing formation. In the quantum regime, the measurementof squeezing allows us to distinguish even and odd total particle number states. Then, afar from equilibrium quantum eld theory method, the so-called two-particle-irreduciblee ective action approach, is presented for the description of the dynamics in largerlattices.