Dynamical Mean-Field Theory Approach for Ultracold Atomic Gases

Chunlei Qu

N. Dupuis

Hugo U. R. Strand, Martin Eckstein, Philipp Werner

Ultracold atomic gases allow scientists to study the out-of-equilibrium dynamics of many-particle systems. A computationally tractable formalism is used to model systems of cold atoms trapped in an optical lattice.

Kaden R. A. Hazzard

Immanuel Bloch, Achim Rosch

Abstract Ultracold quantum gases in optical lattices can be used as novel model system for the exploration of strongly correlated many‐body phases of bosonic or fermionic particles. Here we report on the realization of metallic, Mott‐insulating and band insulating phases in ultracold spin mixtures of fermionic 40K atoms. The experimental results are compared to ab initio dynamical mean field theory (DMFT) calculations.

Stefan K. Baur

Rapid progress in the field of ultracold atoms allows the study of many new and old models of quantum many-body physics. In this doctoral dissertation we theoretically explore exotic phases of ultracold quantum gases, with a special focus spin-imbalanced attractive Fermi gases in lower dimensional situations. Chapter 2 reviews the mean-field theory approach to pairing in twocomponent Fermi gases. Applications of this theory are illustrated in Chapter 3, where we discuss mostly well-known results of mean-field theory applied to imbalanced Fermi gases. Adapted from the author's prior publications, Chapters 4, 5 use the theory developed in Chapters 2, 3. In Chapter 6 we discuss the physics of Fermi gases, squeezed into one spatial dimension. In this and Chapter 7, we go beyond mean-field theory, approaching the problem through the Bethe ansatz, exact solutions to few-body problems and Fermi-Bose mappings ("fermionization"). We also show results from a joint effort with the experimental group of Randy Hulet at Rice University to experimentally realize and probe a strongly interacting one dimensional paired Fermi gas. In Chapter 8, after a brief introduction to rapidly rotating two dimensional Bose gases, we introduce a new protocol to create few atom fractional quantum Hall states. Finally, in Chapter 9 we study the effects of two-body losses on lattice Bose gases with hardcore interactions in one and two spatial dimensions.