Chih-Chun Chien

Nonperturbative Predictions for Cold Atom Bose Gases with Tunable Interactions

We derive a theoretical description for dilute Bose gases as a loop expansion in terms of composite-field propagators by rewriting the Lagrangian in terms of auxiliary fields related to the normal and anomalous densities. We demonstrate that already in leading order this nonperturbative approach describes a large interval of coupling-constant values, satisfies Goldstones theorem, yields a Bose-Einstein transition that is second order, and is consistent with the critical temperature predicted in the weak-coupling limit by the next-to-leading-order large-N expansion.

Large-Napproximation for one- and two-component dilute Bose gases

We discuss the mean-field theories obtained from the leading order in a large-

Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases

N

Auxiliary-field approach to dilute Bose gases with tunable interactions

approximation for one- and two- component dilute Bose gases. For a one-component Bose gas this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature

Quench dynamics and emergence of phase separation in two-component atomic Bose gases at zero temperature and above the Bose-Einstein-condensation critical temperature

T_c

Composite-Field Goldstone States and Higgs Mechanism in Dilute Bose Gases

is not shifted from the non-interacting gas value

Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model

T_0

Fermi-liquid theory of ultracold trapped Fermi gases: Implications for pseudogap physics and other strongly correlated phases

. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intra- species interactions and focus on the stability of the mixture state above

Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

T_c

A large-N expansion based theoretical framework for modeling cold atoms in and out of equilibrium

. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the inter-species interaction strength to the intra-species interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.