"Bosonic Gases with Impurities and Dipolar Interactions"
The behaviors of weakly interacting Bose gases have been successfully modeled within a mean-field framework. To this end, one replaces the true atom-atom potential by a contact interaction, and solves the resulting many-body Schroedinger equation at the Hartree level. The resulting non-linear single-particle Schroedinger equation, also referred to as Gross-Pitaevskii equation, predicts many behaviors of inhomogeneous Bose gases accurately, including the onset of instability for Bose systems with with negative two-body s-wave scattering length for a critical number of particles. Rapid advances in trapping and cooling now allow ions or impurities in ultracold gases to be studied and molecular gases to be created. Motivated by these experimental efforts, the first part of this talk discusses the phase diagram of impurities in inhomogeneous Bose gases. Employing a simple mean-field framework, a regime where the impurity is located at the center of the atom cloud is identified. For negative atom-impurity and positive atom-atom scattering lengths, we find that the system collapses for a critical set of parameters. This behavior shows similarities to the collapse of inhomogeneous pure Bose gases with negative atom-atom scattering length. The second part of this talk discusses the behaviors of dipolar Bose gases. We determine the energetics of a molecular gas, for which the dipole moment can be varied through application of external fields, within a mean-field framework and within an essentially exact many-body Monte Carlo framework. Our results indicate consequences for the collapse of cold Bose gases, consisting of polar molecules with non-negligible dipole moment.