Dynamical effects in ultracold atomic gases : macroscopic quantum tunneling and bulk viscosity

Abstract

Thanks to the development of new techniques in recent decades, experimental- ists have made remarkable progresses in controlling ultracold atomic gas systems. In particular, ultracold atoms confined in finely tuned trapping potential with tunable inter-particle interactions provide an ideal platform for studying many interesting topics in many-particle physics. In this thesis, we investigate some aspect of dy- namical effects in ultracold atomic gases, including the many-particle effect in the macroscopic quantum tunneling of a weakly interacting Bose-Einstein condensate and the bulk viscosity of a strongly interacting Fermi gas. Motivated by the recent experimental progresses of interaction-assisted macro- scopic quantum tunneling, we study the tunneling of an interacting Bose-Einstein condensate from a cubic-plus-quadratic well to open space. By using the Gross- Pitaevskii equation and the WKB method, we investigate the effect of inter-particle interactions on the tunneling rate of a condensate trapped in a cubic-plus-quadratic well. By applying the Thomas-Fermi approximation, we give the explicit depen- dences on the chemical potential of the tunneling rate of the condensate. By a Magnus expansion, we obtain an effective Hamiltonian for a periodically driven sys- tem and study the effect of the modulation on the tunneling rate. We find that both the repulsive interactions and an increase of modulation frequency result in an enhancement of quantum tunneling of a trapped Bose-Einstein condensate in a cubic-plus-quadratic potential well. Furthermore, motivated by the recent progresses of measuring the breaking of scale invariance in s-wave gases, we utilize the virial expansion and the kinetic theory to investigate the bulk viscosity of a strongly interacting s-wave Fermi gas with effective range near unitarity in the high-temperature limit. Also, we take into consideration the imaginary part of the fermion self-energy for the correction to the bulk viscosity. We show that two parameters, relating to the scattering length and the effective range, determine the measure of scale invariance breaking in an s-wave Fermi gas near resonance in the high-temperature limit. We also show that the scale invariance breaking manifests itself in the bulk viscosity in terms of these two scale breaking parameters. Subsequently, motivated by the realization of p-wave resonantly Fermi gases in experiment, we generalize our calculation of the bulk viscosity to the p-wave Fermi gas. We show that the bulk viscosity in the p-wave Fermi gas near resonance, simi- larly, is determined by two scale breaking parameters relating to the scattering length and the effective range. However, the effective range plays a very different role in the two cases. For an s-wave Fermi gas at resonance, the bulk viscosity vanishes, and scale invariance is recovered when the effective range is tuned to zero. Unlike the s-wave case, in the p-wave Fermi gas, even in the limit of vanishing effective range, the scale invariance remains broken which leads to a non-zero bulk viscosity.