Date of Award

Spring 1-1-2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

First Advisor

Chris H. Greene

Second Advisor

Ana Maria Rey

Third Advisor

John L. Bohn

Fourth Advisor

Michael Hermele

Fifth Advisor

Deborah S. Jin

Abstract

In this dissertation, we study the few-body ultracold Bose-Fermi mixture and quasi-1D scattering at ultracold temperature. Degenerate quantum gases have attracted enormous attentions during the past two decades. They have opened new platforms of quantum simulation, precision measurement and quantum chemistry. The scattering properties of degenerate quantum gases are the first things to study in order to gain insight into various novel phenomena at ultracold temperatures.

To address the role of quantum statistics at ultracold temperature, we study the spectrum and dynamics of a few-body Bose-Fermi mixtures. In particular, we focus the dynamical evolution of a few-body Bose-Fermi mixture and concentrate on its universal behavior at large inter-particle scattering length. We predict the molecule formation efficiency in many-body Bose-Fermi mixtures by mapping this critical observable in few-body calculations. We also propose that a the quantum beat experiment could be used to measure the energy of the lowest Efimov trimer at unitarity.

To address the role of dimensionality, we study confinement induced resonances and similar phenomena in general transverse confining potentials. Well-separated energy scales in different dimensions allow the creation of reduced dimensional systems at ultracold temperatures. We develop a general framework to regularize the low-energy quasi-1D scattering phase shift associated with a zero range interaction.

Lastly, we discuss future prospects for the study of an ultracold Bose-Fermi mixture, and scattering in reduced dimensional systems of a more general topology.

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