Dissertation
ULTRACOLD FERMIONIC FEW-BODY SYSTEMS IN REDUCED DIMENSIONS: STATIC AND DYNAMIC PROPERTIES
Doctor of Philosophy (PhD), Washington State University
01/2015
Handle:
https://hdl.handle.net/2376/6232
Abstract
Much progress has been made in the preparation and manipulation of tunable ultracold atomic samples over the last three decades. Small samples of ultracold $^6$Li atoms, e.g., have been prepared experimentally in effectively one-dimensional geometries. The study of few-atom samples is particularly interesting since they serve as building blocks of many-body systems. This thesis studies static and dynamic properties of ultracold fermionic few-body systems. A Lippmann-Schwinger equation based approach is utilized to obtain highly-accurate energies and eigenfunctions of two-component Fermi gases with interspecies zero-range interactions consisting of up to four particles under one-dimensional harmonic confinement. The resulting energy spectra agree quite well with the experimentally measured ones. For infinitely-strong repulsive interaction, the eigenfunctions of the system, which are populated by adiabatically increasing the interaction strength from $0$ to $\\infty$, differ from the eigenfunctions obtained through a generalized Fermi-Fermi mapping, indicating shortcomings of the generalized Fermi-Fermi mapping. The correlations of the “upper branch” reveal, in resemblance with Stoner ferromagnetism, a competition between the repulsive interspecies interaction and the effective repulsion due to the Pauli exclusion principle. Full three-dimensional calculations are performed to assess the applicability regime of strictly one-dimensional models. Moreover, the full three-dimensional energy spectra are utilized to determine the third-order virial coefficient, which plays an important role in determining the equation of state in the high-temperature regime as functions of the interaction strength and confinement geometry. Motivated by recent experiments, the tunneling dynamics of two interacting one-dimensional $^6$Li atoms is simulated within a full time-dependent framework. It is shown that a WKB based trap calibration is, in general, inaccurate and an alternative trap parametrization is proposed.
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Details
- Title
- ULTRACOLD FERMIONIC FEW-BODY SYSTEMS IN REDUCED DIMENSIONS
- Creators
- Seyed Ebrahim Gharashi
- Contributors
- Doerte Blume (Advisor)Peter Engels (Committee Member)Michael M Forbes (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Physics and Astronomy, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 258
- Identifiers
- 99900581436501842
- Language
- English
- Resource Type
- Dissertation