Dissertation
ONE-, TWO-, AND THREE-BODY SYSTEMS WITH SPIN-ORBIT COUPLING
Doctor of Philosophy (PhD), Washington State University
01/2017
Handle:
https://hdl.handle.net/2376/112030
Abstract
The experimental realization of synthetic spin-orbit coupled
Hamiltonians, i.e., Hamiltonians that contain elements of the
non-relativistic Schr\\"odinger equation and the relativistic Dirac
equation, stimulated the theoretical studies on one-, two-, and
three-body cold atom systems with spin-orbit coupling presented in
this thesis. These systems allow for the tuning of the bound state
and scattering properties. The spin-orbit coupling modifies the
single-particle dispersion curve and leads to intriguing
single-particle physics. Beyond the single-particle sector, the
spin-orbit coupling has highly non-trivial effects on the system
properties. This thesis asked the question: How does the spin-orbit
coupling change the few-body physics? This question was answered from
two different angles, namely by studying the bound state properties
and the scattering state properties in the presence of spin-orbit
coupling.
For the bound state studies, an explicitly correlated Gaussian code
for systems with spin-orbit coupling was developed. Bound states of
two identical bosons with 1D spin-orbit coupling were studied. It was
found that the binding energy of two identical bosons is enhanced.
First results for spectra of three identical bosons with 1D spin-orbit
coupling were obtained. A finite number of three-body bound states
were found for all parameter combinations considered.
For the scattering state studies, a general framework, which extends
the standard low-energy scattering theory presented in textbooks, for
systems with 3D isotropic spin-orbit coupling was developed. The
scattering properties for $s$- and $p$-wave dominated cases were
studied. Modifications of the short-range phase accumulation, which
are significant for the $p$-wave dominated case, were found.
The results presented in this thesis provide a guide for future
experimental and theoretical studies of spin-orbit coupled systems.
The parameter regimes considered in this thesis can be realized in
cold atom experiments. Studies of the interplay between interactions
and spin-orbit coupling provide a basic step for the understanding of
crossover-type physics such as the BEC-BCS crossover in degenerate
Fermi gases in the presence of non-abelian gauge fields.
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Details
- Title
- ONE-, TWO-, AND THREE-BODY SYSTEMS WITH SPIN-ORBIT COUPLING
- Creators
- Qingze Guan
- Contributors
- Doerte Blume (Advisor)Peter Engels (Committee Member)Michael McNeil Forbes (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Physics and Astronomy
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 238
- Identifiers
- 99900581717601842
- Language
- English
- Resource Type
- Dissertation