#### Title

Quantum Diffusion in Optical Lattices

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Physics and Astronomy

#### Date of Award

Spring 2012

#### Abstract

While in the optical lattice, molecules and atoms arising from the dissociation of molecules experience a one-dimensional sinusoidal potential induced by focusing and interfering laser beams. The laser field is a superposition of incoming and reflected waves. The idea is that even though the composite objects are classically confined within certain regions in space, these objects are able to 'hop' across the potential barriers. Thus, the physics of optical lattice tunneling of composite objects by molecules generated by the Feshbach resonance method is of large interest in atomic physics and basic quantum phenomena (Donley et al., 2001; Feshbach, 1958; Lewenstein & Liu, 2011). The purpose of the study is to numerically obtain the wave function, as well as the bound state energy levels. I was able to solve the one-dimensional double hump barrier for a composite particle, still of discussion in the literature. The problem consists of a loosely-bound molecule trapped inside of a cavity. The molecule can tunnel through a one-dimensional barrier, described by a potential acting on each of its atoms, and is able to break apart during the tunneling process (C.A. Bertulani, Flambaum, & Zelevinsky, 2007). The actual calculations used to determine the molecule's wave function is found by solving the Schrodinger equation by means of iterative techniques. Since the square of the amplitude of the wave function represents a probability density, the wave function must then be normalized to be of any practical use for physical applications. The inevitable goal would be to solve for a three-dimensional optical lattice. Extending the double hump barrier will cause the potential to turn into a series of barriers in three dimensions; thus, becoming a three-dimensional optical lattice. In order to undertake this project, numerical calculations utilizing computer codes would need to be performed. In addition, the process of clarifying the physics contained in the numerical results, along with a review of consistency tests, and a comparison to previous calculations will need to be performed. The results will provide analytical insights of the diffusion time on the lattice parameters.

#### Advisor

Carlos Bertulani

#### Subject Categories

Physical Sciences and Mathematics | Physics

#### Recommended Citation

Bailey, Taylor Chase, "Quantum Diffusion in Optical Lattices" (2012). *Electronic Theses & Dissertations*. 111.

https://digitalcommons.tamuc.edu/etd/111