An Investigation of Linear and Nonlinear Atom Optics

by Olsen, Murray

Abstract (Summary)
Restricted Item. Print thesis available in the University of Auckland Library or available through Inter-Library Loan. This work is the final result of my PhD research in the Physics Department at the University of Auckland. Some of the main results have already appeared as parts of published papers: with T. Wong, S.M. Tan and D.F. Walls, Phys. Rev. A, 52 2161, 1995. (Bichromatic beamsplitter), with T. Wong, S.M. Tan and D.F. Walls, Phys. Rev. A,52 3358, 1996. (Bichromatic atomic lens) Others are awaiting publication: with S. Choi, H.M. Wiseman, S.M. Tan and D.F. Walls, submitted to Opt. Comm. (Comparison of bichromatic beamsplitters), with L.I. Plimak, S.M. Tan, M.J. Collett and D.F. Walls, submitted to Phys. Rev. Lett., June 1997. (Coherence of BEC) Another is in the process of preparation: with, L.L Plimak, S.M. Tan, M.J. Collett and D.F. Walls, in preparation to be submitted to Phys. Rev. A. (More on coherence of BEC) This thesis, as well as including those parts of the abovementioned papers which were primarily my work, also details the theoretical framework to which they belong. My research has been divided into two distinct, but complementary parts. The first was concerned with linear Atom Optics, primarily dealing with the manipulation of atoms by bichromatic optical fields. This field is considered linear because, in the standard approach, we consider neither interatomic interactions nor back action of the atoms on the light fields. The analysis of the three-level atoms and bichromatic fields is divided into two parts, differing in the eigenvalues of the optical potentials used to manipulate the atoms. One of the potentials can be optimised for use as an atomic beamsplitter, while the other finds use in the channelling and focussing of atomic beams. I have considered the effects of spontaneous emission, changes in the optical profile and atomic velocity distributions on these two systems. A possible beamsplitting experiment has also been analysed in some detail. The bichromatic beamsplitter for three-level atoms has also been compared and contrasted to a bichromatic beamsplitter using only a single atomic transition. I have also examined the use of multi-photon transitions in Atom Optics, primarily to quantify their use in possible beamsplitters. The second part of my research has been concerned with Bose-Einstein condensates. Although definitely involving nonlinear processes, it is not totally obvious that the study of condensates falls into the realm of Atom Optics. I believe it can be treated as Atom Optics for three reasons. The first, and most compelling, is that it is the wave nature of the cold atoms which precipitates condensation, as the de Broglie wavelength becomes larger than the average separation between these atoms. The second is historical, in that it is the Quantum and Atom Optics community who have been the first to achieve Bose-Einstein condensation. The third is that the processes used to trap and manipulate condensates are basically the standard electromagnetic processes of Atom Optics, including magnetic trapping and laser manipulation. My investigations of condensate optics include interference processes between and within condensates and a study of the coherence properties, as affected by fluctuations within the condensate itself. If fluctuations are ignored, condensates can be well modeled using the Gross-Pitaevski equation. This situation has been advanced by a stochastic partial differential equation, developed within our research group, which describes phase and density fluctuations within the condensate. I have used this equation to perform numerical studies of the decay of condensate coherence due to local collisional processes within the condensate mode. I have divided the thesis itself into two parts. Part one gives an introduction to the field of linear Atom Optics, outlining the main theoretical methods used for this research. This is followed by the results of my investigations into Atom Optics, including analyses of proposed atomic beamsplitters and lenses, as well as a theoretical comparison of the two different bichromatic beamsplitters. Also included is a brief examination of atomic diffraction using multi-photon absorptiou, with a view to comparison with the other mechanisms analysed. Part two gives an investigation into the the field of nonlinear Atom Optics, which I shall refer to as condensate optics. I have included a slightly more detailed history of the development of condensate optics. The main experimental and theoretical advances have hopefully all been included. Although it is possible to consider nonlinear Atom Optics that does not involve condensates, this is not included in my work. Included are results of my investigations to date into Bose-Einstein condensates, including work on interference effects, outcoupling (also called atom lasing) and the effects of stochastic fluctuations within the condensates. The majority of my research has been numerical, using the Matlab© programming language. The stochastic integrations have sometimes demanded all ,the power of a Sun Sparc 10© workstation, while typesetting has been done using Latex© on a Macintosh IIfx© Some use has also been made of Mathematica©, particularly for analytic integration.
Bibliographical Information:


School:The University of Auckland / Te Whare Wananga o Tamaki Makaurau

School Location:New Zealand

Source Type:Master's Thesis



Date of Publication:01/01/1997

© 2009 All Rights Reserved.