The quantum phase of a Bose-Einstein condensate has long been a subject fraught with misunderstanding and confusion. In this thesis we provide a consis- tent description of this phenomenon and, in particular, discuss how phase may be defined, created, manipulated, and controlled. We begin by describing how it is possible to set up a reference condensate against which the phase of other condensates can be compared. This allows us to think of relative phases as if they were absolute and gives a clear and precise definition to 'the phase of a condensate'. A relative phase may also be established by coupling condensates and we show how this can be controlled. We then extend this model to explain how the phase along a chain of coupled condensates can lock naturally without the need for any measurements. The second part of the thesis deals primarily with the link between entangle- ment and phase. We show that, in general, the more entangled a state is, the better its phase resolution. This leads us to consider schemes by which maximally entangled states may be able to be created since these should give the best prac- tical advantages over their classical counterparts. We consider two such states: a number correlated pair of condensates and a Schrodinger cat state. Both schemes are shown to be remarkably robust to loss. A comparison of the merits of these two states, as the inputs to an interferom- eter, reveals very different behaviours. In particular, the number correlated state performs significantly better than the cat state in the presence of loss, which means that it might be useful in interferometry and frequency standard schemes where phase resolution is of the utmost importance. Finally, we propose a scheme for concentrating the entanglement between con- densates, which is an important step in quantum communication protocols. This, along with the ability to manipulate phase and entanglement, suggests that the future for condensates holds not only academic interest but great potential for practical applications.

Dissertation (Ph.D.)--Worcester Polytechnic Institute. / Keywords: atom interferometery; Bose-Einstein condensation. Includes bibliographical references (leaves 211-220).

Thesis (BSc. (Hons))--Australian National University, 2002. / Available via the Australian National University Library Electronic Pre and Post Print Repository. Title from title screen (viewed Mar. 28, 2003). "A thesis submitted for the degree of Bachelor of Science with Honours of The Australian National University" Bibliography: p. 45.

Thesis (Ph.D.)--Australian National University, 2005.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 196-204). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2007. / Davidovic, Dragomir, Committee Member ; Kennedy, T.A. Brian, Committee Member ; Chapman, Mike, Committee Member ; Raman, Chandra, Committee Chair ; Bunz, Uwe, Committee Member.

Over the last several years considerable efforts have been made to develop Bose-Einstein condensate (BEC) based devices for a number of applications including fundamental research, precision measurements, and navgation systems. These devices, capable of complex functionality, can be built from simpler components which is currently done in both optics and microelectronics. These components include cold atom equivalents of beamsplitters, mirrors, waveguides, diodes, and transistors. The operation of the individual components must be fully understood before they can be assembled into a more complex device. The primary goal of this dissertation is to present a theoretical analysis of these components. It begins with a theoretical analysis of several different types of cold-atom beamsplitters in the context of BEC interferometry. Next, the dynamics of an interferometer that uses optical pulses to control the dynamics of the BEC will be presented. Finally, a proposal for a BEC based component that has behavior that is similar to an electronic transistor is introduced.

In this thesis we present a theoretical analysis of the instability in a cold atom interferometer. Interferometers are often used to split a signal (e.g. optical beam, matter wave), where each part of the signal evolves separately, then the interferometer recombines the signal. Interference effects from the recombination can be used to extract information about the different environments the the split signal traversed. The interferometer considered here splits a matter wave, the wave function of a Bose-Einstein Condensate, by using a guiding potential and then recombines the matter wave. The recombination process is shown to be unstable and the nature of the instability is characterized.

Chan Chak Ming = 二元玻色-愛因斯坦凝聚態之硏究 / 陳澤明. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [100]-104). / Text in English; abstracts in English and Chinese. / Chan Chak Ming = Er yuan Bose-Aiyinsitan ning ju tai zhi yan jiu / Chen Zeming. / Abstract --- p.i / Acknowledgments --- p.ii / Contents --- p.iii / List of Figures --- p.vi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Theory of Bose-Einstein Condensate (BEC) --- p.4 / Chapter 2.1 --- Trapped Ideal Bose Gas --- p.5 / Chapter 2.2 --- Bogoliubov Theory of Weakly Interacting Bosons --- p.7 / Chapter 2.2.1 --- One-component BEC --- p.7 / Chapter 2.2.2 --- Two-component BEC --- p.12 / Chapter Chapter 3. --- Condensate Wavefunctions and Collective Excitations --- p.16 / Chapter 3.1 --- Properties of Condensate Wavefunctions --- p.16 / Chapter 3.2 --- Collective Excitations --- p.21 / Chapter 3.3 --- Appendix: Numerical Methods and Practical Procedures --- p.26 / Chapter 3.3.1 --- Gradient Descent Method --- p.27 / Chapter 3.3.2 --- Iterative Diagonalization Method --- p.28 / Chapter 3.3.3 --- Practical Procedures --- p.30 / Chapter Chapter 4. --- Noncondensate Atoms in Homogeneous BEC --- p.33 / Chapter 4.1 --- Noncondensate Atoms in One-Component BEC --- p.33 / Chapter 4.2 --- Bogoliubov Theory for Two-species Homogeneous BEC --- p.35 / Chapter 4.3 --- Same Mass System: m1= m2 --- p.37 / Chapter 4.4 --- Unequal Mass System: m1 ≠ m2 --- p.48 / Chapter 4.5 --- Summary --- p.54 / Chapter Chapter 5. --- Noncondensate Atoms in a Trapped BEC --- p.55 / Chapter 5.1 --- Case I: The Noncondensate Atoms in the Mixture of Two Spin States of 87Rb --- p.57 / Chapter 5.2 --- Case II: The Noncondensate Atom in the Mixture of 87Rb and 23Na --- p.61 / Chapter 5.3 --- Summary --- p.64 / Chapter Chapter 6. --- Two-component BEC in Relative Motion --- p.65 / Chapter 6.1 --- Bogoliubov Theory for Motional Two BEC --- p.65 / Chapter 6.2 --- Stability Analysis --- p.69 / Chapter 6.2.1 --- Dynamical Stability Analysis --- p.69 / Chapter 6.2.2 --- Anomalous Mode Analysis --- p.75 / Chapter 6.2.3 --- "Critical Velocity, Anomalous Modes Critical Velocity and Sound Velocities" --- p.78 / Chapter 6.3 --- Motional Two-component BEC in a Ring --- p.80 / Chapter 6.4 --- Two-component BEC of the Same Species --- p.85 / Chapter 6.4.1 --- Moving Particles in Momentum Space --- p.88 / Chapter 6.4.2 --- Moving Particles in Real Space --- p.93 / Chapter 6.4.2.1 --- Strong coupling regime: (g > k02/2) --- p.93 / Chapter 6.4.2.2 --- Weak-coupling regime: (g《<k02/2) --- p.95 / Chapter 6.5 --- Summary --- p.95 / Chapter Chapter 7. --- Conclusion --- p.93 / Bibliography --- p.100

No description available.