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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.

This thesis describes the syntheses of some polyfunctionalised cyclopentanes via intramolecular aldol condensations of sugar δ-lactone precursors. The known azido carbpcycle (1S,2R,3S,4R,5R)-methyl [5-azido-1,2,3,4- tetrahydrpxy-2,3-O-isopropylidene-cyclopentane] carboxylate was prepared from 2- deoxy-2-iodo-3,4:6,7-di-O-isopropylidene-D-glycero-D-talo-heptono-1,5-lactone in five steps. The key reaction was a base-induced intramolecular aldol cyclisation of a 5- iodo-formyl-2,6-lactone. Borohydride reduction of the methyl ester gave an azido triol. Deprotection followed by reduction of the azide functionality produced an amino pentol. The analogous tetrahydroxy β-amino acid was synthesised from the azido carbocycle in three steps. The inhibitory activity of the amino pentol against human liver glycosidases is reported. Two azido bicyclic lactones, (1R,4R,5R,6R,7R)-4-azido-5,6,7-trihydroxy-5,6-0- isopropylidene-2-oxa-bicyclo[2.2.1]heptan-3-one and (1S,4S,5R,6R,7R)-4-azido- 5,6,7-trmydroxy-5,6-O-isopropydilene-2-oxa-bicyclo[2.2.1]heptan-3-one, were prepared from 3,4:6,7-di-O<./em>-isopropylidene-D-glycero-D-talo-heptono-1,5-lactone in five steps. The (1R,4R,5R,6R,7<em.R)-compound was further elaborated to give an amino pentol via a series of borohydride reduction / deprotection / catalytic hydrogenation. A novel carbocyclic spirohydantoin was synthesised by two alternative routes. The second route also provided access to an N'-phenyl spirohydantoin. The inhibitory activities of the amino pentol and the spirohydantoin against human liver glycosidases are reported. The azido bicyclic lactone triol (1R,4S,5R,6R,7R)-4-azido-5,6,7-trihydroxy-2-oxabicyclo[ 2.2.1]heptan-3-one underwent reduction of the azide functionality with concomitant epimerisation to give the (5S)-epimeric amine. The structure of this material was confirmed by X-ray diffraction analysis of a crystalline derivative. Treatment of the azido triol with base under non-aqueous conditions resulted in a retroaldol reaction to give the (5S)-epimeric azide, the relative configuration of which was determined by single crystal X-ray analysis. A third ketal protected azido bicyclic lactone was prepared via a base-induced retro-aldol epimerisation. Five tetrahydroxycyclopentane α-amino acids, including a pair of enantiomers, were synthesised from the azido bicyclic lactones. The structures of two of the α-amino acids were established by X-ray crystallographic analysis, whilst the enantiomeric compounds were identified using circular dichroism spectrometry. The diketal protected (2R,3R,4R,5R)-tetrahydroxy-cyclopentane α-amino acid was incorporated into six oligopeptides. Peptide coupling at the C-terminus of the carbocyclic amino acid was carried out using two amino acid tert-butyl esters. Chain extension at the N-terminus was achieved by reaction with N-benzyloxycarbonyl protected amino acids in the presence of 1-(3-dimethylaminopropyl)-3-ethyl-carbodiimide hydrochloride as the carbodiimide reagent. Complete deprotection of a tetrapeptide is described.

Thesis--University of Washington. / Vita. Bibliography: leaves [102]-109.

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 (M.S.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 57-60).

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 69-70). Also available via the Internet.