Localising Relational Degrees of Freedom in Quantum Mechanics
  This thesis presents a wide-ranging study of localising relational degrees of freedom. Three physical systems are studied in depth, each built upon a simple measurement-based process. For each physical system - light from independent sources leaking onto a beam splitter monitored by photodetectors, spatially interfering Bose-Einstein condensates extracted from separate preparation procedures, and delocalised massive particles or mirrors scattering light which is detected in the far-field - the thesis investigates the key features of the underlying process of localisation, and explores the properties of the induced post-measurement states of the system. A range of analytical and numerical methods are used. Many new results are presented - for example, cases of mixed initial states are considered in addition to the more commonly considered pure states. Up to now there has been little attempt to develop in detail the themes common to studies concerned with specific physical examples. This thesis addresses this, and sets out a "modus operandi" that can be applied widely. A variety of specific applications are considered - both in the context of controlled laboratory experiments, and with a view to understanding processes occurring in nature. The thesis is introduced and summarised in Chapter 1. Chapter 2 studies localising relative optical phase in the canonical interference process. This discussion is extended and applied in Chapter 3. Chapter 4 discusses localising relative atomic phase in interference experiments with Bose-Einstein condensates. The emergence of relative positions between particles scattering light is explored in Chapter 5. The thesis concludes with an Outlook, Chapter 6. 
Hugo Cable