Localising Relational Degrees of Freedom in Quantum Mechanics. Thesis

Preface......Page 12
Executive summary......Page 16
Localising Relative Optical Phase......Page 23
Analysis of the canonical interference procedure for pure initial states......Page 24
Evolution of the localising scalar function......Page 27
The probabilities for different measurement outcomes......Page 30
Symmetries of the localising procedure and relational Schrödinger cat states......Page 34
Robustness of the localised states and operational equivalence to tensor products of coherent states......Page 36
Quantifying the degree of localisation of the relative phase......Page 38
Poissonian initial states......Page 39
Thermal initial states......Page 43
The consequences of non-ideal photodetection......Page 45
Advanced Topics on Localising Relative Optical Phase......Page 48
Derivation of the measurement operators for the canonical interference procedure......Page 50
Analysis of the canonical interference procedure for asymmetric initial states......Page 53
Transitivity of the canonical interference procedure......Page 61
Application to engineering large optical Fock states......Page 64
Relative optical phases and tests of superselection rules......Page 71
Possible extensions......Page 73
Interfering Independently Prepared Bose - Einstein Condensates and Localisation of the Relative Atomic Phase......Page 75
The standard story and conservation of atom number......Page 76
Modelling the atomic detection process and quantifying the visibility of the interference patterns......Page 78
Analytical treatment for Poissonian initial states......Page 83
Numerical simulations for Poissonian initial states......Page 85
Comments on the information available in principle from a pattern of spatial interference......Page 89
Non-destructive measurement of the relative atomic phase by optical methods......Page 92
Joint Scattering off Delocalised Particles and Localising Relative Positions......Page 96
Scattering in a rubber cavity and off delocalised free particles......Page 98
Action of the scattering processes in a basis of Gaussian states......Page 101
Localising thermal particles with monochromatic and thermal light......Page 103
Possible extensions......Page 108
Outlook......Page 112
Derivation of the visibility for Poissonian initial states......Page 117
Calculation of the visibility after a sequence of detections......Page 118
Revised calculation of the visibilities for constituent components localised at one value of the relative phase......Page 119
Derivation of the visibility for thermal initial states......Page 120
Derivation of the visibility for a Gaussian distribution of the relative phase......Page 124
References......Page 125