Linked e-resources
Details
Table of Contents
Parts of this thesis have been published in the following journal articles:; Supervisor's Foreword; Abstract; Preface; Acknowledgments; Contents; 1 Introduction and Theoretical Background; 1.1 Elements of the Theory of Bose-Einstein Condensation in Atomic Gases; 1.1.1 Condensation of the Ideal Bose Gas; 1.1.2 The Weakly Interacting Bose Gas; 1.1.3 Mean-Field Model: The Gross-Pitaevskii Equation; 1.2 Bose-Einstein Condensate in a Double Well: Two-Mode Theory ; 1.2.1 Two-Mode Approximation; 1.2.2 Two-Mode Bose-Hubbard Hamiltonian; 1.2.3 Regimes of the Two-Mode Bose-Hubbard Model
1.2.4 Collective Spin Representation1.2.5 Mean-Field Model in the Josephson Regime; 1.3 Conclusion of the Theoretical Part; References; 2 Experimental Setup and Techniques; 2.1 Experimental Setup; 2.1.1 Vacuum Chamber and Rubidium Source; 2.1.2 External Coils; 2.1.3 Chip Mounting and Copper Structure; 2.1.4 Atom Chip; 2.1.5 Optics and Laser System; 2.1.6 Radio-Frequency Evaporative Cooling; 2.1.7 Computer Control and Acquisition; 2.2 Trapping Atoms Magnetically with an Atom Chip; 2.2.1 Magnetic Trapping with Static Fields; 2.2.2 Double-Well Potentials Created by Radio-Frequency Dressing
2.2.3 Characterization of the Potential and Calibration of the Simulations2.3 Imaging Systems; 2.3.1 Absorption Imaging; 2.3.2 Fluorescence Imaging System (Light Sheet); 2.4 Conclusion of the Experimental Part; References; 3 A Mach-Zehnder Interferometer for Trapped, Interacting Bose-Einstein Condensates; 3.1 Introduction; 3.1.1 A Prototypical Interferometer; 3.1.2 Interferometry with Bose-Einstein Condensates; 3.1.3 The Vienna BEC Mach-Zehnder Interferometer; 3.2 Number and Phase Estimation; 3.2.1 Relative Phase Measurement; 3.2.2 Number Difference Measurement
3.2.3 Conclusion on Number and Phase Measurements3.3 Matter Wave Source; 3.4 Coherent Splitting and Generation of Atomic Squeezed States; 3.4.1 Coherent Splitting of a Condensate; 3.4.2 Squeezing and Adiabatic Splitting; 3.4.3 Results: State of the BEC After Splitting; 3.4.4 A Simple Model to Describe Adiabatic Splitting; 3.4.5 Discussion; 3.5 Phase Evolution; 3.5.1 Phase Accumulation; 3.5.2 Phase Diffusion; 3.5.3 Estimation of the Phase Diffusion Rate; 3.5.4 Conclusion on the Phase Evolution; 3.6 Two Phase-Sensitive Condensate Recombiners; 3.6.1 Josephson Recombiner
3.6.2 Non-Adiabatic Recombiner3.6.3 Comparison of the Two Recombiners; 3.7 Interferometer Signal; 3.7.1 Mach-Zehnder Fringes; 3.7.2 Model for the Interferometric Signal; 3.7.3 Discussion of the Interferometric Signal; References; 4 Outlook: Bosonic Josephson Junctions Beyond the Two-Mode Approximation; 4.1 Observations Beyond the Two-Mode Picture; 4.2 Discussion; References; Appendix AOne-Dimensional Gross-PitaevskiiSimulations in the Transverse Potential; Appendix BList of Symbols; Curriculum Vitae
1.2.4 Collective Spin Representation1.2.5 Mean-Field Model in the Josephson Regime; 1.3 Conclusion of the Theoretical Part; References; 2 Experimental Setup and Techniques; 2.1 Experimental Setup; 2.1.1 Vacuum Chamber and Rubidium Source; 2.1.2 External Coils; 2.1.3 Chip Mounting and Copper Structure; 2.1.4 Atom Chip; 2.1.5 Optics and Laser System; 2.1.6 Radio-Frequency Evaporative Cooling; 2.1.7 Computer Control and Acquisition; 2.2 Trapping Atoms Magnetically with an Atom Chip; 2.2.1 Magnetic Trapping with Static Fields; 2.2.2 Double-Well Potentials Created by Radio-Frequency Dressing
2.2.3 Characterization of the Potential and Calibration of the Simulations2.3 Imaging Systems; 2.3.1 Absorption Imaging; 2.3.2 Fluorescence Imaging System (Light Sheet); 2.4 Conclusion of the Experimental Part; References; 3 A Mach-Zehnder Interferometer for Trapped, Interacting Bose-Einstein Condensates; 3.1 Introduction; 3.1.1 A Prototypical Interferometer; 3.1.2 Interferometry with Bose-Einstein Condensates; 3.1.3 The Vienna BEC Mach-Zehnder Interferometer; 3.2 Number and Phase Estimation; 3.2.1 Relative Phase Measurement; 3.2.2 Number Difference Measurement
3.2.3 Conclusion on Number and Phase Measurements3.3 Matter Wave Source; 3.4 Coherent Splitting and Generation of Atomic Squeezed States; 3.4.1 Coherent Splitting of a Condensate; 3.4.2 Squeezing and Adiabatic Splitting; 3.4.3 Results: State of the BEC After Splitting; 3.4.4 A Simple Model to Describe Adiabatic Splitting; 3.4.5 Discussion; 3.5 Phase Evolution; 3.5.1 Phase Accumulation; 3.5.2 Phase Diffusion; 3.5.3 Estimation of the Phase Diffusion Rate; 3.5.4 Conclusion on the Phase Evolution; 3.6 Two Phase-Sensitive Condensate Recombiners; 3.6.1 Josephson Recombiner
3.6.2 Non-Adiabatic Recombiner3.6.3 Comparison of the Two Recombiners; 3.7 Interferometer Signal; 3.7.1 Mach-Zehnder Fringes; 3.7.2 Model for the Interferometric Signal; 3.7.3 Discussion of the Interferometric Signal; References; 4 Outlook: Bosonic Josephson Junctions Beyond the Two-Mode Approximation; 4.1 Observations Beyond the Two-Mode Picture; 4.2 Discussion; References; Appendix AOne-Dimensional Gross-PitaevskiiSimulations in the Transverse Potential; Appendix BList of Symbols; Curriculum Vitae