From Atom Optics to Quantum Simulation: Interacting Bosons and Fermions in Three-Dimensional Optical Lattice Potentials

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Springer Science & Business Media, Dec 15, 2012 - Science - 258 pages
This thesis explores ultracold quantum gases of bosonic and fermionic atoms in optical lattices. The highly controllable experimental setting discussed in this work, has opened the door to new insights into static and dynamical properties of ultracold quantum matter. One of the highlights reported here is the development and application of a novel time-resolved spectroscopy technique for quantum many-body systems. By following the dynamical evolution of a many-body system after a quantum quench, the author shows how the important energy scales of the underlying Hamiltonian can be measured with high precision. This achievement, its application, and many other exciting results make this thesis of interest to a broad audience ranging from quantum optics to condensed matter physics. A lucid style of writing accompanied by a series of excellent figures make the work accessible to readers outside the rapidly growing research field of ultracold atoms.
 

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Contents

1 Introduction
1
2 Towards Strongly Interacting Bosons and Fermions
12
3 Hubbard Models for Bosons and Fermions
59
4 Detection and Observables
83
5 Experimental Apparatus
99
6 Interacting Fermions in Optical Lattice Potentials
121
7 Quantum Revival Spectroscopy and MultiBody Interactions
151
8 Interacting Mixtures of Bosons and Fermions in Optical Lattice Potentials
193
10 Conclusions and Outlook
233
Appendix A Atomic Data
240
Appendix B 87Rb and 40K in the Presence of Magnetic Fields
243
Appendix C Thermometry of Harmonically Trapped Fermi Gases
247
Appendix D Fourier Analysis of Quantum Phase Revival Traces
249
Appendix E Theory on BoseFermi Quantum Phase Revivals
251
Curriculum Vitae Dr Sebastian Will
257
Copyright

9 Coherent Interaction of a Single Fermion with a Small Bosonic Field
209

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