From Atom Optics to Quantum Simulation: Interacting Bosons and Fermions in Three-Dimensional Optical Lattice Potentials
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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2 Towards Strongly Interacting Bosons and Fermions
3 Hubbard Models for Bosons and Fermions
4 Detection and Observables
5 Experimental Apparatus
6 Interacting Fermions in Optical Lattice Potentials
7 Quantum Revival Spectroscopy and MultiBody Interactions
8 Interacting Mixtures of Bosons and Fermions in Optical Lattice Potentials
10 Conclusions and Outlook
Appendix A Atomic Data
Appendix B 87Rb and 40K in the Presence of Magnetic Fields
Appendix C Thermometry of Harmonically Trapped Fermi Gases
Appendix D Fourier Analysis of Quantum Phase Revival Traces
Appendix E Theory on BoseFermi Quantum Phase Revivals
Curriculum Vitae Dr Sebastian Will
9 Coherent Interaction of a Single Fermion with a Small Bosonic Field
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adiabatically atom cloud atom number Atom Optics atoms in optical attractive interactions band insulating beam Bloch blue-detuned Bose-Bose Bose-Einstein condensate Bose-Fermi mixtures bosonic bosonic and fermionic Brillouin zone calculated coherent collapse and revival compression correlations corresponding delocalized Demler detuning dipole trap double occupancy entropy Erec experimental Fermi gas Fermi-Hubbard model fermionic atoms fermionic filling Feshbach resonances Fock state energies Fölling gases Hamiltonian harmonic confinement harmonic trap Hubbard model in-situ interaction energy interspecies interactions Ketterle laser lattice depth lattice sites Lett magnetic field many-body quantum measured molecules momentum distribution Mott insulator multi-body interactions multi-orbital noninteracting observed occupied optical lattice optical lattice potential parameters particles phase-contrast imaging Phys physics quantum phase revival quantum revival spectroscopy Quantum Simulation revival dynamics rubidium scattering length Sect shift single-particle spin mixture superfluid temperature theoretical thesis three-dimensional time-of-flight trap frequencies trapping potential tunneling ultracold atoms Wannier function wavefunction