## Artificial Gauge Fields with Ultracold Atoms in Optical LatticesThis work reports on the generation of artificial magnetic fields with ultracold atoms in optical lattices using laser-assisted tunneling, as well as on the first Chern-number measurement in a non-electronic system. It starts with an introduction to the Hofstadter model, which describes the dynamics of charged particles on a square lattice subjected to strong magnetic fields. This model exhibits energy bands with non-zero topological invariants called Chern numbers, a property that is at the origin of the quantum Hall effect. The main part of the work discusses the realization of analog systems with ultracold neutral atoms using laser-assisted-tunneling techniques both from a theoretical and experimental point of view. Staggered, homogeneous and spin-dependent flux distributions are generated and characterized using two-dimensional optical super-lattice potentials. Additionally their topological properties are studied via the observation of bulk topological currents. The experimental techniques presented here offer a unique setting for studying topologically non-trivial systems with ultracold atoms. |

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### Contents

1 | |

9 | |

3 Artificial Gauge Fields with LaserAssisted Tunneling | 27 |

4 Overview of the Experimental Setup and Measurement Techniques | 51 |

5 Staggered Magnetic Flux | 67 |

6 HarperHofstadter Model and Spin Hall Effect | 101 |

7 AllOptical Setup for Flux Rectification | 119 |

8 ChernNumber Measurement of Hofstadter Bands | 137 |

9 Conclusions and Outlook | 160 |

Appendix A
Magnetic Translation Operators | 167 |

Appendix B
Propagation Operator | 169 |

Appendix C
Staggered Flux Distribution | 171 |

### Other editions - View all

Artificial Gauge Fields with Ultracold Atoms in Optical Lattices Monika Aidelsburger No preview available - 2019 |

Artificial Gauge Fields with Ultracold Atoms in Optical Lattices Monika Aidelsburger No preview available - 2015 |