ISBN 978-3-8439-2911-0

978-3-8439-2911-0, Reihe Physik

Nick Fläschner
Ultracold Fermions in Tunable Hexagonal Lattices: From High-Precision Spectroscopy to the Measurement of Berry Curvature

198 Seiten, Dissertation Universität Hamburg (2016), Softcover, B5

Zusammenfassung / Abstract

Ultracold atoms constitute versatile quantum systems which can be routinely produced in the laboratory with full control over all crucial parameters. On the one hand, when confined to optical lattices, they can be used to emulate solid-state systems in a wellcontrolled environment and with new observables that are not accessible in their solid-state counterparts. On the other hand, they are a new class of matter in which fundamental quantum mechanical processes can be studied with an unrivaled degree of control. In this thesis, we explore both of these regimes.The major part of this thesis is dedicated to the implementation and characterization of a highly tunable hexagonal lattice and experiments with non-interacting fermions therein. In a first set of experiments, we employ a refined lattice amplitude modulation spectroscopy method to measure the band structure of the honeycomb lattice. This constitutes the first momentum-resolved measurement of the excitation spectrum of ultracold atoms in a nonseparable optical lattice. In recent years, also topological properties of lattice systems have become a major research focus, since they lie at the heart of many fascinating systems in nature, such as topological insulators. A fundamental quantity for the description of topology is the Berry curvature, which however has so far not been measured in a lattice system, as it is not easily accessible in solid-state systems. The central result of this thesis is the first measurement of the Berry curvature in a lattice system. We perform a full eigenstate tomography from which we reconstruct the Berry curvature. We demonstrate that the distribution of Berry curvature can be engineered by near-resonant periodic shaking. Our results pave the way towards a quantitative understanding of interacting topological phases in periodic quantum systems. The last part of the thesis is devoted to the investigation of collective spin-changing collisions in interacting Fermi-Fermi mixtures. We study the collision processes in the few-body and the many-body regimes as well as in the crossover regime and show which mechanisms drive, protect and destroy the collective behavior.The experiments demonstrate how the large control over the internal and external degrees of freedom of ultracold atoms can be employed to study the interplay of microscopic quantum mechanical processes and the resulting macroscopic many-body dynamics on a fundamental level.