Studying Quantum Gases in a Dynamically Tunable Lattice with Sub-Lattice-Site Resolution

Abstract

Ultracold gases in optical lattices provide a versatile simulation platform of real solid-state quantum systems as they offer clean systems with a high degree of control over the systems parameters and access to additional observables. In this thesis, new methods to get access to the real space density distribution and a dynamic control of the systems geometry are presented and employed.

The first main result presented in this thesis is a new imaging approach, which uses matter wave optics to magnify the density distribution in an optical lattice by up to a factor of around 90. In combination with standard absorption imaging, this allows sublattice resolved access to the integrated real space density in our 2D optical lattice. At the heart of the method is a quarter period evolution time in a harmonic potential following the shut off of the optical lattice, transforming the initial atomic positions to their momenta. A subsequent free fall time transfers these momenta to a magnified image of the initial positions. In this way, the depth of focus of the imaging is very large, allowing to image 3D quantum systems. The method is characterized in detail and using the single site populations high precision thermometry of the system across the BEC phase transition is demonstrated. By utilizing magnetic resonance techniques, also the addressing of individual lattice sites is shown.

In the next part, the control over our quantum system is improved by employing a novel type of optical lattice. It uses different frequencies to allow for a dynamic geometry control while offering high passive stability. In the case of our hexagonal lattice beam arrangement, this allows to tune between honeycomb, boron nitride and triangular lattices within a few microseconds. The geometry for a given set of lattice wave vectors and beam balances is fully described by the newly introduced concept of a geometry phase. Its fundamental importance is highlighted by also appearing as a staggered flux in the corresponding momentum space lattices. Using the high tunability, atoms are transferred into higher Bloch bands and their dynamics measured in real space. The tunability can also be used as a tool for full state tomography measurements, which is presented in a set of preliminary measurements. Furthermore, exemplary realizations of a quasiperiodic and a 3D lattice in multifrequency design, both featuring tunable geometry phases, are proposed.

The last part of this thesis reports on real space pattern formations in tilted lattices of different geometries, resolved by using our quantum gas magnifier. This allows in particular the observation of a spontaneously forming density-wave breaking the underlying translational symmetry of the triangular lattice, which is ascribed to interaction-induced pair tunneling processes. Additionally, self-trapping and the formation of ring structures along equipotential lines are observed.