A phase microscope for ultra-cold quantum gases

Abstract

Coherence properties play a central role in quantum systems and are fundamental to phenomena such as superfluidity and superconductivity. Ultracold gases in optical lattices provide an versatile platform for quantum simulation, allowing precise control to explore coherence properties that underlie complex quantum phenomena. In this thesis, we investigate the coherence properties of an ultra cold Bose gas in a two-dimensional optical lattice, focusing on phase coherence and fluctuations across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. We utilize matter-wave microscopy with an optical matter-wave lens to magnify the atomic wavefunction, enabling us to image the density distribution with single-site resolution. The ability to turn off interaction allows us to measure a coherent wavefunction released from a lattice. This reveals the two-dimensional Talbot effect, where the periodic density modulations from the lattice is self-imaged and we capture in-situ images of these periodic revivals. The strength of the revivals are a direct measure for the spatial coherence of the system. Furthermore, we present the implementation of a phase microscope for ultra cold quantum gases. The phase microscope enables us to extract the relative phases on single lattice sites. We measure the phase correlation towards the BKT phase transition and obtain a critical exponent for the algebraic decay in our system. The matter-wave and phase microscopy techniques presented here offer an approach towards exploring coherence in strongly correlated quantum systems, providing full spatial resolution and potential insights into phase transitions and novel quantum phases.