%0 Generic
%A Klemt, Ralf Arne
%C Heidelberg
%D 2021
%F heidok:30200
%R 10.11588/heidok.00030200
%T Correlations from Microscopic to Macroscopic Quantum Systems: Interactions vs Indistinguishability
%U https://archiv.ub.uni-heidelberg.de/volltextserver/30200/
%X In this thesis, I present and discuss correlation measurements of fermionic quantum systems engineered out of ultracold 6Li atoms in optical potentials. A strong emphasis is placed on the complex interplay between interactions and pairing on the one hand and the effects of indistinguishability and the need for symmetrization on the other hand. The starting point will be a strongly correlated two-dimensional quantum fluid, where fermionic pairing significantly above the critical temperature for superfluidity is observed, closely related to a pseudogap regime. It is concluded that additionally measuring higher order correlation functions with full single-particle resolution will be needed to truly unravel the microscopic correlations responsible for the intricate behaviour of such a manybody quantum system.  In pursuit of this ultimate goal, I work out and follow a roadmap composed of both conceptual and technical milestones. As a first step, a novel high fidelity single-particle and hyperfine state resolved imaging system is developed, which is custom-tailored for density correlation measurements in real and momentum space. This imaging scheme is subsequently utilized to identify and quantify strong correlations and entanglement in microscopic systems of two or three atoms in different hyperfine states, deterministically prepared in tunnel-coupled optical tweezer arrays. Effects from strong interactions and Pauli symmetrization are studied both in isolation and in conjunction.  In a further step towards the many-body regime, the preparation of deterministic mesoscopic quantum systems, given by up to twelve particles in a two-dimensional harmonic oscillator potential, is presented. In this system the emergence of manybody behaviour, in the form of the precursor of a Higgs mode, is experimentally observed. This is the basis for measuring single-particle resolved pairing correlations in mesoscopic and ultimately also in macroscopic systems.