Spectroscopic tools are fundamental for the understanding of complex quantum systems. Here we demonstrate high-precision multi-band spectroscopy in a graphene-like lattice using ultracold fermionic atoms. From the measured band structure, we characterize the underlying lattice potential with a relative error of 1.2 10^(-3). Such a precise characterization of complex lattice potentials is an important step towards precision measurements of quantum many-body systems. Furthermore, we explain the excitation strengths into the different bands with a model and experimentally study their dependency on the symmetry of the perturbation operator. This insight suggests the excitation strengths as a suitable observable for interaction effects on the eigenstates.
Recent experiments in our group on the excitation of Rydberg molecules in ultracold quantum gases have been reviewed. Quantum gases are a well‐suited environment to excite Rydberg molecules, due to the high atomic density and the perfect control of the internal spin degrees of freedom and the center of mass motion of the atoms. In parallel, the coupling to Rydberg molecules can be used to probe and manipulate the interaction in ultracold quantum gases. In this Feature Article, a comprehensive introduction to the field of Rydberg molecules, including ultralong‐range molecules and butterfly molecules is given. The Rydberg molecules have been characterized spectroscopically and their internal spin structure is discussed. Then, it is shown how these Rydberg molecules work as a tool to monitor the double occupancy in optical lattice experiments and to change the inter‐particle interaction with the help of a so‐called optical Feshbach resonance.
This dissertation discusses the experimental study of strong fermionic interactions in an optical lattice. Ultracold samples of
40K are prepared in an intricate experimental platform using the combination of various optical and evaporative cooling techniques. The atoms are adiabatically loaded into an optical lattice to realize isolated pair states. Various tools for the coherent manipulation of spin and orbital degrees of freedom of the atoms in the lattice are developed. The inter-particle interactions between pairs are tuned using magnetic Feshbach resonances. Spectroscopic measurements of resonantly enhanced and controllable s-wave and p-wave interaction energies are reported. The measurements extend to the unitary limit of interactions characterized by diverging scattering lengths and universal observables. These measurements show excellent agreements to an exact solution for two harmonically confined atoms interacting via a pseudopotential and numerical solutions using an \textit{ab initio} interaction potential. For p-wave interactions, exquisite experimental control is demonstrated by measuring Rabi oscillations between non-interacting and strongly interacting atomic pairs, which are used to accurately measure highly sensitive properties such as the two-body wavefunction overlap. With the full suppression of three-body loss processes, the lifetime of p-wave interacting pairs is investigated. The experiments demonstrate that losses of p-wave interacting pairs are limited by the intrinsic lifetime of the free-space molecular dimer, resulting in the observation of lifetimes that are fifty times larger than previous measurements in
40K. The observation, control, and comprehensive understanding of strong fermionic interactions demonstrated in this thesis illuminate a path towards the assembly of new many-body states of matter.