Philipp M. Preiss

Quantum simulation is a rapidly advancing tool to gain insight into complex quantum states and their dynamics. Trapped ion systems have pioneered deterministic state preparation and comprehensive state characterization, operating on localized and thus distinguishable particles. With ultracold atom experiments, one can prepare large samples of delocalized particles, but the same level of characterization has not yet been achieved. Here, we present a method to measure the positions and momenta of individual particles to obtain correlations and coherences. We demonstrate this with deterministically prepared samples of two interacting ultracold fermions in a coupled double well. As a first application, we use our technique to certify and quantify different types of entanglement.

High-resolution addressing of individual ultracold atoms, trapped ions or solid state emitters allows for exquisite control in quantum optics experiments. This becomes possible through large aperture magnifying optics that project microscopic light patterns with diffraction limited performance. We use programmable amplitude holograms generated on a digital micromirror device to create arbitrary microscopic beam shapes with full phase and amplitude control. The system self-corrects for aberrations of up to several $λ$ and reduces them to $λ/50$, leading to light patterns with a precision on the $10^{-4}$ level. We demonstrate aberration-compensated beam shaping in an optical lattice experiment and perform single-site addressing in a quantum gas microscope for $^{87}$Rb.