Quantum non-demolition readout for optically trapped alkaline-earth Rydberg atoms

The combination of optical tweezer arrays, which allow trapping of several hundred individual atoms in defect-free crystals, combined with the long-range interaction of Rydberg atoms, render quantum information processing architectures based on neutral atoms a viable contender to more established quantum computation platforms such as trapped ions or superconducting circuits. High-quality single and two-qubit gate operations, quintessential prerequisites for quantum computing, have been demonstrated experimentally. However, the field is still in development, and many open questions remain, particularly with regards to the best approaches and atomic systems to use. In the context of quantum error correction, the need for long-term trapping and non-destructive state readout, which are compatible with in-situ measurement and feedback, become of paramount importance. In this thesis, I present a proposal for a novel readout scheme of Rydberg states of alkaline-earth atoms, which is based on the mutual Coulomb interaction of the two valence electrons of the atom.By exciting one of the electrons to a “circular” Rydberg state, the two valence electrons can be treated almost independently. The electron-electron interaction results in a Rydberg-state-dependent and spectroscopically measurable energy shift of the ionic core of the atom, which I calculate using first-order perturbation theory. Furthermore, I develop a theoretical framework for calculating the atom-laser interaction of an alkaline-earth Rydberg atom. With these results, I show at the example of calcium how an alkaline-earth atom can be continuously trapped using a combination of a red- and blue-detuned optical trap. The red-detuned tweezer allows trapping of the atom during Rydberg excitation by harnessing the polarizability of the second electron, and the blue-detuned trap is needed to additionally confine the core-excited states, which is a requirement for the non-destructive state readout. Besides the theoretical work, I present an experimental setup, which I built for trapping magnesium atoms in a magneto-optical trap (MOT) and exciting the atoms to low orbital angular momentum Rydberg states of principal quantum number n = 48-160. The setup was valuable in allowing us to explore basic elements of Rydberg and atomic systems, preparing the ground for investigating the readout scheme proposed here. I show how the setup was designed, built, characterized, and extended to allow state-dependent detection of Rydberg atoms using a microchannel plate (MCP) detector