Collective Rydberg Excitations in Magic Traps

Abstract

Single photons typically interact only weakly with atoms and, even less so, with each other. By coupling photons to highly excited Rydberg states in atomic ensembles, strong long-range interactions between polaritons are induced, enabling effective photon–photon interactions through the polariton–polariton coupling. <br/> This thesis presents a combined theoretical and experimental investigation of magic trapping for atoms in both the ground and Rydberg states. The central focus is on how the trap geometry determines the magic condition that optimizes photon storage as a collective excitation in an ultracold atomic cloud. <br/> The first part of the thesis introduces electromagnetically induced transparency and the storage of single photons as atomic spin waves. Various mechanisms that lead to dephasing of these coherent collective excitation are discussed, including atomic motion and inhomogeneous differential light shifts across the atomic ensemble. To mitigate these effects, a magic standing-wave trap is considered—one that not only minimizes the differential light shift between the ground and Rydberg states, but also provides spatial confinement of the atoms. <br/> To identify a magic trapping wavelength, optical potentials are calculated for atoms in both the ground and Rydberg states. This analysis goes beyond the standard dipole approximation, which breaks down for Rydberg atoms in standing-wave traps with near-infrared wavelengths, as the wave function of the Rydberg electron can extend over several micrometers. Instead, the full energy shift is evaluated by accounting for the interaction of the almost-free Rydberg electron with the periodic intensity profile of the standing-wave trap. This effect is considered to evaluate the resulting trap potentials for two one-dimensional trap configurations—a running-wave and a standing-wave trap—both of which are later implemented experimentally. <br/> Next, this thesis presents the experimental apparatus for preparing ultracold ensembles of rubidium-87 atoms, which serve as the medium for Rydberg excitations and photon storage. The apparatus was reconstructed during the course of this work, following its relocation from Odense to Bonn in 2021. An overview of the experiment is provided, along with selected characterization steps relevant to the results presented in this thesis. <br/> Based on the calculated trap potentials for the ground and Rydberg states, a one-dimensional trap is implemented into the experimental apparatus. Rydberg states are difficult to trap, because the Rydberg electron is repelled by oscillating electric fields. By coupling a Rydberg <em>nS</em>_1/2 state near-resonantly to the 6<em>P</em>_3/2 state, attractive optical potentials for the Rydberg atoms are created. Magic trapping conditions for both trap geometries are theoretically derived and subsequently tested in photon storage and retrieval experiments. The optimal trap wavelength minimizes the differential light shift-induced dephasing in both the running-wave and standing-wave trap configurations.