Rydberg Excitons in Synthetic Cuprous Oxide (Cu$_2$O)

High-lying Rydberg states of Mott-Wannier excitons are receiving considerable interest due to the possibility of adding long-range interactions to the physics of exciton-polaritons. Here, we study Rydberg excitation in bulk synthetic cuprous oxide grown by the optical float zone technique and compare the result with natural samples. X-ray characterization confirms both materials are mostly single crystal, and mid-infrared transmission spectroscopy revealed little difference between synthetic and natural material. The synthetic samples show principal quantum numbers up to $n=10$, exhibit additional absorption lines, plus enhanced spatial broadening and spatial inhomogeneity. Room temperature and cryogenic photoluminescence measurements reveal a significant excess of copper vacancies in the synthetic material. These measurements provide a route towards achieving \mbox{high-$n$} excitons in synthetic crystals, opening a route to scalable quantum devices.