Long-lived coherence between ground and Rydberg levels in a magic-wavelength lattice

By confining atoms in a state-insensitive optical lattice, the lifetime of the ground-state--Rydberg coherence is increased to $\ensuremath{\ge}20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$, an order of magnitude improvement over previous experiments using freely diffusing atoms. Using these enhanced lifetimes, we measure the so-called magic lattice wavelengths for Rb and use them to extract the $6{p}_{3/2}\text{\ensuremath{-}}n{s}_{1/2}$ reduced electric dipole matrix elements. Good agreement is found with values obtained using an effective one-electron potential for principal quantum numbers $n$ between $n=30$ and $n=70$. We develop a theoretical model based on quantized motion to map out the ground-state--Rydberg coherence as a function of time that is in good agreement with the experimental results. The availability of long coherence times may present new opportunities for high-resolution spectroscopy and quantum information science.