Here is our recent paper on the possibility of decoherence-free design of quantum gates mediated by Rydberg-excited neutral atoms. This quantum computing architecture utilizes atoms trapped in optical fields, e.g., in optical lattices. In order to reduce motional dephasing we determine trapping conditions where AC Stark shifts of both ground and Rydberg levels are the same (so-called magic trapping).
Intensity landscape and the possibility of magic trapping of alkali Rydberg atoms in infrared optical lattices, T. Topcu and A. Derevianko, arxiv.org:1305.6570
Motivated by compelling advances in manipulating cold Rydberg atoms in optical traps, we consider the effect of large extent of Rydberg electron wave function on trapping potentials. We find that when the Rydberg orbit lies outside inflection points in laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron polarizability of Rydberg electron is modulated by intensity landscape and can accept both positive and negative values. We apply these insights to determining magic wavelengths for Rydberg-ground-state transitions for alkali atoms trapped in infrared optical lattices. We find magic wavelengths to be around 10 um, with exact values that depend on Rydberg state quantum numbers.
This result is somewhat unusual and more details can be found in this talk (link to pdf) given at the Dresden workshop on ultracold Rydberg physics.
UPDATE: published: Phys. Rev. A 88, 043407 (2013)