Possibility of ``magic'' trapping of three-level system for Rydberg blockade implementation

The Rydberg blockade mechanism has shown noteworthy promise for scalable quantum computation with neutral atoms. Both qubit states and gate-mediating Rydberg state belong to the same optically-trapped atom. The trapping fields, while being essential, induce detrimental decoherence. Here we theoretically demonstrate that this Stark-induced decoherence may be completely removed using powerful concepts of ``magic'' optical traps. We analyze ``magic'' trapping of a prototype three-level system: a Rydberg state along with two qubit states, which are hyperfine states attached to a $J=1/2$ ground state. Our numerical results show that the group IIIB metals such as Al are suitable candidates. Such trapping may or may not be possible for the alkalis, as ``magic" conditions depend sensitively on the the trap-Rydberg interaction. Calculations of these effects are ongoing, and the results will be presented.