  We propose a protocol for sympathetically cooling neutral atoms without
destroying the quantum information stored in their internal states. This is
achieved by designing state-insensitive Rydberg interactions between the
data-carrying atoms and cold auxiliary atoms. The resulting interactions give
rise to an effective phonon coupling, which leads to the transfer of heat from
the data atoms to the auxiliary atoms, where the latter can be cooled by
conventional methods. This can be used to extend the lifetime of quantum
storage based on neutral atoms and can have applications for long quantum
computations. The protocol can also be modified to realize state-insensitive
interactions between the data and the auxiliary atoms but tunable and
non-trivial interactions among the data atoms, allowing one to simultaneously
cool and simulate a quantum spin-model.
