  Symmetric ensembles of neutral atoms interacting via the Rydberg blockade are
well-described by the Jaynes-Cummings Hamiltonian. We use this framework to
study the problem of generating arbitrary superpositions of Dicke states of
hyperfine qubits in such ensembles. The combination of the symmetric Rydberg
blockade and microwaves that drive the qubits with a time-dependent phase is
sufficient to make these ensembles completely controllable, in the sense that
one can generate an arbitrary unitary transformation on the system. We apply
this to the problem of state mapping. With currently feasible parameters, it is
possible to generate arbitrary symmetric states of ~ 10 hypefine qubits with
high fidelity in ~ 1 microsecond, assuming fast microwave phase switching
times. To reduce the requirements on phase switching, we propose a "dressed
ground control" scheme, in which the control task is simplified by restricting
the system's dynamics to the dressed ground subspace.
