Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

We study the production of arbitrary superpositions of Dicke states via optimal control. We show that N atomic hyperfine qubits, interacting symmetrically via the Rydberg blockade, are well described by the Jaynes-Cummings Hamiltonian and fully controllable by phase-modulated microwaves driving Rydberg-dressed states. With currently feasible parameters, it is possible to generate states of ∼ten hyperfine qubits in ∼1 μs, assuming a fast microwave phase switching time. The same control can be achieved with a "dressed-ground control" scheme, which reduces the demands for fast phase switching at the expense of increased total control time.