Coherent control in a decoherence-free subspace of a collective multilevel system

Decoherence-free subspaces (DFS’s) in systems of dipole-dipole interacting multilevel atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows us to populate the antisymmetric states of the DFS by means of a laser field, without the need for a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a microwave field. Typical operation times of these qubit rotations can be significantly shorter than for a nuclear spin system.