  Decoherence-free subspaces (DFS) in systems of dipole-dipole interacting
multi-level 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 to populate
the antisymmetric states of the DFS by means of a laser field, without the need
of 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.
