  We propose a dissipative scheme to prepare a three-dimensional entangled
state for two atoms trapped in separate coupled cavities. Our work shows that
both atomic spontaneous emission and cavity decay, which are two typical
obstacles in unitary-dynamics-based schemes, could be utilized as resources for
high-dimensional entangled state preparation without specifying initial state
and controlling time precisely. Final numerical simulation with one group of
experimental parameters indicates that the performance of our scheme is better
than the unitary-dynamics-based scheme.
