  We present a proposal for realizing local decoherence-free evolution of given
entangled states of two two-level (TL) ions. For two TL ions coupled to a
single heavily damped cavity, we can use engineering reservoir scheme to obtain
a decoherence-free subspace which can be nonadiabatically controlled by the
system and reservoir parameters. Then the local decoherence-free evolution of
the entangled states are achieved. And we also discuss the relation between the
geometric phases and the entanglement of the two ions under the nonadiabatic
coherent evolution.
