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We present a proposal for realizing local decoherence-free evolution of givenentangled states of two two-level (TL) ions. For two TL ions coupled to asingle heavily damped cavity, we can use engineering reservoir scheme to obtaina decoherence-free subspace which can be nonadiabatically controlled by thesystem and reservoir parameters. Then the local decoherence-free evolution ofthe entangled states are achieved. And we also discuss the relation between thegeometric phases and the entanglement of the two ions under the nonadiabaticcoherent evolution.

Protecting entangled states of two ions by engineering reservoir