The decoherence in a trapped ion induced by coupling the ion to the enginee
red reservoir is studied in this paper. The engineered reservoir is simulat
ed by random variations in the trap frequency, and the trapped ion is treat
ed as a two-level system driven by a far-off-resonant plane wave laser fiel
d. The dependence of the decoherence rate on the amplitude of the superposi
tion state is given.