We study the entanglement between the 2D vibrational motion and two ground
state hyperfine levels of a trapped ion, Under particular conditions this
entanglement depends on the parity of the total initial vibrational quanta. We
study the robustness of this quantum coherence effect with respect to the
presence of non-dissipative sources of decoherence, and of an imperfect initial
state preparation.Comment: 13 pages, 5 figure