of the Rabi oscillation. When the damping exists, due to the damping effects, the system is not a Hamiltonian system but a dissipative one, and the volume of the phase space is reduced by time evolution. Then the stationary chaos disappears, the transient chaos is a common phenomenon before regular stable frequency locked oscillations. Surprisingly, the proper damping strength can keep the localization or MQST long-lived.

In experiments, the long-term average lifetime of the transient chaotic oscillation requires the measurements must be long-term too. So the prediction of the relation between the average lifetime of the transient and the physical parameters $(\eta $, $\Delta E_{0}$, $\Delta E_{1}$ and $%
\Lambda )$ may be a practical problem. And if one want to observe the long-lived localization or MQST, the understanding of the basins of attraction of the eventual FL oscillations in the parameter space will give some useful indication of how to choose the physical parameters. We will report these results in other papers.

M. H. Anderson, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).

K. B. Davis, M. -O. Mews, M. R. Anderson, N. J. van Druten, D. S. Durfee, D. M. Kurn, and 