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We propose a simple method to generate a practical SU(2)-Schrodinger-cat state of a single trapped-ion vibration mode and the light field state, using the method based on a quantum system, which is composed of the onedimensional trapped-ion motion and a single cavity field mode. Moreover, the method proposed can be used for the generation two-mode maximal quantum entangled state. The detection of such a state is also briefly discussed.