Preparation of motional cat states for trapped ions using a standing wave in strong excitation

We propose a scheme to generate cat states for trapped ions using a standin g wave in both the strong excitation regime and the Lamb-Dicke limit. A sin gle strong standing-wave laser, exciting the ion for a short time, will lea ve the ion in an entangled state. After a measurement of the internal state , the external state will collapse to an odd or even coherent state.