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A coherence length for matter waves

We introduce the concept and mathematical description of a coherence length and a coherence momentum for matter states, and explain their significance via the example of the motional states of a single cold trapped ion. These parameters describe the coherence properties of matter waves analogously to the way in which optical coherence determines the coherence time and spectral width. They become apparent in the interference pattern of a matter or light wave interferometer, respectively. While the coherence length is a characteristic length by which two parts of a matter wave packet can be separated so that they still interfere, the coherence momentum describes the time interval of this overlap.