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We have demonstrated the loss of transverse spatial coherence of an atomic wave function after a single spontaneous emission. He^* atoms were both diffracted and excited by a standing light wave with a variable period. After the interaction, the excited atoms decay by a single spontaneously emitted photon. By changing the period of the standing light wave, we have mapped the loss of spatial coherence as a function of the transverse coordinate. By detecting the emitted photon one could "erase" the position information available and recover the transverse coherence in a correlation experiment, or realize a Heisenberg microscope.
Pfau et al. (1994) studied this question.