Diffraction of Atoms from a Measurement Induced Grating

We report on an experiment with polarized atoms passing a standing light wave, where the atom close-quote s position is encoded (entangled) with the excitation amplitude of two long lived electronic states. Position information can be obtained a posteriori by measuring the electronic state. If this measurement is performed, the atom is localized in an array of virtual slits. This gives rise to diffraction of the atomic de Broglie waves from a measurement induced amplitude grating, thus showing the back action onto the momentum due to the localization. We further demonstrate experimentally that the encoding can be totally erased. copyright 1997 The American Physical Society