  Impressive pictures of moving Bose-Einstein condensates have been taken using
phase-contrast imaging M. R. Andrews et al., Science 273, 84 (1996). We
calculate the quantum backaction of this measurement technique. We find that
phase-contrast imaging is not a quantum nondemolition measurement of the atomic
density. Instead, the condensate gets gradually depleted at a rate that is
proportional to the light intensity and to the inverse cube of the optical wave
length. The fewer atoms are condensed the higher is the required intensity to
see a picture, and, consequently, the higher is the induced backaction. To
describe the quantum physics of phase-contrast imaging we put forward a new
approach to quantum-optical propagation. We develop an effective field theory
of paraxial optics in a fully quantized atomic medium.
