Quantum backaction of optical observations on Bose-Einstein condensates

Impressive pictures of moving Bose-Einstein condensates have been taken usi ng phase-contrast imaging [M.R. Andrews et al., Science 273: 84 (1996)]. We calculate the quantum backaction of this measurement technique, assuming t he absence of residual absorption. We find that the condensate gets gradual ly depleted at a universal rate that is proportional to the light intensity and to the inverse cube of the optical wave length. The fewer atoms are co ndensed the higher is the required intensity to see a picture, and, consequ ently, the higher is the induced backaction. To describe the quantum physic s of phase-contrast imaging we put forward a new approach to quantum-optica l propagation. We develop an effective field theory of paraxial optics in a fully quantized atomic medium.