Quantum backaction of optical observations on Bose-Einstein condensates

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, assuming the absence of residual absorption. We find that the condensate gets gradually 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 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