Nondestructive dynamic detectors for Bose-Einstein condensates

We propose and analyze a series of nondestructive dynamic detectors for Bose-Einstein condensates based on photodetectors operating at the shot-noise limit. These detectors are compatible with real-time feedback to the condensate. The signal-to-noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counterintuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily nondestructive. We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily nondestructive for a given signal-to-noise ratio.