Non-Linear Dynamics of Continuously Measured Bose-Einstein Condensates in One-Dimensional Harmonic Traps

Continuous center-of-mass position measurements performed on an interacting harmonically trapped Bose-gas are considered. Using both semi-analytical mean-field approach and completely quantum numerical technique based on positive P-representation, it is demonstrated that the atomic delocalization due to the measurement back action is smaller for a strongly interacting gas. The numerically calculated second-order correlation functions demonstrate appearance of atomic bunching as a result of the center-of-mass measurement. Though being rather small the bunching is present also for strongly interacting gas which is in contrast with the case of unperturbed gas. The performed analysis allows to speculate that for relatively strong interactions the size of atomic cloud determined with a single snapshot measurement can become smaller than the ground-state cloud size.