Nonlinear 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 a semianalytical mean-field approach and a completely quantum numerical technique based on the positive P representation, it is demonstrated that the atomic delocalization due to the measurement backaction is smaller for a strongly interacting gas. The numerically calculated second-order correlation functions demonstrate the appearance of atomic bunching as a result of the center-of-mass measurement. Although rather small, the bunching is also present for a strongly interacting gas, which is in contrast with the case of an unperturbed gas. The performed analysis allows us to speculate that, for relatively strong interactions, the size of the atomic cloud determined with a single snapshot measurement can become smaller than the ground-state cloud size.