Squeezing in driven bimodal Bose-Einstein condensates: Erratic driving versus noise

We study the interplay of squeezing and phase randomization near the hyperbolic instability of a two-site Bose-Hubbard model in the Josephson interaction regime. We obtain results for the quantum Zeno suppression of squeezing far beyond the previously found short time behavior. More importantly, we contrast the expected outcome with the case where randomization is induced by erratic driving with the same fluctuations as the quantum noise source, finding significant differences. These are related to the distribution of the squeezing factor, which has log-normal characteristics: hence its average is significantly different from its median due to the occurrence of rare events.