  Quasi one dimensional Bose-Einstein condensates (BECs) in elongated traps
exhibit significant phase fluctuations even at very low temperatures. We
present recent experimental results on the dynamic transformation of phase
fluctuations into density modulations during time-of-flight and show the
excellent quantitative agreement with the theoretical prediction. In addition
we confirm that under our experimental conditions, in the magnetic trap density
modulations are strongly suppressed even when the phase fluctuates. The paper
also discusses our theoretical results on control of the condensate phase by
employing a time-dependent perturbation. Our results set important limitations
on future applications of BEC in precision atom interferometry and atom optics,
but at the same time suggest pathways to overcome these limitations.
