Interaction induced phase fluctuations in a guided atom laser

In this paper, we determine the magnitude of phase fluctuations caused by atom-atom interaction in a one-dimensional beam of bosonic atoms. We imagine that the beam is created with a large coherence length, and that interactions only act in a specific section of the beam, where the atomic density is high enough to validate a Bogoliubov treatment. The magnitude and coherence length of the ensuing phase fluctuations in the beam after the interaction zone are determined.