The phase diffusion of the order parameter of trapped Bose-Einstein condensates at temperature $k_{B}T\gg ħ\overline{\omega }$ is determined, which gives the fundamental limit of the linewidth $\Delta \nu$ of an atom laser. In addition a prediction of the number fluctuations in the condensate and their correlation time ${\tau }_c$ is made and a general relation for $\Delta \nu {\tau }_c$ is derived from the fluctuation-dissipation relation.

• Received 29 June 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.5262