Abstract

Experimental techniques for the production and manipulation of Bose–Einstein condensates have now advanced to the stage where macroscopic coherence effects have been observed. The usual method for theoretical investigation of the bulk properties of a Bose–Einstein condensate with collisions is to use the Gross–Pitaevski equation, which ignores any contribution made by quantum noise within a condensate. We examine the contribution made by this noise, using a positive P-representation known in quantum optics. The stochastic equations of the P-representation are exact and, in principle, allow for a direct ah initio calculation of the properties of condensates. In practice, they are difficult to work with, and we therefore investigate the validity of a truncated Wigner representation, which is better behaved.

© 1998 Optical Society of America