  A Born-Markov master equation is used to investigate the decoherence of the
state of a macroscopically occupied mode of a cold atom trap due to three-body
loss. In the large number limit only coherent states remain pure for times
longer than the decoherence time: the time it takes for just three atoms to be
lost from the trap. For large numbers of atoms (N>10^4) the decoherence time is
found to be much faster than the phase collapse time caused by intra-trap
atomic collisions.
