Coherence length for a trapped Bose gas

Matter waves can be assigned a coherence length analogous to the correspond ing quantity in optics. We show that there is a dramatic increase in cohere nce length associated with the appearance of Bose-Einstein condensation in a trapped ideal Bose gas. The large increase in coherence length occurs eve n for temperatures just below the critical temperature at which only a smal l proportion of the trapped atoms is to be found in the ground state.