Both Bose-Einstein condensates and optical fields are composed of bosons, so that the majority of the processes which have long been studied in quantum and nonlinear optics have equivalents in the field of Bose-Einsten condensation. However, due to the masses of the condensed atoms, the confining potentials and the huge collisional nonlinearities, the simpler theoretical approaches common to quantum optics can sometimes give misleading answers when applied to condensates. In this work we describe some of the areas where simplified treatments can be misleading, and compare and contrast the predictions of quantum many-body treatments with those of the single-mode type treatments which have been so successful in quantum optics.
