An analysis is made of four-wave mixing of laser radiation interacting with
an ultracold degenerate ensemble of boson atoms trapped in a magnetic trap
. It is shown that the existence of long-range order in this type of atomic
system leads to a new mechanism for the generation of the reversed wave wh
ose experimental manifestation should differ from four-wave mixing in a non
degenerate gas. A similar nonlinear optical effect may be used for diagnost
ics of an ultracold gas at temperatures not much lower than the phase trans
ition temperature. (C) 1999 American Institute of Physics. [S1063-7850(99)0
2611-7].