  We propose a method to generate entangled light with a Bose-Einstein
condensate trapped in a cavity, a system realized in recent experiments. The
atoms of the condensate are trapped in a periodic potential generated by a
cavity mode. The condensate is continuously pumped by a laser and spontaneously
emits a pair of photons of different frequencies in two distinct cavity modes.
In this way, the condensate mediates entanglement between two cavity modes
which leak out and can be separated and exhibit continuous variable
entanglement. The scheme exploits the experimentally demonstrated strong,
steady and collective coupling of condensate atoms to a cavity field.
