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An extended Bose-Einstein condensate (BEC) in an optical lattice provides akind of periodic dielectric and causes band gaps to occur in the spectrum oflight propagating through it. We examine the question whether these band gapscan modify the spontaneous emission rate of atoms excited from the BEC, andwhether they can lead to a self-stabilization of the BEC against spontaneousemission. We find that self-stabilization is not possible for BECs with adensity in the order of $10^{14}$ cm$^{-3}$. However, the correspondingnon-Markovian behavior produces significant effects in the decay of excitedatoms even for a homogeneous BEC interacting with a weak laser beam. Theseeffects are caused by the occurrence of an avoided crossing in the photon (orrather polariton) spectrum. We also predict a new channel for spontaneous decaywhich arises from an interference between periodically excited atoms andperiodic photon modes. This new channel should also occur in ordinary periodicdielectrics.Comment: 18 Pages, 4 figure

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Bose-Einstein condensates in optical lattices: Spontaneous emission in the presence of photonic band gaps