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We have identified a mechanism of collective nuclear de-excitation in aBose-Einstein condensate of $^{135}$Cs atoms in their isomeric states,$^{135m}$Cs, suitable for the generation of coherent gamma photons. The processdescribed here does not correspond to single-pass amplification, which cannotoccur in atomic systems due to the large shift between absorption and emissionlines, nor does it require the large densities associated to standard Dickesuper-radiance. It thus overcome the limitations that have been hindering thegeneration of coherent gamma rays in many systems. Therefore, we propose anapproach for generation of coherent gamma rays, which relies on a combinationof well established techniques of nuclear and atomic physics, and can berealized with currently available technology.

Coherent gamma photon generation in a Bose-Einstein condensate of $^{135m}$Cs