The aim of this project was the description of new nonlinear collective phenomena like entangled and disentangled effects between more large atomic systems, which appear in the mutiquantum processes of interaction of ultra-cold atoms with cavity electromagnetic field for further applications in quantum processing of information. The progress in manipulating and controlling of the trapped neutral atoms in optical lattices by quantum optical exchanges between them open novel applications of atomic collective phenomena like Bose-Einstein condensation scattering super-radiance with applications  in  quantum information processing, atomic interferometer,  and molecular and biological physics.

The objectives of the project were:

1. To propose a new non-linear phase transition, in which correlation function between the cold atoms anomalous increases after which decreases  with increasing of  temperature.

2. Examination of the coherence properties of emitted pairs of entangled photons in such Bose-Einstein condensate and their  application in quantum communication and processing systems.