Quantum many-body theory of coherent output of Bose-Einstein condensation (I) Factorization and atom coherence

Based on the Bogoliubov approximation in the thermodynamical limit, a linea r quantum many-body theory is presented to deal with the output of the boso nic atoms to a free propagating mode from a magnetic trap. It is shown that , when atoms are prepared initially in the Bose-Einstein condensation insid e a trap, the output will be described by a macroscopic quantum state, a ma ny-body coherent state. This is due to the factorization structure of the t otal wave function, showing that the output atom beam is coherent. The gene ral expressions for the spectral density of the output and its spatial dist ribution are given in terms of our linear quantum many-body theory.