  We develop the theory of the resonant formation of coupled
topological-collective coherent modes in the presence of a quantized trap and
classical external field. The coupling between the topological and the
collective modes can be linear as well as non-linear depending upon the tuning
of the external extremely low frequency electromagnetic field. This tuning
depends on the trap frequency and the energy level separation between the
ground and the first excited topological coherent mode modified by the two body
atomic collisions.
