Multiple coupling of topological coherent modes of trapped atoms

The possibility of generating multiple coherent modes in trapped Bose gases is advanced. This requires the usage of several driving fields whose frequencies are tuned close to the corresponding transition frequencies. A general criterion is derived explaining when the driving fields, even when in perfect resonance, cannot generate the topological coherent modes. This criterion is termed the theorem of shape conservation. Bose-Einstein condensates with generated coherent modes display a number of interesting effects, such as interference fringes, interference current, mode locking, dynamic transition, critical phenomena, chaotic motion, harmonic generation, parametric conversion, atomic squeezing, and entanglement production. Approximate solutions, based on the averaging techniques, are found to be in good agreement with direct numerical calculations for the Gross-Pitaevskii equation.