  Applying a many mode Floquet formalism for magnetically trapped atoms
interacting with a polychromatic rf-field, we predict a large two photon
transition probability in the atomic system of cold $^{87}Rb$ atoms. The
physical origin of this enormous increase in the two photon transition
probability is due to the formation of avoided crossings between eigen-energy
levels originating from different Floquet sub-manifolds and redistribution of
population in the resonant intermediate levels to give rise to the resonance
enhancement effect. Other exquisite features of the studied atom-field
composite system include the splitting of the generated avoided crossings at
the strong field strength limit and a periodic variation of the single and two
photon transition probabilities with the mode separation frequency of the
polychromatic rf-field. This work can find applications to characterize
properties of cold atom clouds in the magnetic traps using rf-spectroscopy
techniques.
