A Floquet formalism for the interaction of magnetically trapped atoms with rf fields

A many-mode Floquet theory (MMFT) formalism is applied to study the interaction of a polychromatic rf field with cold atoms trapped in a quadrupole magnetic trap. The validity of the MMFT approach is first established by comparing its results with those of the previously used formalisms for the cases of single-and two-frequency rf fields. The effect of truncation of the infinite matrices has been studied and a suitable truncation order is obtained for the numerical implementations. The results obtained for the composite atom-field system has shown some exquisite features such as lattice-like periodic variation in the eigen-energies and large two-photon transition probabilities between the atomic states. Dependence of the trapping parameters such as trap position, depth and width on the rf field parameters like field strength and mode separation has also been studied. This work predicts the generation of lattice type atom-trapping geometries which can be controlled by varying the rf field parameters of a polychromatic rf field.