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. In this work, the validity of 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. We have then used the MMFT formalism to calculate the eigen-energies and transition probabilities for atoms in the quadrupole trap and interacting with a polychromatic rf-field. This 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. This work thus predicts the generation of a lattice type atom trapping potential using polychromatic rf-field, which can be controlled by varying the rf-field parameters.