Investigations of a two-mode atom-laser model

Atom lasers based on rf outcoupling from a trapped Bose-Einstein condensate can be described by a set of generalized, coupled Gross-Pitaevskii equations (GPEs). If not only one but two radio frequencies are used for outcoupling, the atoms emerging from the trap have two different energies and the total wave function of the untrapped spin state is a coherent superposition which leads to a pulsed atomic beam. We present results for such a situation obtained from a one-dimensional GPE model for magnetically trapped ${}^{87}\mathrm{Rb}$ in the $F=1\mathrm{}$ state. The wave function of the atomic beam can be approximated by a sum of two Airy functions. In the limit of weak coupling we calculate the intensity analytically.