Time-dependent control of ultracold atoms and Bose-Einstein condensates in magnetic traps

With radiofrequency fields one can control ultracold atoms in magnetic traps. These fields couple the atomic spin states, and are used in evaporative cooling which can lead to Bose-Einstein condensation in the atom cloud. Also, they can be used in controlled release of the condensate from the trap, thus providing output couplers for atom lasers. In this paper we show that the time-dependent multistate models for these processes have exact solutions which are polynomials of the solutions of the corresponding two-state models. This allows simple, in many cases analytic descriptions for the time-dependent control of the magnetically trapped ultracold atoms.