Beyond the usual approximations: Time-dependent magnetic traps revisited

The motion of atoms in time-orbiting potential (TOP) traps is usually described by applying adiabatic and time-averaging approximations. In this work we show that careful experimental analysis reveals corrections to both of these approximations in the shape of a micromotion of the atoms at the frequency of the time-dependent trapping field and of a dependence of the equilibrium position of the atoms on the sense of rotation of the bias field. Whereas the former can be easily explained theoretically, the latter requires a more sophisticated analytical treatment involving geometric forces. We present experimental results and numerical simulations which agree well with the data. Furthermore, implications for Bose–Einstein condensation experiments are discussed.