Universal nonmonotonic structure in the saturation curves of magneto-optical-trap-loadedNa+ions stored in an ion-neutral hybrid trap: Prediction and observation

We predict that the maximal, steady-state ion capacity $N_s\left(\lambda \right)$ of radio-frequency (rf) traps, loaded at a rate of $\lambda$ particles per rf cycle, shows universal, nonlinear, nonmonotonic behavior as a function of loading rate $\lambda$. The shape of $N_s\left(\lambda \right)$, characterized by four dynamical regimes, is universal; i.e., it is predicted to manifest itself in all types of rf traps independent of the details of their construction and independent of particle species loaded. For $\lambda \ll$ 1 (region I), as expected, $N_s\left(\lambda \right)$ increases monotonically with $\lambda$. However, contrary to intuition, at intermediate $\lambda \sim 1$ (region II), $N_s\left(\lambda \right)$ reaches a maximum, followed by a local minimum of $N_s\left(\lambda \right)$ (region III). For $\lambda \gg 1$ (region IV), $N_s\left(\lambda \right)$ again rises monotonically. In region IV, numerical simulations, analytical calculations, and experiments show $N_s\left(\lambda \right)\sim {\lambda }^{2/3}$. We confirm our predictions both experimentally with magneto-optical-trap-loaded ${\mathrm{Na}}^{+}$ ions stored in a hybrid ion-neutral trap and numerically with the help of detailed ab initio molecular-dynamics simulations.