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

Abstract

We predict that the maximal, steady-state ion capacity ${N}_{s}(\ensuremath{\lambda})$ of radio-frequency (rf) traps, loaded at a rate of $\ensuremath{\lambda}$ particles per rf cycle, shows universal, nonlinear, nonmonotonic behavior as a function of loading rate $\ensuremath{\lambda}$. The shape of ${N}_{s}(\ensuremath{\lambda})$, 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 $\ensuremath{\lambda}\ensuremath{\ll}$ 1 (region I), as expected, ${N}_{s}(\ensuremath{\lambda})$ increases monotonically with $\ensuremath{\lambda}$. However, contrary to intuition, at intermediate $\ensuremath{\lambda}\ensuremath{\sim}1$ (region II), ${N}_{s}(\ensuremath{\lambda})$ reaches a maximum, followed by a local minimum of ${N}_{s}(\ensuremath{\lambda})$ (region III). For $\ensuremath{\lambda}\ensuremath{\gg}1$ (region IV), ${N}_{s}(\ensuremath{\lambda})$ again rises monotonically. In region IV, numerical simulations, analytical calculations, and experiments show ${N}_{s}(\ensuremath{\lambda})\ensuremath{\sim}{\ensuremath{\lambda}}^{2/3}$. 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.