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

We predict that the maximal, steady-state ion capacity N-s(lambda) 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(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 lambda << 1 (region I), as expected, N-s(lambda) increases monotonically with lambda. However, contrary to intuition, at intermediate lambda similar to 1 (region II), N-s(lambda) reaches a maximum, followed by a local minimum of N-s(lambda) (region III). For lambda >> 1 (region IV), N-s(lambda) again rises monotonically. In region IV, numerical simulations, analytical calculations, and experiments show N-s(lambda) similar to lambda(2/3). We confirm our predictions both experimentally with magneto-optical-trap-loaded Na+ ions stored in a hybrid ion-neutral trap and numerically with the help of detailed ab initio molecular-dynamics simulations.