Mateo Londoño

We have studied the general aspects of the dynamics of an ion trapped in an ideal multipolar radiofrequency trap while interacting with a dense cold atomic gas. In particular, we have explored the dynamical stability, the energy relaxation and the characteristic harmonic motion exhibited by a trapped Yb$^{+}$ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we used two different molecular dynamics simulations; one based on a time-event drive algorithm and the other based on the stochastic Langevin equation. Relevant values for experimental realizations, such as the associated ion's lifetimes and observable distributions, are presented along with some analytical expressions which relate the ion's dynamical properties with the trap parameters.

Based on the Langevin equation, a stochastic formulation is implemented to describe the dynamics of a trapped ion in a bath of ultracold atoms, including an excess of micromotion. The ion dynamics is described following a hybrid analytical-numerical approach in which the ion is treated as a classical impurity in a thermal bath. As a result, the ion energy's time evolution and distribution are derived from studying the sympathetic cooling process. Furthermore, the ion dynamics under different stochastic noise terms is also considered to gain information on the bath properties' role in the system's energy transfer processes. Finally, the results obtained from this formulation are contrasted with those obtained with a more traditional Monte Carlo approach.