We describe and characterize an experimental apparatus that has been used to study interactions between ultracold lithium atoms and ytterbium ions. The preparation of ultracold clouds of Li atoms is described as well as their subsequent transport and overlap with Yb$^+$ ions trapped in a Paul trap. We show how the kinetic energy of the ion after interacting with the atoms can be obtained by laser spectroscopy. From analyzing the dynamics of the ion in the absence of atoms, we conclude that background heating, due to electric field noise, limits attainable buffer gas cooling temperatures. We suspect that this effect can be mitigated by noise reduction and by increasing the density of the Li gas, in order to improve its cooling power. Imperfections in the Paul trap lead to so-called excess micromotion, which poses another limitation to the buffer gas cooling. We describe in detail how we measure and subsequently minimize excess micromotion in our setup. We measure the effect of excess micromotion on attainable ion temperatures after buffer gas cooling and compare this to molecular dynamics simulations which describe the observed data very well.
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