  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.
