  Sympathetic cooling of trapped ions has become an indispensable tool for
quantum information processing and precision spectroscopy. In the simplest
situation a single Doppler-cooled ion sympathetically cools another ion which
typically has a different mass. We analytically investigate the effect of the
mass ratio of such an ion crystal on the achievable temperature limit in the
presence of external heating. As an example, we show that cooling of a single
Al+ with Be+, Mg+ and Ca+ ions provides similar results for heating rates
typically observed in ion traps, whereas cooling ions with a larger mass
perform worse. Furthermore, we present numerical simulation results of the
rethermalisation dynamics after a background gas collision for the Al+/Ca+
crystal for different cooling laser configurations.
