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

Sympathetic Cooling of Mixed Species Two-Ion Crystals for Precision Spectroscopy