Sympathetic cooling of mixed-species two-ion crystals for precision spectroscopy

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 rethermalization dynamics after a background gas collision for the Al+-Ca+ crystal for different cooling laser configurations.