Trapped and laser-cooled ions allow for a high degree of control of atomic quantum systems. They are the basis for modern atomic clocks, quantum computers and quantum simulators. In 2012, we suggested to use ion Coulomb crystals for precision spectroscopy . In the In+ /Yb+ multi-ion clock In+ ions are sympathetically cooled by Yb+ ions. This approach not only allows to cool complex multi-ion crystals rapidly, but also to measure and control systematic shifts in the clock ions with the help of the second species, whose sensitivity to external fields can be much larger. With a differential static polarizability of Da0 = 5 x 10-8 Hz/(V/m)2 between the 1S0 and 3P0 state, 115In+ has one of the smallest sensitivities to ac Stark shifts due to blackbody radiation (BBR) among optical clock candidates . It has been shown in  that optical clock operation with a total relative uncertainty of 10-19 is possible with mixed Coulomb crystals of In+ /Yb+ ions. A prerequisite for this is the control of the external thermal environment, which we demonstrated to allow a control of BBR shifts at the level of 10-20  and the precise determination of the differential polarizability of the clock states, which is currently limiting the relative uncertainty to 1 x 10-18. The routinely applied method of quench cooling on Yb+ ions supplies a new method to precisely measure Stark shifts on the clock transition due to BBR and with this the differential polarizability of the In+ ion.
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 M. S. Safronova et al.,Precision Calculation of Blackbody Radiation Shifts for Optical Frequency Metrology, PRL 107, 143006 (2011)
 J. Keller et al., Controlling systematic frequency uncertainties at the 10-19 level in linear Coulomb crystals, Phys. Rev. A, 99, 013405 (2019)
 T. Nordmann et al., Sub-kelvin temperature management in ion traps for optical clocks, Rev. Sci. Inst., 91, 111301 (2020)