Normal Modes and Gates in Interspecies Trapped-Ion Chains

Scaling up ion trap quantum information processors will likely require at least two co-trapped ion species. Using different species for computation and for sympathetic cooling or photonic interconnects provides spectral isolation that prevents decoherence of the computation ion. However, the different charge to mass ratios of distinct ion species cause their motion to decouple in the radial normal modes that are often used for entangling gates in trapped-ion systems. This decoupling increases the required laser power for these gates and hurts their fidelity by hampering sympathetic cooling. We study the general mass dependence of mutual mode participation in interspecies chains and the laser power required to drive entangling gates with amplitude modulation and amplitude-frequency modulation. We find that co-trapping different isotopes of the same element may be most desirable.