Rotational cooling of heteronuclear molecular ions with $^1$Σ$$, $^2$Σ$$, $^3$Σ$$, and $^2$Π$$ electronic ground states

The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The rovibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of 1Σ electronic ground-state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: 1Σ, 2Σ, 3Σ, and 2Π. The schemes are relying on one or two laser-driven transitions with the possible inclusion of a tailored incoherent far-infrared radiation field.