Rotational cooling of molecular ions through laser-induced coupling to the collective modes of a two-ion Coulomb crystal

We show that the rotational degree of freedom of a polar heteronuclear molecular ion can be cooled through an optical coupling to the collective motional modes of the molecular ion and a simultaneously trapped and laser cooled atomic ion. Since the dissipative part of the rotational cooling is realized through laser cooling of the two-ion systems motional modes, the scheme should be applicable to a large range of molecules. As a test case for our cooling scheme we consider rotational cooling of a MgH+ ion trapped with a laser cooled Ca-40(+) ion.