  In this work we investigate the theory for three different uni-directional
population transfer schemes in trapped multilevel systems which can be utilized
to cool molecular ions. The approach we use exploits the laser-induced coupling
between the internal and motional degrees of freedom so that the internal state
of a molecule can be mapped onto the motion of that molecule in an external
trapping potential. By sympathetically cooling the translational motion back
into its ground state the mapping process can be employed as part of a cooling
scheme for molecular rotational levels. This step is achieved through a common
mode involving a laser-cooled atom trapped alongside the molecule. For the
coherent mapping we will focus on adiabatic passage techniques which may be
expected to provide robust and efficient population transfers. By applying
far-detuned chirped adiabatic rapid passage pulses we are able to achieve an
efficiency of better than 98% for realistic parameters and including
spontaneous emission. Even though our main focus is on cooling molecular
states, the analysis of the different adiabatic methods has general features
which can be applied to atomic systems.
