  Coherent optical bichromatic forces have been shown to be effective tools for
rapidly slowing and cooling simple atomic systems. While previous estimates
suggest that these forces may also be effective for rapidly decelerating
molecules or complex atoms, a quantitative treatment for multilevel systems has
been lacking. We describe detailed numerical modeling of bichromatic forces by
direct numerical solution for the time-dependent density matrix in the
rotating-wave approximation. We describe both the general phenomenology of an
arbitrary few-level system and the specific requirements for slowing and
cooling on a many-level transition in calcium monofluoride (CaF), one of the
molecules of greatest current experimental interest. We show that it should be
possible to decelerate a cryogenic buffer-gas-cooled beam of CaF nearly to rest
without a repumping laser and within a longitudinal distance of about 1 cm. We
also compare a full 16-level simulation for the CaF B$\leftrightarrow$X system
with a simplified numerical model and with a semiquantitative estimate based on
2-level systems. The simplified model performs nearly as well as the complete
version, whereas the 2-level model is useful for making order-of-magnitude
estimates, but nothing more.
