  Polar heavy-atom molecules have been well recognized as promising candidates
for precision measurements and tests of fundamental physics. A much slower
molecular beam to increase the interaction time should lead to a more sensitive
measurement. Here we theoretically demonstrate the possibility of the
stimulated longitudinal slowing of heavy-atom molecules by the coherent optical
bichromatic force with a constant beat phase. Taking the YbF meolecule as an
example, we show that a rapid and short-distance deceleration of heavy
molecules by a phase-compensation method is feasible with moderate conditions.
A molecular beam of YbF with a forward velocity of 120 m/s can be decelerated
below 10 m/s within a distance of 3.5 cm and with a laser irradiance for each
traveling wave of 107.2 W/cm$^2$. We also give a simple approach to estimate
the performance of the BCF on some other heavy molecules, which is helpful for
making a rapid evaluation on the feasibility of the stimulated slowing
experiment. Our proposed slowing method could be a promising approach to break
through the space constraint or the limited capture efficiency of molecules
loadable into a MOT in traditional deceleration schemes, opening the
possibility for a significant improvement of the precision measurement
sensitivity.
