  We report our experiment on sideband cooling with two Raman transitions in a
$\Lambda$ configuration that allows selective coherent population trapping
(CPT) of the motional ground state. The cooling method is applied to $^{87}$Rb
atoms in a circularly-polarized one-dimensional optical lattice. Owing to the
vector polarizability, the vibration frequency of a trapped atom depends on its
Zeeman quantum number, and CPT resonance for a pair of bound states in the
$\Lambda$ configuration depends on their vibrational quantum numbers. We call
this scheme motion-selective coherent population trapping (MSCPT) and it is a
trapped-atom analogue to the velocity-selective CPT developed for free He
atoms. We observe a pronounced dip in temperature near a detuning for the Raman
beams to satisfy the CPT resonance condition for the motional ground state.
Although the lowest temperature we obtain is ten times the recoil limit owing
to the large Lamb-Dicke parameter of 2.3 in our apparatus, the experiment
demonstrates that MSCPT enhances the effectiveness of Raman sideband cooling
and enlarges the range of its application. Discussions on design parameters
optimized for MSCPT on $^{87}$Rb atoms and opportunities provided by diatomic
polar molecules, whose Stark shift shows strong dependence on the rotational
quantum number, are included.
