  We demonstrate a simple technique to prepare and determine the desired
internal quantum states in multi-Zeeman-sublevel atoms. By choosing appropriate
coupling and pumping laser beams, atoms can be easily prepared in a desired
Zeeman sublevel with high purity or in any chosen ground-state population
distributions. The population distributions or state purities of such prepared
atomic states can be determined by using a weak, circularly-polarized probe
beam due to differences in transition strengths among different Zeeman
sublevels. Preparing well-defined internal quantum states in
multi-Zeeman-sublevel atoms (or spin-polarized quantum-state engineering) will
be very important in demonstrating many interesting effects in quantum
information processing with multi-level atomic systems.
