  We observe quantum beats with periodic revivals due to non-linear spacing of
Zeeman levels in the ground state of potassium atoms and demonstrate their
synchronous optical pumping by double modulation of the pumping light at the
Larmor frequency and the revival frequency. We show that synchronous pumping
increases the degree of spin polarization by a factor of 4. As a practical
example, we explore the application of this double-modulation technique to
atomic magnetometers operating in the geomagnetic field range and find that it
can increase the sensitivity and reduce magnetic field orientation-dependent
measurement errors endemic to alkali-metal magnetometers.
