  We provide a universal discussion of the interplay between Rydberg-state
electromagnetically induced transparency (EIT) and optical pumping (OP) in a
thermal Rb87 medium. By pumping the population to one single Hyperfine/Zeeman
state, we can enhance the interaction strength and, in principle, amplify the
EIT peak. According to our measurements, the EIT peak height can be improved by
a factor of two or reduced by one order of magnitude, and linewidth was
slightly narrowed by the pumping effect. Similar behavior is also seen by
increasing the optical density (OD) of the medium. The EIT feature is predicted
quantitatively using a Doppler-free non-perturbation numerical calculation.
With and without the optical pumping field, the EIT peak heights collapse onto
the same theoretical curve, showing that OP and varying OD have the same
effect. In both simulations and measurements, Rydberg EIT enhancement through
OP is dependent on the intensity of the probe field and the OD. Our work
clarifies the underlying mechanisms of optical pumping and advances
Rydberg-atom research.
