Effect of optical pumping in saturated absorption spectroscopy: an analytic study for two-level atoms

We present the analytic solutions of the saturated absorption spectrum for an atomic medium composed of two-level atoms and describe the effects of saturation and optical pumping on the spectrum. The background-subtracted Doppler-free spectrum is Lorentzian-shaped with an amplitude and width given by 1-{1+ s(0)[1+(gamma(2)t/2)]}(-1/2) and gamma(t)[1+{1+s(0)[1+(gamma(2)t/2)]}(1/2)], respectively, where gamma(t) is the transverse decay rate, gamma(2) is the decay rate to energy levels other than the ground state, s0 is the saturation parameter and t is the interaction time of the atoms with laser beams. Analytic results are compared with numerical results and show good agreement with one another. This paper is intended for graduate students who have started to study basic atomic physics.