Kinetic Equations for Optical Pumping

We derive quantum-mechanical kinetic equations for the matter density $\rho$ and radiation density matrix $R$, which describe optical pumping phenomena. The resultant kinetic equations are a set of coupled nonlinear equations for $\rho$ and $R$. With appropriate linearizations, we can obtain the present theories of optical pumping. The nonlinear equations describe multiple scattering and line narrowing due to imprisonment of resonant radiation. We show that the coupled equations for $\rho$ and $R$ are equivalent to coupled equations for $\rho$ and a generalized polarization matrix II, whose matrix elements are the second moments of $R$. The polarization matrix II constitutes a complete description of linear phenomena in the same manner as present theories describe optical pumping phenomena by using the matter density matrix $\rho$ alone. As a consequence of our nonphenomenological treatment of radiation, we can provide a completely microscopic treatment of the externally modulated light-beam experiment of Bell and Bloom. We show that the atom absorbs the modulation envelope directly from the external thermal light beam in the same way that the atom absorbs transverse polarization directly from the light beam in optical pumping experiments.