Analytical solution for the populations of the energy levels of alkali metals under optical pumping and mixing of excited state sublevels

The paper presents the results of an analytical calculation of the system of balance equations describing the populations of the energy levels of the ground state and the total population of the excited state of alkali metals under optical pumping under conditions when collisions with a buffer gas cause complete mixing of the sublevels of the excited state. This situation is realized in a number of quantum sensors, such as frequency standards, gyroscopes, magnetometers, using a cell with alkali metal vapor and a buffer inert gas as a sensitive element. A comparison with the experiment is given. The results can be used for spectroscopic non-destructive testing of the gas composition of such cells.