Analytic calculation of the lineshapes in polarization spectroscopy of rubidium

This paper reports on analytic calculations of the lineshapes for polarization spectroscopy of rubidium atoms. Under the use of a weak circularly polarized pump beam, the time-dependent population of each magnetic sublevel was obtained analytically from the rate equations up to the lowest order of the pump beam intensity, and the associated circular birefringence experienced by a counterpropagating probe beam was calculated. In particular, analytic forms of the polarization spectroscopy spectra were obtained for 87Rb and 85Rb atoms using the mean transit time crossing the pump beam, and the analytic results were compared with the numerical data, experimental results and Nakayama model’s results, showing a good agreement one another.