Optical-Pumping Transients in Rubidium-87 and Application to Excited-State Disorientation Cross Sections

Abstract

Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical-pumping process, both with and without buffer gas present. The observed transients are single exponentials with no buffer gas present, and double exponentials with buffer gas present, over a wide range of pumping intensities and relaxation times. These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin is included and a single relaxation time is assumed. From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section ${\ensuremath{\sigma}}_{\mathrm{eff}}$ is deduced for the disorientation of rubidium-87 within the $5^{2}P_{\frac{1}{2}}$ state as a result of its collision with a buffer-gas atom. It is shown that ${\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}_{\frac{1}{2}}+{\ensuremath{\sigma}}_{\frac{3}{2}}$, where ${\ensuremath{\sigma}}_{\frac{1}{2}}$ is the cross section for disorientation within the $5^{2}P_{\frac{1}{2}}$ level, and ${\ensuremath{\sigma}}_{\frac{3}{2}}$ is the cross section for transfer from the $5^{2}P_{\frac{1}{2}}$ level to the $5^{2}P_{\frac{3}{2}}$ level by means of collisions with the buffer gas. On the basis of recently measured values for ${\ensuremath{\sigma}}_{\frac{3}{2}}$, values are deduced for ${\ensuremath{\sigma}}_{\frac{1}{2}}$. The cross sections are: ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{H}\mathrm{e})=1.5(0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$, ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{N}\mathrm{e})=4.4(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$, and ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{A}\mathrm{r})=3.5(1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$. These cross sections are deduced from a model in which the probabilities for ${\mathrm{Rb}}^{87}$ to relax from any hyperfine level to any other are all equal. This model gives a better fit with the observed transients than the assumption that the electron spin only is randomized in the ${P}_{\frac{1}{2}}$ state with the nuclear spin unaffected. We show that accurate relaxation-time measurements can be made by measuring the time constants associated with the double exponentials as a function of light intensity, and extrapolating them to zero light intensity. Moreover, since no shutter is required, relaxation times ${10}^{\ensuremath{-}3}$ sec can be easily observed.