Spin-Exchange Cross Sections for Rb87-Rb87 and Rb87-Cs133 Collisions

Abstract

In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{87}$-${\mathrm{Cs}}^{133}$ collisions at 78°C. Values determined in this way were: $\sigma ({\mathrm{Rb}}^{87}-{\mathrm{Rb}}^{87})=(1.9\mathrm{}\pm 0.2)\times {10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ and $\sigma ({\mathrm{Rb}}^{87}-{\mathrm{Cs}}^{133})=(2.3\mathrm{}\pm 0.2)\times {10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\tau }=\frac{1}{T}+\frac{1}{T_{S1\mathrm{}}}+\frac{1}{T_{E1\mathrm{}}}$, where $T$ is the non-spin-exchange relaxation time and $T_{S1\mathrm{}}$ and $T_{E1\mathrm{}}$ are the self- and cross-exchange times. Then $\tau$ was obtained by fitting the signal to a single exponential and applying a small correction ($\approx 10\%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.