Accurate Determination of an alkali-inert gas diffusion coefficient using coherent transient emission from a density grating

We demonstrate a new technique for the accurate measurement of diffusion coefficients for alkali vapor in an inert buffer gas. The measurement was performed by establishing a spatially periodic density grating in isotopically pure $^{87}$Rb vapor and observing the decaying coherent emission from the grating due to the diffusive motion of the vapor through N$_2$ buffer gas. We obtain a diffusion coefficient of $0.245 \pm0.002 ~\textrm{cm}^{2}/\textrm{s}$ at 50$\degree$C and 564~Torr. Scaling to atmospheric pressure, we obtain $D_0 = 0.1819 \pm 0.0024~\textrm{cm}^2/\textrm{s}$. To the best of our knowledge, this represents the most accurate determination of the Rb--N$_2$ diffusion coefficient to date. Our measurements can be extended to different buffer gases and alkali vapors used for magnetometry and can be used to constrain theoretical diffusion models for these systems.