Measurements of diffusion coefficients for rubidium--inert gas mixtures using coherent scattering from optically pumped population gratings

Abstract

We present comprehensive determinations of the diffusion coefficients $D$ at $T=24\,\degree$C for trace amounts of naturally abundant Rb atoms in inert, naturally abundant He, Ne, N$_2$, Ar, Kr, and Xe buffer gases using a single measurement technique. We establish a spatially periodic population grating in the Rb sample using two laser beams that intersect at a small angle $\theta$ of a few milliradians. The atomic population grating decays exponentially in time due to diffusive motion induced by momentum-changing elastic collisions between Rb and buffer gas atoms or molecules, and is monitored by observing the scattered field from a read-out beam. We distinguish the contribution of diffusion from other collisional processes by measuring the characteristic $\theta^2$ dependence of the decay rate. We also measure the systematic dependence of the decay rate on the buffer gas pressure over a range of $7\,000$ Pa to $90\,000$ Pa. In this manner, we obtain diffusion coefficients at standard atmospheric pressure of $101\,325$ Pa and at a temperature of 24.0(5)~$^\circ$C. We obtain weighted averages of $0.33(5)$ cm$^2$/s, $0.214(14)$ cm$^2$/s, $0.132(7)$ cm$^2$/s, $0.123(9)$ cm$^2$/s, $0.093(9)$ cm$^2$/s, and $0.073(4)$ cm$^2$/s for Rb in He, Ne, N$_2$, Ar, Kr, and Xe, respectively. We compare this data with diffusion coefficients obtained using quantum, classical, and semi-classical theoretical methods based on the most accurate interatomic interaction potentials from the literature. Our computed diffusion coefficients based on the quantum theory agree with the experimental determinations when systematic effects are taken into account. Our measurements and modeling are relevant to the optimization of magnetometers, imaging using spin-polarized noble gases, tests of collision models based on interatomic potentials, and the development of pressure sensors.