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

We present comprehensive determinations of the diffusion coefficients $D$ at $T=24\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\circ}}\mathrm{C}$ for trace amounts of naturally abundant Rb atoms in inert, naturally abundant He, Ne, ${\mathrm{N}}_{2}$, Ar, Kr, and Xe buffer gases using a single measurement technique. They have been measured by establishing a spatially periodic population grating in the Rb sample using two laser beams that intersect at a small angle $\ensuremath{\theta}$ 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. This decay is monitored by observing the scattered field from a readout beam aligned along the direction of one of the excitation beams. We distinguish the contribution of diffusion from other collisional processes by measuring the characteristic ${\ensuremath{\theta}}^{2}$ dependence of the decay rate. We also measure the systematic dependence of the decay rate on the buffer gas pressure over a range of 7000 to $90\phantom{\rule{0.16em}{0ex}}000$ Pa. In this manner, we obtain diffusion coefficients at standard atmospheric pressure of $101\phantom{\rule{0.16em}{0ex}}325$ Pa and at a temperature of $24.0(5)\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\circ}}\mathrm{C}$. We use two models to correct for systematic effects due to the transit time, one assuming a rectangular profile of the population distribution and a rectangular readout beam profile, and a second using Gaussian profiles. We obtain weighted averages of 0.33(5), 0.214(14), 0.132(7), 0.123(9), 0.093(9), and $0.073(4)\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$/s for Rb in He, Ne, ${\mathrm{N}}_{2}$, Ar, Kr, and Xe, respectively. The number in parentheses represents one standard deviation of the combined statistical and systematic uncertainty. We also compare these data with diffusion coefficients obtained using quantum, classical, and semiclassical theoretical methods based on the most accurate interatomic interaction potentials from the literature. Near room temperature, simulations of $D$ using classical and quantum methods agree within their intrinsic, sub-1% standard uncertainties. We find that the semiclassical model only gives the correct orders of magnitude for $D$. 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, biomedical imaging using spin-polarized noble gases, tests of collision models based on interatomic potentials, and the development of pressure sensors.

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