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

Published

March 12, 2025

Author(s)

Alex Pouliot, E. Chomen-Ramos, G. Carlse, T. Vacheresse, J. Randhawa, L. Marmet, A. Kumarakrishnan, Jacek Klos, Eite Tiesinga

Abstract

We present comprehensive determinations of 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. They have been measured by establishing a spatially periodic population grating in the Rb sample using two laser beams intersecting at a small angle $\theta$ of order 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 read-out 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 $\theta^2$ dependence of the decay rate. We also measure the systematic dependence of the decay rate on the buffer gas pressure over a typical range of 50 Torr to 700 Torr (or $7\,000$ 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. Assuming a rectangular profile of the population distribution, and a rectangular read-out beam profile, our values are $0.332(5)$ cm$^2$/s, $0.220(2)$ cm$^2$/s, $0.1338(8)$ cm$^2$/s, $0.1239(13)$ cm$^2$/s, $0.1003(16)$ cm$^2$/s, and $0.0752(10)$ cm$^2$/s for Rb in He, Ne, N$_2$, Ar, Kr, and Xe, respectively. Assuming a Gaussian profile of the population distribution, and a Gaussian read-out beam profile, our values are $0.325(5)$ cm$^2$/s, $0.215(2)$ cm$^2$/s, $0.1306(8)$ cm$^2$/s, $0.1214(13)$ cm$^2$/s, $0.0960(15)$ cm$^2$/s, and $0.0732(10)$ cm$^2$/s for Rb in He, Ne, N$_2$, Ar, Kr, and Xe, respectively. The number in parentheses represents one standard deviation of the combined statistical and systematic uncertainty. Our measurements represent the smallest statistical uncertainty to date for these Rb-buffer gas systems. We also compare this data with diffusion coefficients obtained using \em quantum}, \em classical}, and \em semi-classical} 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. Additionally, the theoretical diffusion coefficients for $^85}$Rb and $^87}$Rb are indistinguishable given these theoretical uncertainties. We find that the analytical, semi-classical model, which solely relies on the attractive long-range van-der-Waals interaction, only gives the correct orders of magnitude for $D$. We also observe that the temperature dependence of the quantum and classical calculations of $D$ are nearly the same with a purely repulsive exponential potential. Our computed diffusion coefficients deviate from the experimental determinations by 4\,\% to 12\,\% when using the rectangular profile assumptions, and by 0\,\% to 14\,\% when using the Gaussian profile assumptions. Nevertheless, experiment and theory show a similar systematic variation as a function of the mass of the buffer gas. 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.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Volume

111

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevA.111.033108

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Keywords

diffusion coefficient, quantum optics

Citation

Pouliot, A. , Chomen-Ramos, E. , Carlse, G. , Vacheresse, T. , Randhawa, J. , Marmet, L. , Kumarakrishnan, A. , Klos, J. and Tiesinga, E. (2025), Measurements of diffusion coefficients for rubidium--inert gas mixtures using coherent scattering from optically pumped population gratings, Physical Review A (Atomic, Molecular and Optical Physics), [online], https://doi.org/10.1103/PhysRevA.111.033108, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=958494 (Accessed April 1, 2026)