We present comprehensive determinations of the diffusion coefficients for rubidium atoms in six commonly used buffer gases using a newly developed coherent transient technique. The experiments are carried out by establishing a spatially periodic rubidium population grating using two laser beams intersecting at an angle of a few milliradians. The grating decays exponentially in time due to diffusive motion induced by momentum-changing elastic collisions with buffer gas atoms. The decay can be monitored over a large dynamic range using a heterodyne detection system that records the coherently scattered light from the grating. We are able to distinguish the contribution of diffusion from other collisional processes by measuring the characteristic dependence of the decay rate on the angle between excitation beams. These experiments are carried out in a non-magnetic atomic vapour cell manifold that allows magnetic fields and magnetic field gradients to be cancelled so that rubidium atoms can be manipulated in targeted internal ground states in the presence of different inert gases that can be maintained at pressures ranging from a few hundred pascals to one atmosphere. Our measurements agree with theoretical calculations of diffusion coefficients after reconciling key systematic effects, and this agreement appears to resolve both the widespread scatter in the values of diffusion coefficients using other techniques obtained over several decades and their disagreement with theory. Our measurements lay the groundwork for the development of a quantum pressure sensor that will rely on the intrinsic properties of atoms to calibrate commercial pressure gauges and impact emerging quantum technologies such as magnetometry, spin polarized imaging, and quantum memory that rely on accurate knowledge of diffusion coefficients. We also describe preliminary, comparative studies of a traditional population magnetometer and a unique coherence magnetometer developed by our group, which led to the development of the technique for measuring diffusion. All our experiments were carried out using a low-cost, home-built diode laser system. We present a detailed characterization of this system, which has supported wide-ranging experiments in precision metrology such as optical tweezers-based determination of micro-particle masses, measurements of atomic lifetimes, and atom interferometric measurements of velocity and gravitational acceleration.
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,
N2, 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
90000 Pa. In this manner, we obtain diffusion coefficients at standard atmospheric pressure of
101325 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)cm2/s for Rb in He, Ne,
N2, 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.
We demonstrate a 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 87Rb vapor and observing the decaying coherent emission from the grating due to the diffusive motion of the vapor through N2 buffer gas. We obtain a diffusion coefficient of 0.245 ± 0.002 cm2 /s at 50°C and 564 Torr. Scaling to atmospheric pressure, we obtain D0 = 0.1819 ± 0.0024 cm2 /s. To the best of our knowledge, this represents the most accurate determination of the Rb-N2 diffusion coefficient. 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
We investigate the temperature dependence of diffusion coefficients of Rb atoms DRb(T,p) in the presence of N2 buffer gas. This work follows recent determinations of DRb(T,p) in 6 buffer gas mixtures over the pressure range of p = 50 to 760 Torr and at a constant temperature of T = 24°C. These measurements agree with quantum mechanical and classical calculations of collisions based on ab-initio interatomic potentials, to an accuracy ranging from 5.5% to 15% [Pouliot et. al., Phys. Rev. A 111, 033108 (2025)], suggesting that the determinations of diffusion coefficients D(T,p) can become the basis for a quantum pressure sensor. We report progress on these measurements and discuss suppression of systematic uncertainties arising from the heterodyne detection system.
We demonstrate a 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
87Rb vapor and observing the decaying coherent emission from the grating due to the diffusive motion of the vapor through
N2 buffer gas. We obtain a diffusion coefficient of $0.245\ifmmode\pm\else\textpm\fi{}0.002\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{2}/\text{s}$ at $50{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ and 564 Torr. Scaling to atmospheric pressure, we obtain ${D}_{0}=0.1819\ifmmode\pm\else\textpm\fi{}0.0024\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{2}/\text{s}$. To the best of our knowledge, this represents the most accurate determination of the $\mathrm{Rb}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ 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.
A spatially periodic distribution of excited electronic states is produced in ruby which is placed into the interference region of two light beams derived from a pulsed laser (wavelength 530 nm). The spatially modulated population density acts like an optical grating and is detected by diffraction of a quasi-cw laser beam (488 nm). The lifetimes of the population density gratings are measured for ruby crystals with 0.05 to 5% Cr-doping and compared with the fluorescence lifetimes of the R-lines (694 nm). For the 0.05% ruby both lifetimes are nearly equal. At higher Cr-concentrations the grating decay is considerably faster than the fluorescent decay. The grating lifetimes are independent of the grating period A = 1 to 100 μm. From this observation an upper limit of the diffusion constant for energy transfer between excited electronic states in ruby is estimated.