We present a robust method for measuring diffusion coefficients of warm atoms in buffer gases. Using optical pumping, we manipulate the atomic spin in a thin cylinder inside the cell. Then, we observe the spatial spread of optically pumped atoms in time using a camera, which allows us to determine the diffusion coefficient. As an example, we demonstrate measurements of diffusion coefficients of rubidium in neon, krypton and xenon acting as buffer gases. We have determined the normalized (273 K, 760 Torr) diffusion coefficients to be 0.18 ± 0.03 cm 2 /s for neon, 0.07 ± 0.01 cm 2 /s for krypton and 0.052 ± 0.006 cm 2 /s for xenon.
The hyperfine relaxation of a population difference, produced by optical pumping, between the
F=1 mF=0 and
F=2 mF=0 energy levels of the ground state of
Rb87, has been studied in cells containing neon, argon, helium, or krypton as a buffer gas. The relaxation times
T1 and
T2 have been measured as a function of the rubidium vapor pressure in the cell. The relaxation rate due to spin exchange in
Rb87-
Rb87 collisions has been found equal to 65 ${\mathrm{sec}}^{\ensuremath{-}1}$ at 44\ifmmode^\circ\else\textdegree\fi{}C, and the diffusion coefficients of
Rb87 atoms in He, Ne, and Ar evaluated as 0.6, 0.31, and 0.22
cm2 ${\mathrm{sec}}^{\ensuremath{-}1}$, respectively. The cross section for
Rb87-Ne and
Rb87-Ar collisions are found to be 1.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$
cm2 and 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$
cm2. These values are in general agreement with values previously obtained by other methods. The extrapolated values of
T21 for zero vapor pressure of rubidium are 185, 237, and 318 ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne, He, or Ar, respectively. Relaxations by the pumping light or by the magnetic field inhomogeneities are also discussed.
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.
A new optical method for studying the spin relaxation of optically aligned rubidium vapor is described. In this method, the pumping radiation, consisting of circularly polarized
D1 resonance radiation, is suddenly shut off and then turned on again after a known time interval. The relaxation which takes place during the interval of darkness causes the vapor to become more opaque to the pumping radiation at a rate which is determined by the relaxation time. A large degree of alignment, as well as a relaxation time of about 80 milliseconds, were observed in a closed-off evacuated cylindrical glass cell completely lined, except for
2001 of the wall area, with a thin film of tetracontane (
C40H82). The variation of relaxation time with buffer gas pressure was studied in this cell and in an unlined glass cell. From the observations with the unlined cell, diffusion coefficients for rubidium in neon and argon of 0.31
cm2/sec and 0.24
cm2/sec, respectively, can be deduced. Observed cross sections for disorientation collisions between aligned ground-state rubidium atoms and neon, argon, krypton, and xenon atoms are 5.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}23}$
cm2, 3.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$
cm2, 5.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$
cm2, and 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}20}$
cm2, respectively. In the evacuated tetracontane-lined cell, the relaxation time decreased by 30% for a tenfold increase in rubidium vapor pressure. An explanation for this relatively weak dependence is suggested. The longest observed relaxation time was approximately 0.4 seconds in a tetracontanelined cell filled with neon to a pressure of 3 cm Hg.