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arXiv:1302.0060 · Physical Review A

Collision kernels from velocity-selective optical pumping with magnetic depolarization

Tejal Bhamre, R. Marsland, Iannis K. Kominis, B. H. McGuyer, W. Happer

Published Apr 12, 2013• 6 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate how magnetic depolarization of velocity-selective optical pumping can be used to single out the collisional cusp kernel best describing spin- and velocity-relaxing collisions between potassium atoms and low-pressure helium. The range of pressures and transverse fields used simulate the optical pumping regime pertinent to sodium guidestars employed in adaptive optics. We measure the precession of spin-velocity modes under the application of transverse magnetic fields, simulating the natural configuration of mesospheric sodium optical pumping in the geomagnetic field. We also provide a full theoretical account of the experimental data using the recently developed cusp kernels, which realistically quantify velocity damping collisions in this optical pumping regime. A single cusp kernel with a sharpness $s=13\ifmmode\pm\else\textpm\fi{}2$ provides a global fit to the K-He data.

DOI
10.1103/physreva.87.043412

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We experimentally demonstrate how magnetic depolarization of velocity-selective optical pumping can be used to single out the collisional cusp kernel best describing spin- and velocity-relaxing collisions between potassium atoms and low-pressure helium. The range of pressures and transverse fields used simulate the optical pumping regime pertinent to sodium guidestars employed in adaptive optics. We measure the precession of spin-velocity modes under the application of transverse magnetic fields, simulating the natural configuration of mesospheric sodium optical pumping in the geomagnetic field. We also provide a full theoretical account of the experimental data using the recently developed cusp kernels, which realistically quantify velocity damping collisions in this optical pumping regime. A single cusp kernel with a sharpness s=13\ifmmode±\else\textpm\fi2s=13\ifmmode\pm\else\textpm\fi{}2s=13\ifmmode±\else\textpm\fi2 provides a global fit to the K-He data.
We present efficient theoretical tools for describing the optical pumping of atoms by light propagating at arbitrary directions with respect to an external magnetic field, at buffer-gas pressures that are small enough for velocity-selective optical pumping (VSOP) but large enough to cause substantial collisional relaxation of the velocities and the spin. These are the conditions for the sodium atoms at an altitude of about 100 km that are used as guidestars for adaptive optics in modern ground-based telescopes to correct for aberrations due to atmospheric turbulence. We use spin and velocity relaxation modes to describe the distribution of atoms in spin space (including both populations and coherences) and velocity space. Cusp kernels are used to describe velocity-changing collisions. Optical pumping operators are represented as a sum of poles in the complex velocity plane. Signals simulated with these methods are in excellent agreement with previous experiments and with preliminary experiments in our laboratory.
We report on a quantitative experimental investigation of velocity-changing collisions by means of velocity-selective optical pumping (VSOP). We have calculated the VSOP line shape for an atom with hyperfine structure with the use of two phenomenological kernels for the collision effects: the Keilson-Storer kernel, and a two-term kernel consisting of a broad Keilson-Storer part and a narrower Gaussian component. Corrections were included to account for the finite absorption in the sample and the backward reflection of the pumping beam. The experiments were carried out in sodium vapor with neon as the perturber gas. The D1{D}_{1}D1​ line of sodium was used for optical pumping, and the orientation of the ground state was detected. Free parameters of the theory were determined by fitting the predicted line shapes to experimental curves. The Keilson-Storer kernel proved unsatisfactory, but the two-term kernel reproduced well the observed line shapes over the entire collision profiles in the neon pressure range 0-57 mtorr. In an independent experiment using rapidly modulated VSOP we also measured directly the cross section of velocity-changing collisions: $\ensuremath{\sigma}=(1.13\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2. The large weight obtained for the narrow Gaussian from the fits, as well as the collision cross section which is three times as large as the cross section deduced from tabulated gas kinetic radii, may indicate the presence of collisions with relatively small velocity changes in addition to hard-sphere encounters.
Optical pumping performed with a quasi monochromatic laser beam in an atomic gas introduces a redistribution of Zeeman populations selectively in a single velocity class. In the limit of low pumping intensity the rate theory is valid for a description of velocity-selective optical pumping (V.S.O.P.). Well-defined atomic observables (population, orientation, alignment) and their velocity-correlated collisional relaxation can be studied. Also, a modified scheme for the detection of second order effects of optical pumping allows one to observe light shift induced signals. In particular, V.S.O.P. and its combination with modulated pumping, magnetic depolarization (level crossing), and magnetic resonance techniques provide information about the atomic collision characteristics such as collision rates and kernels for velocity-changing collisions.
Measurements of velocity-changing collision (VCC) kernels are obtained using velocity-selective optical pumping. This is the first measurement of the shape of an elastic VCC kernel over the full thermal range of velocity changes. Since ground-state collisions are studied (5s1/2{\mathit{s}}_{1/2}s1/2​ Rb and He, Ne, Ar, Kr, or Xe), very low buffer-gas pressures can be used, and therefore pressure broadening (dephasing collisions) does not obscure the effects of VCC's. The data are deconvolved to eliminate the effects of the natural linewidth and are then extrapolated with respect to buffer-gas pressure to determine the single-collision limit. For small initial velocities, the measured kernels are consistent with a hard-sphere model for large velocity changes, but differ significantly for small velocity changes. The measured VCC kernels for large initial velocities and large velocity changes do not exhibit this agreement with the hard-sphere kernel. This implies that information about the inter- atomic potential can be obtained from a measurement of VCC kernels. We also show the inadequacy of the much-used Keilson-Storer kernel [J. Appl. Math. 10, 243 (1952)].
We consider optical pumping with a quasi monochromatic tunable light beam, in the low intensity limit where a rate equation regime is obtained The velocity selective optical pumping (V.S.O.P.) introduces a correlation between atomic velocity and internal variables in the ground (or metastable) state. The aim of this article is to evaluate these atomic observables (orientation, alignment, population) as a function of velocity, using a phenomenological description of the relaxation effect of collisions. The V.S.O.P. line shapes, obtained by scanning the pumping beam frequency and using a counterpropagating detection beam with the same frequency, are given in various circumstances. The combination of V.S.O.P. with modulated pumping, magnetic resonance, and level crossing methods is considered; the corresponding line shapes can provide useful information on the relaxation characteristics, such as collision rates and kernels.
We discuss optical pumping when (a) the collision rates of optically pumped atoms with atoms or molecules of the background gas are small enough that individual velocity groups can be preferentially excited by a monochromatic light beam, (b) the collision rates are still fast enough to partially transfer the spin polarization to other velocity groups, and (c) there are nonnegligible losses of polarization due to collisional spin relaxation and Larmor precession. These conditions lead to a strong correlation between the velocity and the spin polarization of the atoms---that is, to ``spin-tagging'' of the different velocity groups. This regime is similar to that of optically pumped 23Na^{23}\mathrm{Na}23Na atoms of the Earth's upper atmosphere, but it is seldom encountered in laboratory experiments. For cooling and trapping experiments, the collision rates with background gas are negligible. For gas-cell experiments the velocity-changing rates are normally so fast compared to spin relaxation or Larmor precession rates that the atoms have a Maxwellian velocity distribution with negligible correlation between the spin polarization and the velocity. We analyze the limiting cases of strong and weak collisions, which change the velocity by a large or small fraction, respectively, of the mean thermal velocity. The Keilson-Storer model [J. Keilson and A. E. Storer, Q. Appl. Math. 10, 243 (1952)] is used to discuss strong collisions, with memory parameter $\ensuremath{\alpha}=0$ and weak collisions with $\ensuremath{\alpha}\ensuremath{\rightarrow}1$. For weak collisions, the physics can be modeled by coupled Fokker-Planck equations, identical to those for forced diffusion in a harmonic-oscillator potential well. In this limit there are solutions analogous to the quantum mechanical coherent states of a harmonic oscillator.