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Physical Review A

Isolated multipole echoes for study of anisotropic moment collision kernels

John E. Thomas, A. P. Ghosh, M. A. Attili

Published May 1, 1986• 12 citations
Publisher

Abstract

Isolated-multipole-moment photon-echo techniques for atomic collision studies are described and analyzed. The techniques employ three-pulse photon echoes observed in a polarization rotation configuration such that the echo intensity depends on the square of an isolated J=1 multipole moment for which the velocity-changing kernel is diagonal. This scheme is applied to resolve clearly classical and wave-mechanical features of $^{3}\mathrm{P}_{1}$ orientation kernels for $^{174}\mathrm{gas}$ scattering. The diagonality (in the sense to be described) of the one-dimensional kernels chosen for study is discussed physically and derived in detail.

DOI
10.1103/physreva.33.3029

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Effects of Mixing Collisions on Photon Echoes in Gases

C. H. Wang

Effects of electric dipole reorienting collisions on photon echoes are investigated. In an extension of the author's earlier work, a general expression is derived, including terms from binary collisions, for the photonecho dipole moment amplitude. The explicit results are worked out for simple cases such as ${j}_{1}=\frac{1}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=0$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=1$, and ${j}_{1}=\frac{3}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$ transitions. While it is shown that echoes resulting from the above simple transitions will not be depolarized by atomic collisions, photon echoes induced by any other transitions are necessarily depolarized by collisions. In addition, it is possible to show that the general expression for the echo dipole moment can be written as a sum of multipole moments. Only the odd moments contribute to the echoes. The importance of this picture is that collision-induced relaxation of each moment is described by a single time constant---as in the model commonly used for Hanle-effect experiments. As a result, for an echo arising from a ${j}_{1}\ensuremath{\leftrightarrow}{j}_{2}$ transition (${j}_{1}\ensuremath{\ge}{j}_{2}$), there must be $\frac{1}{2}{j}_{1}({j}_{1}+1)$ time constants to describe the collision damping of the echo intensity, ${j}_{1}$ being an integer. The corresponding formula for the half-integer case is $\frac{1}{2}({j}_{2}+\frac{1}{2})({j}_{2}+\frac{3}{2})$.

Physical review. B, Solid state•Jan 1, 1970•20 citations
Isolated-multipole-moment photon-echo techniques for atomic collision studies are described and analyzed. The techniques employ three-pulse photon echoes observed in a polarization rotation configuration such that the echo intensity depends on the square of an isolated J=1 multipole moment for which the velocity-changing kernel is diagonal. This scheme is applied to resolve clearly classical and wave-mechanical features of 3P1^{3}\mathrm{P}_{1}3P1​ orientation kernels for 174gas^{174}\mathrm{gas}174gas scattering. The diagonality (in the sense to be described) of the one-dimensional kernels chosen for study is discussed physically and derived in detail.
We report studies of 174Yb^{174}\mathrm{Yb}174Yb 3P1^{3}P_{1}3P1​-orientation velocity-changing kernels with resolution sufficient to observe both classical and wave mechanical features. The measurements employ photon-echo techniques in which the echo intensity depends on the square of an isolated J=1J=1J=1 multipole moment for which the velocity-changing kernel is diagonal.
We present experiments which study velocity-changing collisions for 174Yb^{174}\mathrm{Yb}174Yb 3P1^{3}P_{1}3P1​ atomic multipoles. New laser polarization-rotation-transient techniques are used to select anisotropic moments for which the velocity-changing collision kernel is diagonal. The results are compared to those obtained for the collisional evolution of the state populations, and demonstrate that wave mechanical effects play an important role in anisotropic-moment scattering.
The collisional scattering of magnetically polarized atoms is of fundamental interest since the scattering process couples translational and internal degrees of freedom.1 Photon-echo techniques have recently been used to study this coupling by preparing active atoms in a superposition of magnetic sublevels and then quantitatively correlating collisional velocity changes with collisional depolarization.2–5 These experiments provide previously unmeasured information about the collision process. For example, they elucidate the differential relaxation experienced by different types of magnetic order (k-multipoles) and clarify the structure of polarization preserving collision kernels.
Coherent transient (echo) techniques have been employed in a high-precision study of collisional velocity thermalization in a sample of (6s6p)3P1(6s6p)^{3}P_{1}(6s6p)3P1​, excited-state, 174Yb^{174}\mathrm{Yb}174Yb atoms perturbed by He or Ar. This work probes the comparative response of aligned and oriented atoms to both depolarizing and to weak, nondepolarizing and/or velocity-changing collisions. By direct inversion of our time-domain echo relaxation data, we also provide a model-independent determination of velocity-change spectra (collision kernels) for nondepolarizing collisions.
Effects of electric dipole reorienting collisions on photon echoes are investigated. In an extension of the author's earlier work, a general expression is derived, including terms from binary collisions, for the photonecho dipole moment amplitude. The explicit results are worked out for simple cases such as ${j}_{1}=\frac{1}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=0$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=1$, and ${j}_{1}=\frac{3}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$ transitions. While it is shown that echoes resulting from the above simple transitions will not be depolarized by atomic collisions, photon echoes induced by any other transitions are necessarily depolarized by collisions. In addition, it is possible to show that the general expression for the echo dipole moment can be written as a sum of multipole moments. Only the odd moments contribute to the echoes. The importance of this picture is that collision-induced relaxation of each moment is described by a single time constant---as in the model commonly used for Hanle-effect experiments. As a result, for an echo arising from a ${j}_{1}\ensuremath{\leftrightarrow}{j}_{2}$ transition (${j}_{1}\ensuremath{\ge}{j}_{2}$), there must be 12j1(j1+1)\frac{1}{2}{j}_{1}({j}_{1}+1)21​j1​(j1​+1) time constants to describe the collision damping of the echo intensity, j1{j}_{1}j1​ being an integer. The corresponding formula for the half-integer case is 12(j2+12)(j2+32)\frac{1}{2}({j}_{2}+\frac{1}{2})({j}_{2}+\frac{3}{2})21​(j2​+21​)(j2​+23​).