Physical Review A

Nuclear-Spin Effects Are Important in Analyzing Spin-Exchange Experiments

Hyatt M. Gibbs

Published Jan 1, 1971• 5 citations

Abstract

Lambert's proof that the inclusion of nuclear spin does not alter the equation of motion for the electronic polarization is shown to be valid only when the hyperfine interaction is negligible. Usually the hyperfine frequency is much greater than the frequency of spin-exchange collisions; then the effect of the hyperfine interaction between collisions invalidates Lambert's proof. In general, spin exchange with a second depolarized species relaxes the electronic polarization as the sum of two exponentials, as shown by Gibbs and Grosset\^ete.

DOI: 10.1103/physreva.3.500

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Physical Review A

Nuclear-Spin Effects Are Important in Analyzing Spin-Exchange Experiments

Hyatt M. Gibbs

Published Jan 1, 1971• 5 citations

Publisher

Abstract

DOI: 10.1103/physreva.3.500

Related papers

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R. H. Lambert

Physical Review AJun 1, 19705 citations

Evolution of Electron Angular Momentum due to Spin-Exchange Collisions Involving Nuclear Spin

S. B. Crampton

Physical Review AJan 1, 19714 citations

Collisions of spin-polarized atoms and ions in magnetic fields

Wolfgang Jitschin, S. Osimitsch, Hans O. Lutz

Collision experiments employing a preparation and/or an analysis of spin polarization provide a powerful tool to study individual interaction mechanisms. For atoms or ions with nonvanishing nuclear moments the hyperfine interaction before and after the collision may affect the spin polarization and any collision-induced orientation and alignment, thereby substantially reducing experimentally observable effects. This disturbance can be avoided by applying an external magnetic field, as is demonstrated here for the inelastic collision process ${\mathrm{He}}^{+}$ +Na(\ensuremath{\uparrow}) \ensuremath{\rightarrow} ${\mathrm{He}}^{+}$ + ${\mathrm{Na}}^{\mathrm{*}}$ (3p). Easily attainable magnetic field strengths are sufficient to decouple electronic and nuclear spins whereby the figure of merit for both, orientation and alignment, is increased by more than one order of magnitude.Collision experiments employing a preparation and/or an analysis of spin polarization provide a powerful tool to study individual interaction mechanisms. For atoms or ions with nonvanishing nuclear moments the hyperfine interaction before and after the collision may affect the spin polarization and any collision-induced orientation and alignment, thereby substantially reducing experimentally observable effects. This disturbance can be avoided by applying an external magnetic field, as is demonstrated here for the inelastic collision process ${\mathrm{He}}^{+}$+Na(\ensuremath{\uparrow}) \ensuremath{\rightarrow}${\mathrm{He}}^{+}$+${\mathrm{Na}}^{\mathrm{*}}$(3p). Easily attainable magnetic field strengths are sufficient to decouple electronic and nuclear spins whereby the figure of merit for both, orientation and alignment, is increased by more than one order of magnitude.

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Importance of Nuclear-Spin Effects in Extracting Alkali Spin-Exchange Cross Sections from Zeeman Optical-Pumping Signals

Hyatt M. Gibbs

The importance of the nuclear spins in the analysis of alkali spin-exchange experiments employing optical pumping by circularly polarized light and performed in low magnetic fields is demonstrated. Since the exchange interaction is an electronic process, the spin-exchange cross section is expected to be essentially independent of the nuclear spins. However, the hyperfine coupling is sufficient to make the expressions for the signals depend upon the nuclear spins. Failure to include the nuclear-spin effects in the analysis can lead to errors as large as several hundred percent in the deduced cross sections. The signal for general nuclear spin is found for the Franzen-type transient experiment and for the Dehmelt-type steady-state experiment in the limit of low light intensity. The results are quite sensitive to the process assumed for the relaxation of the ground-state populations. The solutions are given for a general process in which randomly oriented disorientation fields interact with the spins of the alkali atom only through the electron spin. The steady-state-signal expression includes the effects of self spin exchange and partial disorientation in the excited state. Only the diagonal elements of the density matrix are included.The importance of the nuclear spins in the analysis of alkali spin-exchange experiments employing optical pumping by circularly polarized light and performed in low magnetic fields is demonstrated. Since the exchange interaction is an electronic process, the spin-exchange cross section is expected to be essentially independent of the nuclear spins. However, the hyperfine coupling is sufficient to make the expressions for the signals depend upon the nuclear spins. Failure to include the nuclear-spin effects in the analysis can lead to errors as large as several hundred percent in the deduced cross sections. The signal for general nuclear spin is found for the Franzen-type transient experiment and for the Dehmelt-type steady-state experiment in the limit of low light intensity. The results are quite sensitive to the process assumed for the relaxation of the ground-state populations. The solutions are given for a general process in which randomly oriented disorientation fields interact with the spins of the alkali atom only through the electron spin. The steady-state-signal expression includes the effects of self spin exchange and partial disorientation in the excited state. Only the diagonal elements of the density matrix are included.

Physical ReviewAug 30, 196536 citations

Spin-Exchange Cross Sections for Rb87 - Rb87 and Rb87 - Cs133 Collisions

Hyatt M. Gibbs, Robert J. Hull

In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for ${\mathrm{Rb}}^{87}$ - ${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{87}$ - ${\mathrm{Cs}}^{133}$ collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ . A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where $T$ is the non-spin-exchange relaxation time and ${T}_{S1}$ and ${T}_{E1}$ are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{87}$-${\mathrm{Cs}}^{133}$ collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where $T$ is the non-spin-exchange relaxation time and ${T}_{S1}$ and ${T}_{E1}$ are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.

Physical ReviewJan 5, 196769 citations

Spin Exchange in Collisions between Atoms

A. E. Glassgold

Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, ${F}_{d}$ and ${F}_{x}$ . All cross sections must be expressible in terms of $|{F}_{d}|$ and $|{F}_{x}|$ , and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, ${F}_{d}$ and ${F}_{x}$. All cross sections must be expressible in terms of $|{F}_{d}|$ and $|{F}_{x}|$, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.

Physical ReviewDec 1, 196331 citations

{\mathrm{He}}^{+}

+Na(\ensuremath{\uparrow}) \ensuremath{\rightarrow}

{\mathrm{He}}^{+}

{\mathrm{Na}}^{\mathrm{*}}

(3p). Easily attainable magnetic field strengths are sufficient to decouple electronic and nuclear spins whereby the figure of merit for both, orientation and alignment, is increased by more than one order of magnitude.

In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for

{\mathrm{Rb}}^{87}

{\mathrm{Rb}}^{87}

and

{\mathrm{Rb}}^{87}

{\mathrm{Cs}}^{133}

collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$

{\mathrm{cm}}^{2}

and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$

{\mathrm{cm}}^{2}

. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where

T

is the non-spin-exchange relaxation time and

{T}_{S1}

and

{T}_{E1}

are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.

{F}_{d}

and

{F}_{x}

. All cross sections must be expressible in terms of

|{F}_{d}|

and

|{F}_{x}|

, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.