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Physical Review

Spin Exchange in a Cesium-Electron System

L. C. Balling, F. M. Pipkin

Published Oct 5, 1964• 31 citations
Publisher

Abstract

A spin-exchange optical pumping experiment to study collisions between cesium atoms and quasifree electrons is reported. In this experiment, electrons in a weak magnetic field were polarized through spin-exchange collisions with optically pumped cesium atoms. The cesium-electron collisions were the principal source of the electron-resonance linewidth, and they also gave rise to a shift in the center frequency of the electron resonance. The magnitudes of the linewidth and frequency shift depend upon the two-body scattering amplitude for elastic collisions, the cesium polarization, and the cesium density. From measurements of the electron linewidth and the frequency shift, a value is derived for the electron-cesium spin-flip cross section. The spin-flip cross section at 20\ifmmode^\circ\else\textdegree\fi{}C is found to be approximately 3.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. The expressions for the linewidth and frequency shift due to spin-exchange collisions of electrons with alkali-metal atoms are generalized to cover the case where there is a spin-orbit interaction between the electron-alkali-metal-atom systems.

DOI
10.1103/physrev.136.a46

Related papers

Sodium-Electron Spin-Exchange Collisions

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A spin-exchange optical pumping experiment to study collisions between sodium atoms and free electrons is reported. In this experiment, electrons in a weak magnetic field were polarized by spin-exchange collisions with optically pumped sodium atoms. The sodium-electron collisions were the principal source of the electron resonance linewidth, and they also produced a shift in the electron resonance frequency. The magnitudes of the linewidth and the frequency shift depend upon the scattering amplitude for sodium-electron collisions, the sodium polarization, and the sodium atom density. The ratio of the frequency shift to the linewidth was 0.03. The sodium polarization was approximately 30%. The electron resonance frequency was lower when the sodium polarization was positive. The measurements of the electron linewidth and the frequency shift agree with theoretical values of the linewidth and frequency shift obtained from the sodium-electron scattering phase shifts which have been recently calculated by Garrett.

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Frequency Shifts in Spin-Exchange Optical Pumping Experiments

L. C. Balling, R. J. Hanson, F. M. Pipkin

A theory is derived to predict the density matrices describing two atoms after a spin-exchange collision from the density matrices before the collision and the scattering amplitude for binary collisions. This theory is then applied to a system of quasifree electrons interacting with optically pumped rubidium atoms. For calculating the change in the electron density matrix, the ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ are replaced by a fictitious rubidium isotope with no nuclear spin. Expressions are derived for the change in the light transmission when a radiofrequency field is present at the electron frequency. In addition to the linewidth for the electron signal, the spin-exchange theory predicts a frequency shift the magnitude of which depends upon the two-body scattering amplitude, the rubidium polarization and the rubidium density. Experiments performed to test various aspects of the theory are then reported. The measurements were made on a system of quasifree electrons interacting with rubidium atoms. Measurements of the electron linewidth as a function of temperature indicated that spin-exchange collisions dominated the electron relaxation. The predicted frequency shift was measured by observing the electron resonance frequency first with left circularly polarized light and then with right circularly polarized light. For electrons colliding with rubidium atoms the shift is negative when the rubidium polarization is positive and the ratio of the shift to the linewidth is $\frac{\ensuremath{\delta}{\ensuremath{\nu}}_{0}}{\ensuremath{\Delta}\ensuremath{\nu}}=\ensuremath{-}0.025\ifmmode\pm\else\textpm\fi{}0.005$. From the measured values of the shift and the linewidth, a value is derived for the electron-rubidium spin-flip cross section. In one Appendix the replacement of the ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ by the fictitious rubidium isotope with no nuclear spin is justified. In a second Appendix the calculations for the simple electron-rubidium system are generalized and applied to more complicated systems. Results are reported for the change in the density matrix of hydrogen atoms when they collide with polarized electrons, the change in the density matrix of ${\mathrm{Rb}}^{87}$ atoms when they collide with polarized electrons, and the change in the density matrix of hydrogen atoms when they collide with hydrogen atoms.

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Temperature Dependence of the Electron-Rubidium Spin-Exchange Cross Section

Steve J. Davis, L. C. Balling

A spin-exchange optical-pumping experiment to study the temperature dependence of the electron-rubidium spin-exchange cross section is reported. In this experiment, electrons were polarized in a weak magnetic field by spin-exchange collisions with optically pumped Rb atoms. The electron-Rb collisions were the principal source of the electron-spin-resonance linewidth, and they also produced a shift in the resonance frequency. The magnitudes of the linewidth and frequency shift are functions of the electron-Rb-scattering phase shifts. The electron linewidth at fixed Rb density was essentially constant over the temperature range 200-840 \ifmmode^\circ\else\textdegree\fi{}K indicating the spin-exchange cross section is well approximated by a $\frac{1}{v}$ velocity dependence. The ratio of the frequency shift to linewidth was 0.075\ifmmode\pm\else\textpm\fi{}0.005 at 300 \ifmmode^\circ\else\textdegree\fi{}K with an estimated Rb polarization of (20\ifmmode\pm\else\textpm\fi{}10)%, and the ratio was 0.027\ifmmode\pm\else\textpm\fi{}0.007 at 600 \ifmmode^\circ\else\textdegree\fi{}K with a Rb polarization of (10\ifmmode\pm\else\textpm\fi{}5)%.

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Interaction between spin polarized alkali atoms

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Collisions of alkali-metal atoms in the ground state with the electron spin S = 1/2 are accompanied by exchange of electron coordinates between colliding particles, which leads to polarization transfer between them (i.e., to the well-known phenomenon of spin exchange). In addition, along with the polarization transfer from one partner to another, the magnetic resonance lines of colliding atoms are broadened and shifted in spin-exchange collisions. In particular the last two processes depend on the complex spin-exchange cross section. The real part of the cross section determines the so-called "spin-exchange cross section," which is responsible for the broadening of magnetic resonance lines, while the imaginary part determines the shift cross section, which governs the frequency shift of magnetic resonance. In order to describe the spin-exchange process one have to know complex spin-exchange cross sections. Complex spin-exchange cross sections are calculated on the basis of the data on the singlet (X 1 Σ + ) and triplet (a 3 Σ + ) potentials describing the interaction alkali-metal atoms in the ground state. Collisions of alkali-metal atoms Cs, Rb, K, Na in the ground state are considered in the energy interval of 10 −4 −10 −2 au.

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Collisions with Participation of Polarized Cesium and Lithium Alkali Atoms

Victor A. Kartoshkin

Abstract The spin-exchange cross sections and the magnetic resonance frequency shift in collision of lithium and cesium atoms in the ground state are calculated. The calculations are performed based on the data on the singlet ($$X{}^{1}{{\Sigma }^{ + }}$$) and triplet ($$a{}^{3}{{\Sigma }^{ + }}$$) interaction potentials of 7Li 133Cs dimer. The passage from the energy dependences of the real and imaginary parts of the complex spin-exchange cross section to the temperature dependences makes it possible to obtain information on both the broadening and the frequency shift of the magnetic resonance line in collisions of the atoms under study.

Optics and Spectroscopy•Apr 1, 2020•0 citations

Observation of magnetization transfer in spin-exchange collisions of cesium and rubidium atoms

Sergei P. Dmitriev, N. A. Dovator, Victor A. Kartoshkin +1 more

Abstract Spin exchange is one of the effective processes for obtaining spin-polarized atoms. Such mechanism of spin polarization is usually used to transmit and observe the longitudinal (along magnetic field) component magnetization of atoms. However, spin-exchange collisions can also lead to the transfer of the transverse component of magnetization, which occurs when the atoms involved in the collisions are exposed to an alternating resonant magnetic field. This article describes experiments to observe the transmission of transverse magnetization between alkali metal atoms 133Cs and 85Rb in spin-exchange collisions. The calculation of the spin exchange in a mixture of Cs and Rb under magnetic resonance conditions gave a qualitative agreement with the experimental results.

Journal of Physics Conference Series•Nov 1, 2019•1 citation
A spin-exchange optical pumping experiment to study collisions between cesium atoms and quasifree electrons is reported. In this experiment, electrons in a weak magnetic field were polarized through spin-exchange collisions with optically pumped cesium atoms. The cesium-electron collisions were the principal source of the electron-resonance linewidth, and they also gave rise to a shift in the center frequency of the electron resonance. The magnitudes of the linewidth and frequency shift depend upon the two-body scattering amplitude for elastic collisions, the cesium polarization, and the cesium density. From measurements of the electron linewidth and the frequency shift, a value is derived for the electron-cesium spin-flip cross section. The spin-flip cross section at 20\ifmmode^\circ\else\textdegree\fi{}C is found to be approximately 3.5\ifmmode\times\else\texttimes\fi{}10\ensuremath−14{10}^{\ensuremath{-}14}10\ensuremath−14 cm2{\mathrm{cm}}^{2}cm2. The expressions for the linewidth and frequency shift due to spin-exchange collisions of electrons with alkali-metal atoms are generalized to cover the case where there is a spin-orbit interaction between the electron-alkali-metal-atom systems.
A spin-exchange optical pumping experiment to study collisions between sodium atoms and free electrons is reported. In this experiment, electrons in a weak magnetic field were polarized by spin-exchange collisions with optically pumped sodium atoms. The sodium-electron collisions were the principal source of the electron resonance linewidth, and they also produced a shift in the electron resonance frequency. The magnitudes of the linewidth and the frequency shift depend upon the scattering amplitude for sodium-electron collisions, the sodium polarization, and the sodium atom density. The ratio of the frequency shift to the linewidth was 0.03. The sodium polarization was approximately 30%. The electron resonance frequency was lower when the sodium polarization was positive. The measurements of the electron linewidth and the frequency shift agree with theoretical values of the linewidth and frequency shift obtained from the sodium-electron scattering phase shifts which have been recently calculated by Garrett.
A theory is derived to predict the density matrices describing two atoms after a spin-exchange collision from the density matrices before the collision and the scattering amplitude for binary collisions. This theory is then applied to a system of quasifree electrons interacting with optically pumped rubidium atoms. For calculating the change in the electron density matrix, the Rb85{\mathrm{Rb}}^{85}Rb85 and Rb87{\mathrm{Rb}}^{87}Rb87 are replaced by a fictitious rubidium isotope with no nuclear spin. Expressions are derived for the change in the light transmission when a radiofrequency field is present at the electron frequency. In addition to the linewidth for the electron signal, the spin-exchange theory predicts a frequency shift the magnitude of which depends upon the two-body scattering amplitude, the rubidium polarization and the rubidium density. Experiments performed to test various aspects of the theory are then reported. The measurements were made on a system of quasifree electrons interacting with rubidium atoms. Measurements of the electron linewidth as a function of temperature indicated that spin-exchange collisions dominated the electron relaxation. The predicted frequency shift was measured by observing the electron resonance frequency first with left circularly polarized light and then with right circularly polarized light. For electrons colliding with rubidium atoms the shift is negative when the rubidium polarization is positive and the ratio of the shift to the linewidth is $\frac{\ensuremath{\delta}{\ensuremath{\nu}}_{0}}{\ensuremath{\Delta}\ensuremath{\nu}}=\ensuremath{-}0.025\ifmmode\pm\else\textpm\fi{}0.005$. From the measured values of the shift and the linewidth, a value is derived for the electron-rubidium spin-flip cross section. In one Appendix the replacement of the Rb85{\mathrm{Rb}}^{85}Rb85 and Rb87{\mathrm{Rb}}^{87}Rb87 by the fictitious rubidium isotope with no nuclear spin is justified. In a second Appendix the calculations for the simple electron-rubidium system are generalized and applied to more complicated systems. Results are reported for the change in the density matrix of hydrogen atoms when they collide with polarized electrons, the change in the density matrix of Rb87{\mathrm{Rb}}^{87}Rb87 atoms when they collide with polarized electrons, and the change in the density matrix of hydrogen atoms when they collide with hydrogen atoms.
A spin-exchange optical-pumping experiment to study the temperature dependence of the electron-rubidium spin-exchange cross section is reported. In this experiment, electrons were polarized in a weak magnetic field by spin-exchange collisions with optically pumped Rb atoms. The electron-Rb collisions were the principal source of the electron-spin-resonance linewidth, and they also produced a shift in the resonance frequency. The magnitudes of the linewidth and frequency shift are functions of the electron-Rb-scattering phase shifts. The electron linewidth at fixed Rb density was essentially constant over the temperature range 200-840 \ifmmode^\circ\else\textdegree\fi{}K indicating the spin-exchange cross section is well approximated by a 1v\frac{1}{v}v1​ velocity dependence. The ratio of the frequency shift to linewidth was 0.075\ifmmode\pm\else\textpm\fi{}0.005 at 300 \ifmmode^\circ\else\textdegree\fi{}K with an estimated Rb polarization of (20\ifmmode\pm\else\textpm\fi{}10)%, and the ratio was 0.027\ifmmode\pm\else\textpm\fi{}0.007 at 600 \ifmmode^\circ\else\textdegree\fi{}K with a Rb polarization of (10\ifmmode\pm\else\textpm\fi{}5)%.
Collisions of alkali-metal atoms in the ground state with the electron spin S = 1/2 are accompanied by exchange of electron coordinates between colliding particles, which leads to polarization transfer between them (i.e., to the well-known phenomenon of spin exchange). In addition, along with the polarization transfer from one partner to another, the magnetic resonance lines of colliding atoms are broadened and shifted in spin-exchange collisions. In particular the last two processes depend on the complex spin-exchange cross section. The real part of the cross section determines the so-called "spin-exchange cross section," which is responsible for the broadening of magnetic resonance lines, while the imaginary part determines the shift cross section, which governs the frequency shift of magnetic resonance. In order to describe the spin-exchange process one have to know complex spin-exchange cross sections. Complex spin-exchange cross sections are calculated on the basis of the data on the singlet (X 1 Σ + ) and triplet (a 3 Σ + ) potentials describing the interaction alkali-metal atoms in the ground state. Collisions of alkali-metal atoms Cs, Rb, K, Na in the ground state are considered in the energy interval of 10 −4 −10 −2 au.
Abstract The spin-exchange cross sections and the magnetic resonance frequency shift in collision of lithium and cesium atoms in the ground state are calculated. The calculations are performed based on the data on the singlet (X1Σ+X{}^{1}{{\Sigma }^{ + }}X1Σ+) and triplet (a3Σ+a{}^{3}{{\Sigma }^{ + }}a3Σ+) interaction potentials of 7Li 133Cs dimer. The passage from the energy dependences of the real and imaginary parts of the complex spin-exchange cross section to the temperature dependences makes it possible to obtain information on both the broadening and the frequency shift of the magnetic resonance line in collisions of the atoms under study.
Abstract Spin exchange is one of the effective processes for obtaining spin-polarized atoms. Such mechanism of spin polarization is usually used to transmit and observe the longitudinal (along magnetic field) component magnetization of atoms. However, spin-exchange collisions can also lead to the transfer of the transverse component of magnetization, which occurs when the atoms involved in the collisions are exposed to an alternating resonant magnetic field. This article describes experiments to observe the transmission of transverse magnetization between alkali metal atoms 133Cs and 85Rb in spin-exchange collisions. The calculation of the spin exchange in a mixture of Cs and Rb under magnetic resonance conditions gave a qualitative agreement with the experimental results.