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.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.

Physical ReviewFeb 3, 1964131 citations

Spin Relaxation of Optically Pumped Rubidium Atoms in Molecular Buffer Gases

Robert J. McNeal

Short spin relaxation times for rubidium atoms, oriented by optical pumping, have been observed in the presence of benzene, ammonia, and dimethyl ether buffer gases. The disorientation cross sections of these gases in rubidium are obtained from relaxation times measured in mixtures with molecular nitrogen. The partial pressures of the gases were low compared to the nitrogen pressures in the mixtures, and the diffusion coefficient of rubidium in the mixtures was assumed to be the same as in pure nitrogen. The disorientation cross sections at 55°C are 7±1×10—19 cm2 for benzene, 8±2×10—18 cm2 for ammonia, and 3±1×10—18 cm2 for dimethyl ether. The cross section of carbon monoxide has also been obtained from the longer rubidium spin relaxation time in this gas. These measurements, complicated by a slow reaction of carbon monoxide with liquid rubidium, yield a cross section of 1±0.5×10—22 cm2 for carbon monoxide. The cross sections of ammonia, dimethyl ether, and benzene are much larger than cross sections of other molecular buffer gases. A discussion of the relaxation processes in these gases is given. The large cross sections of polar gases with appreciable dipole moments are found to result from an interaction of the rubidium atoms with the electric field of the polar molecules during a collision. Virtual excitation to the p states of the atom by the electric field gives rise to an interaction of the spin of the valence electron with the orbital angular momentum of the p states. The direct contribution of the magnetic field of the moving polar molecule is also considered and found to be small compared to the electric interaction. The large cross section of benzene is assumed to result from a spin exchange interaction with a charge transfer complex of rubidium and benzene formed in very small amounts. If the assumed complex is responsible for the large benzene cross section, the equilibrium constant for its formation can be calculated from an estimate of the spin exchange cross section.Short spin relaxation times for rubidium atoms, oriented by optical pumping, have been observed in the presence of benzene, ammonia, and dimethyl ether buffer gases. The disorientation cross sections of these gases in rubidium are obtained from relaxation times measured in mixtures with molecular nitrogen. The partial pressures of the gases were low compared to the nitrogen pressures in the mixtures, and the diffusion coefficient of rubidium in the mixtures was assumed to be the same as in pure nitrogen. The disorientation cross sections at 55°C are 7±1×10—19 cm2 for benzene, 8±2×10—18 cm2 for ammonia, and 3±1×10—18 cm2 for dimethyl ether. The cross section of carbon monoxide has also been obtained from the longer rubidium spin relaxation time in this gas. These measurements, complicated by a slow reaction of carbon monoxide with liquid rubidium, yield a cross section of 1±0.5×10—22 cm2 for carbon monoxide. The cross sections of ammonia, dimethyl ether, and benzene are much larger than cross sections of other molecular buffer gases. A discussion of the relaxation processes in these gases is given. The large cross sections of polar gases with appreciable dipole moments are found to result from an interaction of the rubidium atoms with the electric field of the polar molecules during a collision. Virtual excitation to the p states of the atom by the electric field gives rise to an interaction of the spin of the valence electron with the orbital angular momentum of the p states. The direct contribution of the magnetic field of the moving polar molecule is also considered and found to be small compared to the electric interaction. The large cross section of benzene is assumed to result from a spin exchange interaction with a charge transfer complex of rubidium and benzene formed in very small amounts. If the assumed complex is responsible for the large benzene cross section, the equilibrium constant for its formation can be calculated from an estimate of the spin exchange cross section.

The Journal of Chemical PhysicsFeb 15, 196421 citations

Determination of the polarizability of the 6 2 P 1/2 state of rubidium

Eugene Simon Polzik, М. П. Чайка

Optics and SpectroscopyJun 1, 19820 citations

Production of highly spin-polarized atomic hydrogen and deuterium by spin-exchange optical pumping

S. G. Redsun, R. J. Knize, G. D. Cates +1 more

We have produced highly spin-polarized atomic hydrogen by spin-exchange optical pumping. A tunable ring dye laser is used to polarize rubidium atoms by optical pumping. The cell containing the rubidium vapor is coated with paraffin in order to reduce spin relaxation due to wall collisions. Hydrogen gas is dissociated in an inductive discharge and flows continuously through the cell, in which the hydrogen atoms are polarized by spin-exchange collisions with the polarized rubidium atoms. Atomic-hydrogen polarization as high as 2〈 ${\mathit{J}}_{\mathit{z}}$ ${\mathrm{〉}}_{\mathrm{H}}$ =0.72(6) has been observed, which is the highest polarization yet produced by this method. However, the rubidium polarization may be limited to this value due to radiation trapping at higher rubidium densities. The spin-relaxation rate of atomic hydrogen on a paraffin-coated cell is also measured and corresponds to about 7600 wall bounces between wall relaxation.We have produced highly spin-polarized atomic hydrogen by spin-exchange optical pumping. A tunable ring dye laser is used to polarize rubidium atoms by optical pumping. The cell containing the rubidium vapor is coated with paraffin in order to reduce spin relaxation due to wall collisions. Hydrogen gas is dissociated in an inductive discharge and flows continuously through the cell, in which the hydrogen atoms are polarized by spin-exchange collisions with the polarized rubidium atoms. Atomic-hydrogen polarization as high as 2〈${\mathit{J}}_{\mathit{z}}$${\mathrm{〉}}_{\mathrm{H}}$=0.72(6) has been observed, which is the highest polarization yet produced by this method. However, the rubidium polarization may be limited to this value due to radiation trapping at higher rubidium densities. The spin-relaxation rate of atomic hydrogen on a paraffin-coated cell is also measured and corresponds to about 7600 wall bounces between wall relaxation.

Physical Review AAug 1, 199035 citations

{\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.

{\mathit{J}}_{\mathit{z}}

{\mathrm{〉}}_{\mathrm{H}}

=0.72(6) has been observed, which is the highest polarization yet produced by this method. However, the rubidium polarization may be limited to this value due to radiation trapping at higher rubidium densities. The spin-relaxation rate of atomic hydrogen on a paraffin-coated cell is also measured and corresponds to about 7600 wall bounces between wall relaxation.