Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.

Jul 1, 199213 citations

Optical Methods of Atomic Orientation and of Magnetic Resonance*

Alfred Kastler

In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.

Journal of the Optical Society of AmericaJun 1, 1957223 citations

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

Influence of Nuclear Spin on Collisional Relaxation within the Alkali-Metal P322 Excited State

John F. Papp, F. A. Franz

The effect of the hyperfine interaction on collisional relaxation among Zeeman sublevels is evaluated for a $J=\frac{3}{2}$ state coupled to nuclear spins of $\frac{3}{2}$ , $\frac{5}{2}$ , and $\frac{7}{2}$ . Standard depolarization experiments, performed on atoms with hyperfine structure, are discussed in terms of relaxation-probability matrices parametrized in terms of the relative collisional-transition probabilities for a nuclear-spin-zero atom. Experimental results involving ${D}_{2}$ optical pumping of $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ are shown to support the approximation of nuclear decoupling in collisional relaxation. The cross sections for electronic collisional relaxation, assuming a van der Waals model for the collisional interaction, are, in units of ${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ , 1.19 ( $^{85}\mathrm{Rb}$ -He), 1.09 ( $^{85}\mathrm{Rb}$ -Ne), 2.44 ( $^{85}\mathrm{Rb}$ -Ar), 1.13 ( $^{87}\mathrm{Rb}$ -He), 1.03 ( $^{87}\mathrm{Rb}$ -Ne), and 2.26 ( $^{87}\mathrm{Rb}$ -Ar).The effect of the hyperfine interaction on collisional relaxation among Zeeman sublevels is evaluated for a $J=\frac{3}{2}$ state coupled to nuclear spins of $\frac{3}{2}$, $\frac{5}{2}$, and $\frac{7}{2}$. Standard depolarization experiments, performed on atoms with hyperfine structure, are discussed in terms of relaxation-probability matrices parametrized in terms of the relative collisional-transition probabilities for a nuclear-spin-zero atom. Experimental results involving ${D}_{2}$ optical pumping of $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ are shown to support the approximation of nuclear decoupling in collisional relaxation. The cross sections for electronic collisional relaxation, assuming a van der Waals model for the collisional interaction, are, in units of ${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$, 1.19 ($^{85}\mathrm{Rb}$-He), 1.09 ($^{85}\mathrm{Rb}$-Ne), 2.44 ($^{85}\mathrm{Rb}$-Ar), 1.13 ($^{87}\mathrm{Rb}$-He), 1.03 ($^{87}\mathrm{Rb}$-Ne), and 2.26 ($^{87}\mathrm{Rb}$-Ar).

Physical Review AApr 1, 197230 citations

Optical Pumping Theory and Experiments

Reuben Benumof

The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrödinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrödinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.

American Journal of PhysicsFeb 1, 196519 citations

Alkali-Rare-Gas van der Waals Molecules and Ground-State Relaxation Processes in Optical Pumping

Claude C. Bouchiat, Marie-Anne Bouchiat

Relaxation experiments performed on alkali atoms polarized in their ground state by optical pumping in the presence of a rare gas have been previously reported and interpreted. It was shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. The previous theoretical analysis, restricted to the longitudinal relaxation, is extended here to relaxation processes involving the transverse components of the electronic polarization and hyperfine "coherences" (elements of the density matrix between different hyperfine states). The effects resulting from the action of a rf field are also examined. The main results of this work, among others, are (a) the prediction of a Zeeman transition-line pressure shift, in some circumstances larger by several orders of magnitude than the one calculated by Herman, and having a very peculiar variation with the rare-gas pressure; (b) a quantitative explanation of the anomalous pressure dependence of the hyperfine transition linewidth discovered by Bender and Cohen; (c) a proposal of a method of detection of rf transitions between states of the alkali---rare-gas molecules by their effect on the relaxation process.Relaxation experiments performed on alkali atoms polarized in their ground state by optical pumping in the presence of a rare gas have been previously reported and interpreted. It was shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. The previous theoretical analysis, restricted to the longitudinal relaxation, is extended here to relaxation processes involving the transverse components of the electronic polarization and hyperfine "coherences" (elements of the density matrix between different hyperfine states). The effects resulting from the action of a rf field are also examined. The main results of this work, among others, are (a) the prediction of a Zeeman transition-line pressure shift, in some circumstances larger by several orders of magnitude than the one calculated by Herman, and having a very peculiar variation with the rare-gas pressure; (b) a quantitative explanation of the anomalous pressure dependence of the hyperfine transition linewidth discovered by Bender and Cohen; (c) a proposal of a method of detection of rf transitions between states of the alkali---rare-gas molecules by their effect on the relaxation process.

Physical Review AOct 1, 197023 citations

The effect of the hyperfine interaction on collisional relaxation among Zeeman sublevels is evaluated for a

J=\frac{3}{2}

state coupled to nuclear spins of

\frac{3}{2}

\frac{5}{2}

, and

\frac{7}{2}

. Standard depolarization experiments, performed on atoms with hyperfine structure, are discussed in terms of relaxation-probability matrices parametrized in terms of the relative collisional-transition probabilities for a nuclear-spin-zero atom. Experimental results involving

{D}_{2}

optical pumping of

^{85}\mathrm{Rb}

and

^{87}\mathrm{Rb}

are shown to support the approximation of nuclear decoupling in collisional relaxation. The cross sections for electronic collisional relaxation, assuming a van der Waals model for the collisional interaction, are, in units of ${10}^{\ensuremath{-}14}$

{\mathrm{cm}}^{2}

, 1.19 (

^{85}\mathrm{Rb}

-He), 1.09 (

^{85}\mathrm{Rb}

-Ne), 2.44 (

^{85}\mathrm{Rb}

-Ar), 1.13 (

^{87}\mathrm{Rb}

-He), 1.03 (

^{87}\mathrm{Rb}

-Ne), and 2.26 (

^{87}\mathrm{Rb}

-Ar).