Some remarks on excited state mixing in optical pumping

The effect of excited-state mixing on the optical pumping of alkali-metal vapors is considered for the case where the energy separation between the $^{2}P_{\frac{1}{2}}$ and $^{2}P_{\frac{3}{2}}$ first excited states is relatively large, allowing the isolation of mixing effects within a particular $J$ level. Two models for the mixing process are proposed, one a random reorientation of the total electronic angular momentum J, and the other a reorientation of J subject to the selection rule $\ensuremath{\Delta}{m}_{J}=0, \ifmmode\pm\else\textpm\fi{}2$. The probabilities for mixing transitions among $J$ -state sublevels have been calculated for an alkali atom of nuclear spin $\frac{3}{2}$ , and can be used to calculate the optical-pumping transition probabilities for a vapor subject to any degree of excited-state mixing. Several possible experiments suggested by these calculations are discussed.The effect of excited-state mixing on the optical pumping of alkali-metal vapors is considered for the case where the energy separation between the $^{2}P_{\frac{1}{2}}$ and $^{2}P_{\frac{3}{2}}$ first excited states is relatively large, allowing the isolation of mixing effects within a particular $J$ level. Two models for the mixing process are proposed, one a random reorientation of the total electronic angular momentum J, and the other a reorientation of J subject to the selection rule $\ensuremath{\Delta}{m}_{J}=0, \ifmmode\pm\else\textpm\fi{}2$. The probabilities for mixing transitions among $J$-state sublevels have been calculated for an alkali atom of nuclear spin $\frac{3}{2}$, and can be used to calculate the optical-pumping transition probabilities for a vapor subject to any degree of excited-state mixing. Several possible experiments suggested by these calculations are discussed.

Physical ReviewAug 5, 196661 citations

A Theoretical Study of Double Resonance Optical Pumping

Heung‐Ryoul Noh, Han-Seb Moon

Proceedings of the Optical Society of Korea ConferenceJan 1, 20090 citations

Optical Pumping in Four-Wave Mixing.

Geoffrey L. Rogers

Jan 1, 19920 citations

Forward gain suppression of optically pumped stimulated emissions due to self-induced wave-mixing interference during a pump pulse

W. R. Garrett

Theoretical and experimental presentations are given of a drastic suppression, during the interval of the excitation pulse, of forward-directed optically pumped stimulated emission from a two-photon resonantly excited state to a lower state which is also coupled to the ground state. The effect is caused by a self-induced interference from the difference-frequency mixing field that is generated during the time that the excitation fields are present. Several other implications of this effect are given and some puzzling observations in other studies are noted and clarified.Theoretical and experimental presentations are given of a drastic suppression, during the interval of the excitation pulse, of forward-directed optically pumped stimulated emission from a two-photon resonantly excited state to a lower state which is also coupled to the ground state. The effect is caused by a self-induced interference from the difference-frequency mixing field that is generated during the time that the excitation fields are present. Several other implications of this effect are given and some puzzling observations in other studies are noted and clarified.

Physical Review LettersJun 28, 199338 citations

Cross Sections for Excited-State Mixing in Cesium-Noble-Gas Collisions from D2 Optical Pumping

Jochen Fricke, J. Haas, E. Lüscher +1 more

Cross sections for random collisional reorientation of J within the sublevels of the $6^{2}P_{\frac{3}{2}}$ excited state of cesium have been measured using the ${D}_{2}$ optical-pumping technique. The measured cross sections ${{\ensuremath{\sigma}}_{M}}^{2}$ are: Cs-He (3.2\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ , Cs-Ne (2.9\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ , Cs-Ar (6.0\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ , Cs-Kr (9.2\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ , Cs-Xe (11.3\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ . Simplified equations for ${\mathrm{D}}_{1}$ and ${\mathrm{D}}_{2}$ pumping with zero, partial, and complete excited-state mixing are derived for a hypothetical alkali atom with zero nuclear spin. The calculations are extended to cesium atoms with nuclear spin $\frac{7}{2}$ pumped by ${\ensuremath{\sigma}}^{+}$ ${\mathrm{D}}_{2}$ radiation. The equilibrium value ${〈{S}_{z}〉}_{0}$ and the time dependence $〈{S}_{z}(t)〉$ of the electronic spin polarization are computed for various degrees of excited-state mixing. $〈{S}_{z}(t)〉$ is found to be nearly single-exponential in the zero- and the complete-mixing cases, but shows a distinct double-exponential behavior in the intermediate region. ${〈{S}_{z}〉}_{0}$ is shown to be dependent on the degree of mixing, and to change sign as the degree of mixing increases. Measurements were performed with a new transmission technique by passing a separate ${\ensuremath{\sigma}}^{+}$-polarized ${\mathrm{D}}_{2}$ pumping beam and an alternately ${\ensuremath{\sigma}}^{+}$- and ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized ${\mathrm{D}}_{1}$ testing beam through the cesium absorption cell. The cross sections for collisionally induced mixing were evaluated by measuring the buffer pressure at which ${〈{S}_{z}〉}_{0}$ passed through zero.Cross sections for random collisional reorientation of J within the sublevels of the $6^{2}P_{\frac{3}{2}}$ excited state of cesium have been measured using the ${D}_{2}$ optical-pumping technique. The measured cross sections ${{\ensuremath{\sigma}}_{M}}^{2}$ are: Cs-He (3.2\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, Cs-Ne (2.9\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, Cs-Ar (6.0\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, Cs-Kr (9.2\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, Cs-Xe (11.3\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$. Simplified equations for ${\mathrm{D}}_{1}$ and ${\mathrm{D}}_{2}$ pumping with zero, partial, and complete excited-state mixing are derived for a hypothetical alkali atom with zero nuclear spin. The calculations are extended to cesium atoms with nuclear spin $\frac{7}{2}$ pumped by ${\ensuremath{\sigma}}^{+}$ ${\mathrm{D}}_{2}$ radiation. The equilibrium value ${〈{S}_{z}〉}_{0}$ and the time dependence $〈{S}_{z}(t)〉$ of the electronic spin polarization are computed for various degrees of excited-state mixing. $〈{S}_{z}(t)〉$ is found to be nearly single-exponential in the zero- and the complete-mixing cases, but shows a distinct double-exponential behavior in the intermediate region. ${〈{S}_{z}〉}_{0}$ is shown to be dependent on the degree of mixing, and to change sign as the degree of mixing increases. Measurements were performed with a new transmission technique by passing a separate ${\ensuremath{\sigma}}^{+}$-polarized ${\mathrm{D}}_{2}$ pumping beam and an alternately ${\ensuremath{\sigma}}^{+}$- and ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized ${\mathrm{D}}_{1}$ testing beam through the cesium absorption cell. The cross sections for collisionally induced mixing were evaluated by measuring the buffer pressure at which ${〈{S}_{z}〉}_{0}$ passed through zero.

Physical ReviewNov 5, 196734 citations

Quantum Theory of Optical Pumping

Claude N. Cohen-Tannoudji

Jan 1, 19610 citations

The effect of excited-state mixing on the optical pumping of alkali-metal vapors is considered for the case where the energy separation between the

^{2}P_{\frac{1}{2}}

and

^{2}P_{\frac{3}{2}}

first excited states is relatively large, allowing the isolation of mixing effects within a particular

J

level. Two models for the mixing process are proposed, one a random reorientation of the total electronic angular momentum J, and the other a reorientation of J subject to the selection rule $\ensuremath{\Delta}{m}_{J}=0, \ifmmode\pm\else\textpm\fi{}2$. The probabilities for mixing transitions among

J

-state sublevels have been calculated for an alkali atom of nuclear spin

\frac{3}{2}

, and can be used to calculate the optical-pumping transition probabilities for a vapor subject to any degree of excited-state mixing. Several possible experiments suggested by these calculations are discussed.

Cross sections for random collisional reorientation of J within the sublevels of the

6^{2}P_{\frac{3}{2}}

excited state of cesium have been measured using the

{D}_{2}

optical-pumping technique. The measured cross sections ${{\ensuremath{\sigma}}_{M}}^{2}$ are: Cs-He (3.2\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$

{\mathrm{cm}}^{2}

, Cs-Ne (2.9\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$

{\mathrm{cm}}^{2}

, Cs-Ar (6.0\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$

{\mathrm{cm}}^{2}

, Cs-Kr (9.2\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$

{\mathrm{cm}}^{2}

, Cs-Xe (11.3\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$

{\mathrm{cm}}^{2}

. Simplified equations for

{\mathrm{D}}_{1}

and

{\mathrm{D}}_{2}

pumping with zero, partial, and complete excited-state mixing are derived for a hypothetical alkali atom with zero nuclear spin. The calculations are extended to cesium atoms with nuclear spin

\frac{7}{2}

pumped by ${\ensuremath{\sigma}}^{+}$

{\mathrm{D}}_{2}

radiation. The equilibrium value

{〈{S}_{z}〉}_{0}

and the time dependence

〈{S}_{z}(t)〉

of the electronic spin polarization are computed for various degrees of excited-state mixing.

〈{S}_{z}(t)〉

is found to be nearly single-exponential in the zero- and the complete-mixing cases, but shows a distinct double-exponential behavior in the intermediate region.

{〈{S}_{z}〉}_{0}

is shown to be dependent on the degree of mixing, and to change sign as the degree of mixing increases. Measurements were performed with a new transmission technique by passing a separate ${\ensuremath{\sigma}}^{+}$-polarized

{\mathrm{D}}_{2}

pumping beam and an alternately ${\ensuremath{\sigma}}^{+}$- and ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized

{\mathrm{D}}_{1}

testing beam through the cesium absorption cell. The cross sections for collisionally induced mixing were evaluated by measuring the buffer pressure at which

{〈{S}_{z}〉}_{0}

passed through zero.