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Physical Review A

Resonance broadening of Hanle-effect signals in rubidium

Alan C. Gallagher, E L Lewis

Published Jul 1, 1974• 37 citations
Publisher

Abstract

We have measured the broadening of ${\mathrm{Rb}}^{87}$ level-crossing signals due to collisions with ${\mathrm{Rb}}^{85}$. The depolarization or broadening rates for the $5^{2}P_{\frac{1}{2}}$ state orientation, the $5^{2}P_{\frac{3}{2}}$ state orientation and alignment, and the $5^{2}P_{\frac{3}{2}}$ state 58-G crossing were measured. Theoretical resonance-broadening depolarization rates for the electronic angular momentum, due to Carrington, Stacey, and Cooper, have been incorporated into calculations of the Hanle-effect signals in the presence of nuclear-spin coupling. The experimental broadening rates are corrected for a minor amount of coherence narrowing. The measured broadening rate for the three $5^{2}P_{\frac{3}{2}}$ state level-crossing signals are in 20% agreement with the theory. The measured $5^{2}P_{\frac{1}{2}}$ state broadening rate exceeds the theoretical by about a factor of 2. This discrepancy may be due to the action of the hyperfine interaction during these unusually long duration collisions. The natural lifetimes of the $5^{2}P_{\frac{3}{2}}$ and $5^{2}P_{\frac{1}{2}}$ states are determined from the low-density linewidth to be 27.0 \ifmmode\pm\else\textpm\fi{} 0.5 and 29.4 \ifmmode\pm\else\textpm\fi{} 0.7 nsec, respectively.

DOI
10.1103/physreva.10.231

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Hanle-effect measurements yield values for the collisional depolarization rates of $^{2}P_{\frac{1}{2}}$ excited atomic states that are about three times too small unless one explicitly includes the effects of nuclear spin. The broadening also becomes a nonlinear function of foreign-gas pressure. We present experimental evidence for nuclear-spin effects on pressure-broadened Hanle-effect signals of ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ in helium.

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A Hanle experiment has been used to determine the following radiative lifetimes (in nsec) of rubidium: ${\mathrm{\ensuremath{\tau}}}_{6\mathit{D}3/2}$=298\ifmmode\pm\else\textpm\fi{}8, ${\mathrm{\ensuremath{\tau}}}_{7\mathit{D}3/2}$=345\ifmmode\pm\else\textpm\fi{}9, ${\mathrm{\ensuremath{\tau}}}_{8\mathit{D}3/2}$=586\ifmmode\pm\else\textpm\fi{}15, and ${\mathrm{\ensuremath{\tau}}}_{9\mathit{D}3/2}$=638\ifmmode\pm\else\textpm\fi{}17. These data were taken at a temperature of 293 K and are not corrected for effects due to blackbody radiation. The effect of the hyperfine interaction on the Hanle signal is discussed in detail for an excited state of arbitrary angular momentum.

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Hyperfine structure and lifetime measurements of the second-excited D states of rubidium and cesium by cascade fluorescence spectroscopy

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The hyperfine structure of the second-excited $D$ states of $^{85}\mathrm{Rb}$, $^{85}\mathrm{Rb}$, and $^{133}\mathrm{Cs}$ has been measured by the method of cascade-radio-frequency spectroscopy and cascade-level crossing. The sign of the magnetic-dipole coupling constant $A$ is determined by the method of cascade-decoupling and cascade-radio-frequency spectroscopy with narrow-band excitation. Lifetimes $\ensuremath{\tau}$ of some of these states are measured by the cascade-Hanle effect. We find that for $^{87}\mathrm{Rb}$, $A(5^{2}D_{\frac{3}{2}})=14.43\ifmmode\pm\else\textpm\fi{}0.23$ MHz, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}7.44\ifmmode\pm\else\textpm\fi{}0.10$ MHz, $\ensuremath{\tau}(5^{2}D_{\frac{3}{2}})=205\ifmmode\pm\else\textpm\fi{}40$ nsec; for $^{85}\mathrm{Rb}$, $A(5^{2}D_{\frac{3}{2}})=4.18\ifmmode\pm\else\textpm\fi{}0.20$ MHz, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}2.12\ifmmode\pm\else\textpm\fi{}0.20$ MHz; for $^{133}\mathrm{Cs}$, $A(6^{2}D_{\frac{3}{2}})=16.30\ifmmode\pm\else\textpm\fi{}0.15$ MHz, $A(6^{2}D_{\frac{5}{2}})=\ensuremath{-}3.6\ifmmode\pm\else\textpm\fi{}1.0$ MHz, $\ensuremath{\tau}(6^{2}D_{\frac{3}{2}})=57\ifmmode\pm\else\textpm\fi{}15$ nsec.

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Resonant Broadening of Double-Resonance and Level-Crossing Signals: Application to the P13 State in Mercury

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A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the $6^{3}P_{1}$ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.

Physical Review•May 5, 1968•78 citations

Resonant Collision Broadening of the (6s26p7s)P13∘ State in Lead

W. Happer, E. B. Saloman

Orientation and alignment depolarization cross sections have been measured for the $(6{s}^{2}6p7s){^{3}P_{1}}^{\ensuremath{\circ}}$ excited state of lead. The cross sections are characteristic of resonance collision broadening; ${\ensuremath{\sigma}}_{\mathrm{al}}=7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$ for ${v}_{\mathrm{rel}}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ cm/sec. The ratio of orientation broadening to alignment broadening was found to be $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}=1.21(5)$. Expressions are derived for the signal shapes in Hanle-effect, optical-double-resonance, and light-beat experiments that show which components of the signals depend on orientation and alignment relaxation times, respectively.

Physical Review•Aug 5, 1967•68 citations

Level-Crossing Spectroscopy in 7S2 Thallium. I. Studies of Coherence-Narrowing, Collision-Broadening, and Buffer-Gas Effects

Jin-Yuan Hsieh, James C. Baird

The lifetime, coherence narrowing, and collision broadening of the $7^{2}S_{\frac{1}{2}}$ excited state of atomic thallium has been studied by the technique of zero-field level-crossing spectroscopy. The lifetime of the $7^{2}S_{\frac{1}{2}}$ state is determined to be 7.55 (0.08) nsec. The full coherence-narrowing effect gave a branching ratio, from $F=0$ of $7^{2}S_{\frac{1}{2}}$ to the ground state, of 43%. The cross section for thallium-thallium resonance-broadening collisions is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{5.38(0.49)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$ ${\mathrm{cm}}^{2}$. The effect of 426-torr helium on the thallium lifetime, coherence narrowing, and resonance broadening was also investigated. From the low-thallium-density region the cross section for helium depolarization of the thallium $7^{2}S$ state is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{H}\mathrm{e}}\ensuremath{\cong}\frac{7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}}{\overline{v}}$ ${\mathrm{cm}}^{2}$. There is also indication of a buildup of population in the metastable $6^{2}P_{\frac{3}{2}}$ thallium state. From the data, the cross section for the process $\mathrm{Tl}(6^{2}P_{\frac{3}{2}})\ensuremath{\rightarrow}\mathrm{Tl}(6^{2}P_{\frac{1}{2}})$ by helium collisions is $\ensuremath{\sigma}\ensuremath{\simeq}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ ${\mathrm{cm}}^{2}$. The Tl branching ratio in the presence of helium is 39%. It was also found that the thallium-thallium resonance-broadening cross section is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{4.04(0.32)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$ ${\mathrm{cm}}^{2}$ in the presence of 426 torr of helium. In the presence of 113 torr of He, the resonance-broadening cross section was found to be ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{5.22(0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$ ${\mathrm{cm}}^{2}$. In the case of Ar as the buffer gas, ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{A}\mathrm{r}}=\frac{8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}}{\overline{v}}$ ${\mathrm{cm}}^{2}$.

Physical Review A•Jul 1, 1972•28 citations
We have measured the broadening of Rb87{\mathrm{Rb}}^{87}Rb87 level-crossing signals due to collisions with Rb85{\mathrm{Rb}}^{85}Rb85. The depolarization or broadening rates for the 52P125^{2}P_{\frac{1}{2}}52P21​​ state orientation, the 52P325^{2}P_{\frac{3}{2}}52P23​​ state orientation and alignment, and the 52P325^{2}P_{\frac{3}{2}}52P23​​ state 58-G crossing were measured. Theoretical resonance-broadening depolarization rates for the electronic angular momentum, due to Carrington, Stacey, and Cooper, have been incorporated into calculations of the Hanle-effect signals in the presence of nuclear-spin coupling. The experimental broadening rates are corrected for a minor amount of coherence narrowing. The measured broadening rate for the three 52P325^{2}P_{\frac{3}{2}}52P23​​ state level-crossing signals are in 20% agreement with the theory. The measured 52P125^{2}P_{\frac{1}{2}}52P21​​ state broadening rate exceeds the theoretical by about a factor of 2. This discrepancy may be due to the action of the hyperfine interaction during these unusually long duration collisions. The natural lifetimes of the 52P325^{2}P_{\frac{3}{2}}52P23​​ and 52P125^{2}P_{\frac{1}{2}}52P21​​ states are determined from the low-density linewidth to be 27.0 \ifmmode\pm\else\textpm\fi{} 0.5 and 29.4 \ifmmode\pm\else\textpm\fi{} 0.7 nsec, respectively.
Hanle-effect measurements yield values for the collisional depolarization rates of 2P12^{2}P_{\frac{1}{2}}2P21​​ excited atomic states that are about three times too small unless one explicitly includes the effects of nuclear spin. The broadening also becomes a nonlinear function of foreign-gas pressure. We present experimental evidence for nuclear-spin effects on pressure-broadened Hanle-effect signals of Rb85{\mathrm{Rb}}^{85}Rb85 and Rb87{\mathrm{Rb}}^{87}Rb87 in helium.
A Hanle experiment has been used to determine the following radiative lifetimes (in nsec) of rubidium: ${\mathrm{\ensuremath{\tau}}}_{6\mathit{D}3/2}$=298\ifmmode\pm\else\textpm\fi{}8, ${\mathrm{\ensuremath{\tau}}}_{7\mathit{D}3/2}$=345\ifmmode\pm\else\textpm\fi{}9, ${\mathrm{\ensuremath{\tau}}}_{8\mathit{D}3/2}$=586\ifmmode\pm\else\textpm\fi{}15, and ${\mathrm{\ensuremath{\tau}}}_{9\mathit{D}3/2}$=638\ifmmode\pm\else\textpm\fi{}17. These data were taken at a temperature of 293 K and are not corrected for effects due to blackbody radiation. The effect of the hyperfine interaction on the Hanle signal is discussed in detail for an excited state of arbitrary angular momentum.
The hyperfine structure of the second-excited DDD states of 85Rb^{85}\mathrm{Rb}85Rb, 85Rb^{85}\mathrm{Rb}85Rb, and 133Cs^{133}\mathrm{Cs}133Cs has been measured by the method of cascade-radio-frequency spectroscopy and cascade-level crossing. The sign of the magnetic-dipole coupling constant AAA is determined by the method of cascade-decoupling and cascade-radio-frequency spectroscopy with narrow-band excitation. Lifetimes $\ensuremath{\tau}$ of some of these states are measured by the cascade-Hanle effect. We find that for 87Rb^{87}\mathrm{Rb}87Rb, $A(5^{2}D_{\frac{3}{2}})=14.43\ifmmode\pm\else\textpm\fi{}0.23$ MHz, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}7.44\ifmmode\pm\else\textpm\fi{}0.10$ MHz, $\ensuremath{\tau}(5^{2}D_{\frac{3}{2}})=205\ifmmode\pm\else\textpm\fi{}40$ nsec; for 85Rb^{85}\mathrm{Rb}85Rb, $A(5^{2}D_{\frac{3}{2}})=4.18\ifmmode\pm\else\textpm\fi{}0.20$ MHz, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}2.12\ifmmode\pm\else\textpm\fi{}0.20$ MHz; for 133Cs^{133}\mathrm{Cs}133Cs, $A(6^{2}D_{\frac{3}{2}})=16.30\ifmmode\pm\else\textpm\fi{}0.15$ MHz, $A(6^{2}D_{\frac{5}{2}})=\ensuremath{-}3.6\ifmmode\pm\else\textpm\fi{}1.0$ MHz, $\ensuremath{\tau}(6^{2}D_{\frac{3}{2}})=57\ifmmode\pm\else\textpm\fi{}15$ nsec.
A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the 63P16^{3}P_{1}63P1​ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.
Orientation and alignment depolarization cross sections have been measured for the $(6{s}^{2}6p7s){^{3}P_{1}}^{\ensuremath{\circ}}$ excited state of lead. The cross sections are characteristic of resonance collision broadening; ${\ensuremath{\sigma}}_{\mathrm{al}}=7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2 for ${v}_{\mathrm{rel}}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ cm/sec. The ratio of orientation broadening to alignment broadening was found to be $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}=1.21(5)$. Expressions are derived for the signal shapes in Hanle-effect, optical-double-resonance, and light-beat experiments that show which components of the signals depend on orientation and alignment relaxation times, respectively.
The lifetime, coherence narrowing, and collision broadening of the 72S127^{2}S_{\frac{1}{2}}72S21​​ excited state of atomic thallium has been studied by the technique of zero-field level-crossing spectroscopy. The lifetime of the 72S127^{2}S_{\frac{1}{2}}72S21​​ state is determined to be 7.55 (0.08) nsec. The full coherence-narrowing effect gave a branching ratio, from F=0F=0F=0 of 72S127^{2}S_{\frac{1}{2}}72S21​​ to the ground state, of 43%. The cross section for thallium-thallium resonance-broadening collisions is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{5.38(0.49)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$ cm2{\mathrm{cm}}^{2}cm2. The effect of 426-torr helium on the thallium lifetime, coherence narrowing, and resonance broadening was also investigated. From the low-thallium-density region the cross section for helium depolarization of the thallium 72S7^{2}S72S state is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{H}\mathrm{e}}\ensuremath{\cong}\frac{7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}}{\overline{v}}$ cm2{\mathrm{cm}}^{2}cm2. There is also indication of a buildup of population in the metastable 62P326^{2}P_{\frac{3}{2}}62P23​​ thallium state. From the data, the cross section for the process $\mathrm{Tl}(6^{2}P_{\frac{3}{2}})\ensuremath{\rightarrow}\mathrm{Tl}(6^{2}P_{\frac{1}{2}})$ by helium collisions is $\ensuremath{\sigma}\ensuremath{\simeq}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ cm2{\mathrm{cm}}^{2}cm2. The Tl branching ratio in the presence of helium is 39%. It was also found that the thallium-thallium resonance-broadening cross section is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{4.04(0.32)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$ cm2{\mathrm{cm}}^{2}cm2 in the presence of 426 torr of helium. In the presence of 113 torr of He, the resonance-broadening cross section was found to be ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{5.22(0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$ cm2{\mathrm{cm}}^{2}cm2. In the case of Ar as the buffer gas, ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{A}\mathrm{r}}=\frac{8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}}{\overline{v}}$ cm2{\mathrm{cm}}^{2}cm2.