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Physical Review

Lifetime of the First Excited Atomic States of Rb87

J. D. Feichtner, Joe H. Gallagher, Masataka Mizushima

Published Dec 5, 1967• 17 citations
Publisher

Abstract

The Hanle effect on the resonance lines of the ${\mathrm{Rb}}^{87}$ atom has been observed. The line shape of the signal for the $5^{2}S_{\frac{1}{2}}\ensuremath{\leftrightarrow}5^{2}P_{\frac{3}{2}}$ is found to be Lorentzian, while that for the $5^{2}S_{\frac{1}{2}}\ensuremath{\leftrightarrow}5^{2}P_{\frac{1}{2}}$ is dispersion-type. The half-width of these lines was observed to be 3.146\ifmmode\pm\else\textpm\fi{}0.13 G and 23.0 G\ifmmode\pm\else\textpm\fi{}5%, respectively. These values yield the lifetime of (2.71\ifmmode\pm\else\textpm\fi{}0.14) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$sec and (3.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$sec for the $5^{2}P_{\frac{3}{2}}$ and $5^{2}P_{\frac{1}{2}}$ states, respectively. The oscillator strengths for the corresponding transitions are found to be 0.673\ifmmode\pm\else\textpm\fi{}0.03 and 0.32\ifmmode\pm\else\textpm\fi{}0.03, respectively. When the temperature of the scattering cell was changed from 0 to 36\ifmmode^\circ\else\textdegree\fi{}C, an apparent increase of the linewidth at higher temperature was observed. This effect has been explained as a magnetic-field-dependent radiative transfer effect at optical depth of the order of the scattering cell dimensions. When the data were analyzed with such an effect included, the reduced Hanle signal showed no temperature dependence of the half-width.

DOI
10.1103/physrev.164.44

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Hanle Effect In The Singlet-2p State Of Helium.

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The oscillator strength for the resonance (11S-21P) transition in atomic helium has been determined from a measurement of the lifetime of the 2^ state.This life time was obtained using a modified zero field level crossing (Hanle) method.The scattering sample was a thermal velocity beam of 2^8 metastable atoms.Resonant 2 micron (218-2^2) radiation is absorbed by the 21S atoms, which are excited to the 2^P state.This state then primarily decays to the ground 1^8 state with the emission of resonance ($84A) radiation.The lifetime of the 21P state was determined from measurements of the magnetic field dependence of the 584Â intensity.This new technique eliminates the problem of constructing a vacuum ultra violet resonance lamp.The measured lifetime t(2 P) is (5.69 ±0.23) x Id"10 sec.The resulting absorption oscillator strength for the resonance transition is 0.270 ±0.011.This oscillator strength agrees with tie theoretical value.

•Jan 1, 1969•0 citations
The Hanle effect on the resonance lines of the Rb87{\mathrm{Rb}}^{87}Rb87 atom has been observed. The line shape of the signal for the 52S12\ensuremath↔52P325^{2}S_{\frac{1}{2}}\ensuremath{\leftrightarrow}5^{2}P_{\frac{3}{2}}52S21​​\ensuremath↔52P23​​ is found to be Lorentzian, while that for the 52S12\ensuremath↔52P125^{2}S_{\frac{1}{2}}\ensuremath{\leftrightarrow}5^{2}P_{\frac{1}{2}}52S21​​\ensuremath↔52P21​​ is dispersion-type. The half-width of these lines was observed to be 3.146\ifmmode\pm\else\textpm\fi{}0.13 G and 23.0 G\ifmmode\pm\else\textpm\fi{}5%, respectively. These values yield the lifetime of (2.71\ifmmode\pm\else\textpm\fi{}0.14) \ifmmode\times\else\texttimes\fi{}10\ensuremath−8{10}^{\ensuremath{-}8}10\ensuremath−8sec and (3.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}10\ensuremath−8{10}^{\ensuremath{-}8}10\ensuremath−8sec for the 52P325^{2}P_{\frac{3}{2}}52P23​​ and 52P125^{2}P_{\frac{1}{2}}52P21​​ states, respectively. The oscillator strengths for the corresponding transitions are found to be 0.673\ifmmode\pm\else\textpm\fi{}0.03 and 0.32\ifmmode\pm\else\textpm\fi{}0.03, respectively. When the temperature of the scattering cell was changed from 0 to 36\ifmmode^\circ\else\textdegree\fi{}C, an apparent increase of the linewidth at higher temperature was observed. This effect has been explained as a magnetic-field-dependent radiative transfer effect at optical depth of the order of the scattering cell dimensions. When the data were analyzed with such an effect included, the reduced Hanle signal showed no temperature dependence of the half-width.
The oscillator strength for the resonance ($1^{1}S\ensuremath{-}2^{1}P$) transition in atomic helium has been determined from a measurement of the lifetime of the 21P2^{1}P21P state. This lifetime was obtained using a modified zero-field level crossing (Hanle) method. The scattering sample was a thermal velocity beam of 21S2^{1}S21S metastable atoms. Resonant 2-\ensuremath{\mu} ($2^{1}S\ensuremath{-}2^{1}P$) radiation is absorbed by the 21S2^{1}S21S atoms, which are excited to the 21P2^{1}P21P state. This state then primarily decays to the ground 11S1^{1}S11S state with the emission of resonance (584 \AA{}) radiation. The lifetime of the 21P2^{1}P21P state was determined from measurements of the magnetic-field dependence of the angular distribution of the 584 \AA{} intensity. This new technique eliminates the problem of constructing a vacuum ultraviolet resonance lamp. The measured lifetime $\ensuremath{\tau} (2^{1}P)$ is (5.63 \ifmmode\pm\else\textpm\fi{} 0.22) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ sec. The resulting absorption oscillator strength for the resonance transition is 0.273 \ifmmode\pm\else\textpm\fi{} 0.011. This oscillator strength agrees with the theoretical value.
The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.
The optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ three-level system and of a $J=0\ensuremath{\rightarrow}1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\ensuremath{\lambda}=5535$ \AA{} and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{{P}_{L}}{\ensuremath{\delta}}$ (PL{P}_{L}PL​; beam power; $\ensuremath{\delta}$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.
The nonlinear Hanle effect is generally considered in the modern literature as a particular case of coherent population trapping (CPT) at degenerate Zeeman sublevels of the ground atomic state. The shape, amplitude, and sign of observed resonances and their dependence on the excitation parameters and observation geometry were investigated theoretically and experimentally in many studies because of the wide range of application of this effect. The sensitivity of Hanle resonances to the experimental conditions increases significantly in cells with antirelaxation coating, because the atomic ensemble retains its coherence after a large number of collisions with the cell walls. In this paper, the main attention is paid to the joint influence of the excitation radiation intensity and spurious magnetic fields on CPT resonances observed in fluorescence. The theoretical description is based on the numerical solution of an algebraic system of equations for density matrix ρ^\hat {\rho }ρ^​ in the formalism of irreducible tensor operators. The parameters relating different polarization moments in each equation are visualized using the modified sparse matrix of the system. It is established by numerical simulation that the shape, width, amplitude, and sign of nonlinear magnetooptical resonances change nonmonotonically with a change in the parameters of the excitation radiation and atomic system. The presented theoretical results are in good agreement with the experimental data obtained under various conditions.
The oscillator strength for the resonance (11S-21P) transition in atomic helium has been determined from a measurement of the lifetime of the 2^ state.This life time was obtained using a modified zero field level crossing (Hanle) method.The scattering sample was a thermal velocity beam of 2^8 metastable atoms.Resonant 2 micron (218-2^2) radiation is absorbed by the 21S atoms, which are excited to the 2^P state.This state then primarily decays to the ground 1^8 state with the emission of resonance ($84A) radiation.The lifetime of the 21P state was determined from measurements of the magnetic field dependence of the 584Â intensity.This new technique eliminates the problem of constructing a vacuum ultra violet resonance lamp.The measured lifetime t(2 P) is (5.69 ±0.23) x Id"10 sec.The resulting absorption oscillator strength for the resonance transition is 0.270 ±0.011.This oscillator strength agrees with tie theoretical value.