Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

STUDY OF NUTATIONAL RESONANCE IN OPTICALLY PUMPED RUBIDIUM VAPOR

W. Franzen

Published Aug 21, 1961• 0 citations
OpenAlex

Abstract

Abstract : A method for the optical observation of nutational resonance in optically pumped rubidium vapor has been studied both experimentally and theoretically. The method consists of pulsemodulating an rf magnetic field a one of the Zeeman resonance frequencies of the vapor and observing the resulting damped transient modulation in the transmitted light intensity. Of particular interest is the application of this method to a study of the spin relaxation of vapor atoms as influenced by the physical parameters of the system, in the case where the applied steady magnetic field is intense enough to cause individual Zeeman intervals to become noticeably unequal. Both single and double quantum resonances at a wide spectrum of Zeeman transitions of Rb-85 vapor diffusing through neon and helium buffer gases have been observed and identified, and the damping of the transient nutations in light intensity has been recorded under a variety of conditions. (Author)

Related papers

Spin Relaxation of Optically Aligned Rubidium Vapor

W. Franzen

A new optical method for studying the spin relaxation of optically aligned rubidium vapor is described. In this method, the pumping radiation, consisting of circularly polarized ${D}_{1}$ resonance radiation, is suddenly shut off and then turned on again after a known time interval. The relaxation which takes place during the interval of darkness causes the vapor to become more opaque to the pumping radiation at a rate which is determined by the relaxation time. A large degree of alignment, as well as a relaxation time of about 80 milliseconds, were observed in a closed-off evacuated cylindrical glass cell completely lined, except for $\frac{1}{200}$ of the wall area, with a thin film of tetracontane (${\mathrm{C}}_{40}$${\mathrm{H}}_{82}$). The variation of relaxation time with buffer gas pressure was studied in this cell and in an unlined glass cell. From the observations with the unlined cell, diffusion coefficients for rubidium in neon and argon of 0.31 ${\mathrm{cm}}^{2}$/sec and 0.24 ${\mathrm{cm}}^{2}$/sec, respectively, can be deduced. Observed cross sections for disorientation collisions between aligned ground-state rubidium atoms and neon, argon, krypton, and xenon atoms are 5.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}23}$ ${\mathrm{cm}}^{2}$, 3.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ ${\mathrm{cm}}^{2}$, 5.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ ${\mathrm{cm}}^{2}$, and 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}20}$ ${\mathrm{cm}}^{2}$, respectively. In the evacuated tetracontane-lined cell, the relaxation time decreased by 30% for a tenfold increase in rubidium vapor pressure. An explanation for this relatively weak dependence is suggested. The longest observed relaxation time was approximately 0.4 seconds in a tetracontanelined cell filled with neon to a pressure of 3 cm Hg.

Physical Review•Aug 15, 1959•279 citations

OPTICAL PUMPING TRANSIENTS IN RUBIDIUM- 87 AND APPLICATION TO DISORIENTATION CROSS SECTIONS

Richard Marrus, Joseph Yellin

Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical pumping process, both with and without buffel" gas present.The observed transients are single expo .. nentials with no buffer gas present, and double exponentials with buf'fel" gas present over a wide range of pumping intensities and relaxation times.These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin in included a.nd a single relaxation time is assumed.From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section (] eff is deduced for the disorientation of 2 .' .'•.• I'..

•Jun 23, 1965•0 citations

Hyperfine Relaxation of Optically Pumped Rb87 Atoms in Buffer Gases

Maurice Arditi, T. R. Carver

The hyperfine relaxation of a population difference, produced by optical pumping, between the $F=1$ ${m}_{F}=0$ and $F=2$ ${m}_{F}=0$ energy levels of the ground state of ${\mathrm{Rb}}^{87}$, has been studied in cells containing neon, argon, helium, or krypton as a buffer gas. The relaxation times ${T}_{1}$ and ${T}_{2}$ have been measured as a function of the rubidium vapor pressure in the cell. The relaxation rate due to spin exchange in ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ collisions has been found equal to 65 ${\mathrm{sec}}^{\ensuremath{-}1}$ at 44\ifmmode^\circ\else\textdegree\fi{}C, and the diffusion coefficients of ${\mathrm{Rb}}^{87}$ atoms in He, Ne, and Ar evaluated as 0.6, 0.31, and 0.22 ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, respectively. The cross section for ${\mathrm{Rb}}^{87}$-Ne and ${\mathrm{Rb}}^{87}$-Ar collisions are found to be 1.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ ${\mathrm{cm}}^{2}$ and 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ ${\mathrm{cm}}^{2}$. These values are in general agreement with values previously obtained by other methods. The extrapolated values of $\frac{1}{{T}_{2}}$ for zero vapor pressure of rubidium are 185, 237, and 318 ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne, He, or Ar, respectively. Relaxations by the pumping light or by the magnetic field inhomogeneities are also discussed.

Physical Review•Nov 2, 1964•38 citations

Modulation of a Fluorescent Light Beam by an Optically Pumped Vapor Undergoing a Double-Quantum Resonance

W. Franzen, P.B. Newell, Dean S. Edmonds

The high-frequency modulation of a light beam scattered by optically-pumped ${\mathrm{Rb}}^{85}$ vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a ${\ensuremath{\sigma}}^{+}$-polarized ${D}_{1}$ pumping beam and a $\ensuremath{\pi}$-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a $\ensuremath{\sigma}$ polarizer and a ${D}_{2}$ filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of ${\mathrm{Rb}}^{85}$, such a modulation has been observed, and its resonant behavior has been found to agree with theory.

Physical Review•Jun 5, 1968•7 citations

Optical-Pumping Transients in Rubidium-87 and Application to Excited-State Disorientation Cross Sections

Richard Marrus, Joseph Yellin

Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical-pumping process, both with and without buffer gas present. The observed transients are single exponentials with no buffer gas present, and double exponentials with buffer gas present, over a wide range of pumping intensities and relaxation times. These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin is included and a single relaxation time is assumed. From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section ${\ensuremath{\sigma}}_{\mathrm{eff}}$ is deduced for the disorientation of rubidium-87 within the $5^{2}P_{\frac{1}{2}}$ state as a result of its collision with a buffer-gas atom. It is shown that ${\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}_{\frac{1}{2}}+{\ensuremath{\sigma}}_{\frac{3}{2}}$, where ${\ensuremath{\sigma}}_{\frac{1}{2}}$ is the cross section for disorientation within the $5^{2}P_{\frac{1}{2}}$ level, and ${\ensuremath{\sigma}}_{\frac{3}{2}}$ is the cross section for transfer from the $5^{2}P_{\frac{1}{2}}$ level to the $5^{2}P_{\frac{3}{2}}$ level by means of collisions with the buffer gas. On the basis of recently measured values for ${\ensuremath{\sigma}}_{\frac{3}{2}}$, values are deduced for ${\ensuremath{\sigma}}_{\frac{1}{2}}$. The cross sections are: ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{H}\mathrm{e})=1.5(0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$, ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{N}\mathrm{e})=4.4(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$, and ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{A}\mathrm{r})=3.5(1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$. These cross sections are deduced from a model in which the probabilities for ${\mathrm{Rb}}^{87}$ to relax from any hyperfine level to any other are all equal. This model gives a better fit with the observed transients than the assumption that the electron spin only is randomized in the ${P}_{\frac{1}{2}}$ state with the nuclear spin unaffected. We show that accurate relaxation-time measurements can be made by measuring the time constants associated with the double exponentials as a function of light intensity, and extrapolating them to zero light intensity. Moreover, since no shutter is required, relaxation times ${10}^{\ensuremath{-}3}$ sec can be easily observed.

Physical Review•Jan 7, 1966•15 citations

Magnetic resonance line shapes in optical pumping and light-shift experiments in alkali atomic vapors

J. Skalla, Swen Lang, Gerhard Wäckerle

Cs and Rb atomic vapors have been optically pumped in their ground states. The optical/rf-field configuration used allowed for the optical detection of magnetic resonance spectra with subkilohertz resolution by a pump–probe beam technique, in which the free-precessional motion of spins is recorded in the time domain. A six-level system serves as a model to describe the dependence of the observed spectra on the optical frequencies involved. With an intense laser beam applied during the free-precession period, Zeeman light-shift effects are observed. The spatial electric-field distribution of the laser beams and particle diffusion have to be taken into account to let us explain the observed magnetic resonance line shapes adequately.

Journal of the Optical Society of America B•May 1, 1995•13 citations
Abstract : A method for the optical observation of nutational resonance in optically pumped rubidium vapor has been studied both experimentally and theoretically. The method consists of pulsemodulating an rf magnetic field a one of the Zeeman resonance frequencies of the vapor and observing the resulting damped transient modulation in the transmitted light intensity. Of particular interest is the application of this method to a study of the spin relaxation of vapor atoms as influenced by the physical parameters of the system, in the case where the applied steady magnetic field is intense enough to cause individual Zeeman intervals to become noticeably unequal. Both single and double quantum resonances at a wide spectrum of Zeeman transitions of Rb-85 vapor diffusing through neon and helium buffer gases have been observed and identified, and the damping of the transient nutations in light intensity has been recorded under a variety of conditions. (Author)
A new optical method for studying the spin relaxation of optically aligned rubidium vapor is described. In this method, the pumping radiation, consisting of circularly polarized D1{D}_{1}D1​ resonance radiation, is suddenly shut off and then turned on again after a known time interval. The relaxation which takes place during the interval of darkness causes the vapor to become more opaque to the pumping radiation at a rate which is determined by the relaxation time. A large degree of alignment, as well as a relaxation time of about 80 milliseconds, were observed in a closed-off evacuated cylindrical glass cell completely lined, except for 1200\frac{1}{200}2001​ of the wall area, with a thin film of tetracontane (C40{\mathrm{C}}_{40}C40​H82{\mathrm{H}}_{82}H82​). The variation of relaxation time with buffer gas pressure was studied in this cell and in an unlined glass cell. From the observations with the unlined cell, diffusion coefficients for rubidium in neon and argon of 0.31 cm2{\mathrm{cm}}^{2}cm2/sec and 0.24 cm2{\mathrm{cm}}^{2}cm2/sec, respectively, can be deduced. Observed cross sections for disorientation collisions between aligned ground-state rubidium atoms and neon, argon, krypton, and xenon atoms are 5.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}23}$ cm2{\mathrm{cm}}^{2}cm2, 3.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ cm2{\mathrm{cm}}^{2}cm2, 5.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ cm2{\mathrm{cm}}^{2}cm2, and 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}20}$ cm2{\mathrm{cm}}^{2}cm2, respectively. In the evacuated tetracontane-lined cell, the relaxation time decreased by 30% for a tenfold increase in rubidium vapor pressure. An explanation for this relatively weak dependence is suggested. The longest observed relaxation time was approximately 0.4 seconds in a tetracontanelined cell filled with neon to a pressure of 3 cm Hg.
Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical pumping process, both with and without buffel" gas present.The observed transients are single expo .. nentials with no buffer gas present, and double exponentials with buf'fel" gas present over a wide range of pumping intensities and relaxation times.These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin in included a.nd a single relaxation time is assumed.From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section (] eff is deduced for the disorientation of 2 .' .'•.• I'..
The hyperfine relaxation of a population difference, produced by optical pumping, between the F=1F=1F=1 mF=0{m}_{F}=0mF​=0 and F=2F=2F=2 mF=0{m}_{F}=0mF​=0 energy levels of the ground state of Rb87{\mathrm{Rb}}^{87}Rb87, has been studied in cells containing neon, argon, helium, or krypton as a buffer gas. The relaxation times T1{T}_{1}T1​ and T2{T}_{2}T2​ have been measured as a function of the rubidium vapor pressure in the cell. The relaxation rate due to spin exchange in Rb87{\mathrm{Rb}}^{87}Rb87-Rb87{\mathrm{Rb}}^{87}Rb87 collisions has been found equal to 65 ${\mathrm{sec}}^{\ensuremath{-}1}$ at 44\ifmmode^\circ\else\textdegree\fi{}C, and the diffusion coefficients of Rb87{\mathrm{Rb}}^{87}Rb87 atoms in He, Ne, and Ar evaluated as 0.6, 0.31, and 0.22 cm2{\mathrm{cm}}^{2}cm2 ${\mathrm{sec}}^{\ensuremath{-}1}$, respectively. The cross section for Rb87{\mathrm{Rb}}^{87}Rb87-Ne and Rb87{\mathrm{Rb}}^{87}Rb87-Ar collisions are found to be 1.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ cm2{\mathrm{cm}}^{2}cm2 and 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ cm2{\mathrm{cm}}^{2}cm2. These values are in general agreement with values previously obtained by other methods. The extrapolated values of 1T2\frac{1}{{T}_{2}}T2​1​ for zero vapor pressure of rubidium are 185, 237, and 318 ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne, He, or Ar, respectively. Relaxations by the pumping light or by the magnetic field inhomogeneities are also discussed.
The high-frequency modulation of a light beam scattered by optically-pumped Rb85{\mathrm{Rb}}^{85}Rb85 vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a ${\ensuremath{\sigma}}^{+}$-polarized D1{D}_{1}D1​ pumping beam and a $\ensuremath{\pi}$-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a $\ensuremath{\sigma}$ polarizer and a D2{D}_{2}D2​ filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of Rb85{\mathrm{Rb}}^{85}Rb85, such a modulation has been observed, and its resonant behavior has been found to agree with theory.
Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical-pumping process, both with and without buffer gas present. The observed transients are single exponentials with no buffer gas present, and double exponentials with buffer gas present, over a wide range of pumping intensities and relaxation times. These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin is included and a single relaxation time is assumed. From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section ${\ensuremath{\sigma}}_{\mathrm{eff}}$ is deduced for the disorientation of rubidium-87 within the 52P125^{2}P_{\frac{1}{2}}52P21​​ state as a result of its collision with a buffer-gas atom. It is shown that ${\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}_{\frac{1}{2}}+{\ensuremath{\sigma}}_{\frac{3}{2}}$, where ${\ensuremath{\sigma}}_{\frac{1}{2}}$ is the cross section for disorientation within the 52P125^{2}P_{\frac{1}{2}}52P21​​ level, and ${\ensuremath{\sigma}}_{\frac{3}{2}}$ is the cross section for transfer from the 52P125^{2}P_{\frac{1}{2}}52P21​​ level to the 52P325^{2}P_{\frac{3}{2}}52P23​​ level by means of collisions with the buffer gas. On the basis of recently measured values for ${\ensuremath{\sigma}}_{\frac{3}{2}}$, values are deduced for ${\ensuremath{\sigma}}_{\frac{1}{2}}$. The cross sections are: ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{H}\mathrm{e})=1.5(0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm2{\mathrm{cm}}^{2}cm2, ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{N}\mathrm{e})=4.4(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm2{\mathrm{cm}}^{2}cm2, and ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{A}\mathrm{r})=3.5(1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2. These cross sections are deduced from a model in which the probabilities for Rb87{\mathrm{Rb}}^{87}Rb87 to relax from any hyperfine level to any other are all equal. This model gives a better fit with the observed transients than the assumption that the electron spin only is randomized in the P12{P}_{\frac{1}{2}}P21​​ state with the nuclear spin unaffected. We show that accurate relaxation-time measurements can be made by measuring the time constants associated with the double exponentials as a function of light intensity, and extrapolating them to zero light intensity. Moreover, since no shutter is required, relaxation times ${10}^{\ensuremath{-}3}$ sec can be easily observed.
Cs and Rb atomic vapors have been optically pumped in their ground states. The optical/rf-field configuration used allowed for the optical detection of magnetic resonance spectra with subkilohertz resolution by a pump–probe beam technique, in which the free-precessional motion of spins is recorded in the time domain. A six-level system serves as a model to describe the dependence of the observed spectra on the optical frequencies involved. With an intense laser beam applied during the free-precession period, Zeeman light-shift effects are observed. The spatial electric-field distribution of the laser beams and particle diffusion have to be taken into account to let us explain the observed magnetic resonance line shapes adequately.