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

Canadian Journal of Physics

Pumping light intensity transmitted through an inhomogeneously broadened line system: application to passive rubidium frequency standards

Pierre Tremblay, Normand Cyr, M. Têtu

Published Dec 1, 1985• 5 citations
Publisher

Abstract

This paper presents a theoretical evaluation of the pumping light intensity transmitted through an inhomogeneously broadened line system submitted to a coherent microwave excitation. A model is developed for the case of rubidium 87 atoms interacting with a buffer gas and optically pumped by all components of the D1 and D2 lines. The light generated by an electrodeless lamp is considered incoherent and the coherent signal is produced in a microwave cavity. The spatial distribution of the light intensity transmitted through the absorption cell is shown to be related to the microwave magnetic-field axial-component distribution. Then the resonance curve obtained with a photodetector is a function of its shape and location. When applied to the case of a passive rubidium frequency standard, this model allows the calculation of the ultimate short-term frequency stability of the device.

DOI
10.1139/p85-260

Related papers

CAVITY OPEBATED IN lIODE "Eoll, Tell AND

Pierre Tremblay, Normand Cyr

Summary This paper presents a theoretical evaluation of the performance of passive Rb frequency standard operated under various modes of microwave excitation such as TEOll, TElll or TElO1. Assuming that the pumping light is generated by an electrodeless lamp and taking into account the inhomogeneity of the atomic system the spatial distribution of the light transmftted through the absorption cell is found. The resonance curve, given by the integral of the light intensity over the photodetector surface as function of microwave excitation frequency, is then calculated. It is shown that the resonance curve pattern depends not only on the light intensity and the microwave power when the atomic system parameters are held constant but also on the area and the location of the photodetector. The ultimate short term frequency stability of a passive rubidium frequency standard is evaluated through its white frequency noise. This noise contribution can be estimated from the resonance curve and the system parameters. It is presented as function of light intensity and microwave power for various photodetectors and for the three modes of microwave excitation considered. These curves show that optimization of the short term frequency stability could be achieved and give insight toward its realization.

•Jan 1, 1984•0 citations

Investigation of Rubidium Hyperfine Structure Frequency Stabilization Mechanisms.

T. McClelland, T. M. Kwon

The linewidth and frequency associated with the ground state hyperfine energy fo Rb 87 has been studied. A stable single mode semiconductor laser is used to optically pump Rb, in order to obtain a highly collimated, monochromatic light source. The laser is stabilized by locking its optical frequency to the Rb absorption line center. The dependence of the hyperfine frequency and resonance linewidth have been measured as a function of temperature, light intensity and microwave power; and a theoretical description of the linewidth vs. temperature data is presented. Keywords: Optical pumping; Rubidium; Frequency standard; Frequency shift; Light shift; Density matrix; Buffer gas; Linewidth; and Magnetic resonance.

•Aug 1, 1984•0 citations

Pulsed optically pumped Rb87 vapor cell frequency standard: A multilevel approach

Salvatore Micalizio, Aldo Godone, Filippo Levi +1 more

We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) $^{87}\mathrm{Rb}$ frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.

Physical Review A•Jan 6, 2009•50 citations

Possible Avenues of Improvement of the Short and Long Term Stability of Optically Pumped Passive Rubidium Frequency Standards

L.-G. Bernier, Anne Brisson, M. Têtu +2 more

The paper describes work done on the Passive Rubidium Frequency Standard in order to identify and possibly improve its frequency stability in the short and long term region. In relation to the short term region, experiments are described which permit the identification of the major sources of noise and measurements are reported. A theoretical model is developed and conclusions are drawn relative to the optimization of the various parameters. In relation to the long term region, earlier work has shown that the power shift created by inhomogeneous broadening in the presence of a buffer gas and light shift could be a cause of instabilities. To avoid that effect we have started experiments on a wall coated cell without buffer gas and we report results on the wall shift and its temperature dependence. Although that type of cell avoids the power shift, it is observed that the temperature dependence of the wall shift is relatively large. These results are discussed in terms of earlier data obtained on rubidium masers.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jan 1, 1980•2 citations

The Passive Optically Pumped Rb Frequency Standard: the Laser Approach

Jaques Vanier, C. Mandache

This paper provides an overview of the efforts accomplished during the last few decades in the attempt of implementing a Rb-cell frequency standard using optical-microwave double resonance and laser optical pumping. The results of a new analysis based on a three-level model are summarized. Pumping rates, line widths, light shifts, cell radiation transmission and resonance signal size relative to background are calculated making use of the coherence property of the pumping laser. The expected frequency stability is calculated. The results obtained by several research groups are reviewed, compared to the analysis, and evaluated in the context of the implementation of a practical frequency standard. It is concluded that compromises must be made between the goal of obtaining a frequency stability close to the shot noise limit and that of minimizing complexity. Two directions that address such compromises are outlined.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•May 1, 2007•4 citations

Modulation transfer and optical Stark effect in a rubidium atomic clock pumped by a semiconductor laser

Minora Hashimoto, Motoichi Ohtsu

Novel spectral line shapes of optical-microwave double resonance with an extremely narrow line width were observed in a rubidium atomic clock pumped by a semiconductor laser. It was confirmed that these novel spectral line shapes of double resonance were due to the modulation-transfer effect. These spectral line shapes were calculated by solving the equation of motion of the density matrix that describes the modulation-transfer process. The calculated results agree with the experimental results. By using the calculated results of the influence of the optical Stark effect on these spectral line shapes, characteristics of the inhomogeneous light shift were evaluated quantitatively for the frequency-modulated microwave. Furthermore, optimum values of modulation parameters were found by computer simulation in order to obtain the highest microwave frequency stability of the atomic clocks. An experiment was carried out employing these optimum parameters, and a short-term frequency stability as high as σy(τ) = 7.9 × 10−13τ−1/2 was obtained, where τ is an integration time of measurement.

Journal of the Optical Society of America B•Oct 1, 1989•27 citations
This paper presents a theoretical evaluation of the pumping light intensity transmitted through an inhomogeneously broadened line system submitted to a coherent microwave excitation. A model is developed for the case of rubidium 87 atoms interacting with a buffer gas and optically pumped by all components of the D1 and D2 lines. The light generated by an electrodeless lamp is considered incoherent and the coherent signal is produced in a microwave cavity. The spatial distribution of the light intensity transmitted through the absorption cell is shown to be related to the microwave magnetic-field axial-component distribution. Then the resonance curve obtained with a photodetector is a function of its shape and location. When applied to the case of a passive rubidium frequency standard, this model allows the calculation of the ultimate short-term frequency stability of the device.
Summary This paper presents a theoretical evaluation of the performance of passive Rb frequency standard operated under various modes of microwave excitation such as TEOll, TElll or TElO1. Assuming that the pumping light is generated by an electrodeless lamp and taking into account the inhomogeneity of the atomic system the spatial distribution of the light transmftted through the absorption cell is found. The resonance curve, given by the integral of the light intensity over the photodetector surface as function of microwave excitation frequency, is then calculated. It is shown that the resonance curve pattern depends not only on the light intensity and the microwave power when the atomic system parameters are held constant but also on the area and the location of the photodetector. The ultimate short term frequency stability of a passive rubidium frequency standard is evaluated through its white frequency noise. This noise contribution can be estimated from the resonance curve and the system parameters. It is presented as function of light intensity and microwave power for various photodetectors and for the three modes of microwave excitation considered. These curves show that optimization of the short term frequency stability could be achieved and give insight toward its realization.
The linewidth and frequency associated with the ground state hyperfine energy fo Rb 87 has been studied. A stable single mode semiconductor laser is used to optically pump Rb, in order to obtain a highly collimated, monochromatic light source. The laser is stabilized by locking its optical frequency to the Rb absorption line center. The dependence of the hyperfine frequency and resonance linewidth have been measured as a function of temperature, light intensity and microwave power; and a theoretical description of the linewidth vs. temperature data is presented. Keywords: Optical pumping; Rubidium; Frequency standard; Frequency shift; Light shift; Density matrix; Buffer gas; Linewidth; and Magnetic resonance.
We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) 87Rb^{87}\mathrm{Rb}87Rb frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.
The paper describes work done on the Passive Rubidium Frequency Standard in order to identify and possibly improve its frequency stability in the short and long term region. In relation to the short term region, experiments are described which permit the identification of the major sources of noise and measurements are reported. A theoretical model is developed and conclusions are drawn relative to the optimization of the various parameters. In relation to the long term region, earlier work has shown that the power shift created by inhomogeneous broadening in the presence of a buffer gas and light shift could be a cause of instabilities. To avoid that effect we have started experiments on a wall coated cell without buffer gas and we report results on the wall shift and its temperature dependence. Although that type of cell avoids the power shift, it is observed that the temperature dependence of the wall shift is relatively large. These results are discussed in terms of earlier data obtained on rubidium masers.
This paper provides an overview of the efforts accomplished during the last few decades in the attempt of implementing a Rb-cell frequency standard using optical-microwave double resonance and laser optical pumping. The results of a new analysis based on a three-level model are summarized. Pumping rates, line widths, light shifts, cell radiation transmission and resonance signal size relative to background are calculated making use of the coherence property of the pumping laser. The expected frequency stability is calculated. The results obtained by several research groups are reviewed, compared to the analysis, and evaluated in the context of the implementation of a practical frequency standard. It is concluded that compromises must be made between the goal of obtaining a frequency stability close to the shot noise limit and that of minimizing complexity. Two directions that address such compromises are outlined.
Novel spectral line shapes of optical-microwave double resonance with an extremely narrow line width were observed in a rubidium atomic clock pumped by a semiconductor laser. It was confirmed that these novel spectral line shapes of double resonance were due to the modulation-transfer effect. These spectral line shapes were calculated by solving the equation of motion of the density matrix that describes the modulation-transfer process. The calculated results agree with the experimental results. By using the calculated results of the influence of the optical Stark effect on these spectral line shapes, characteristics of the inhomogeneous light shift were evaluated quantitatively for the frequency-modulated microwave. Furthermore, optimum values of modulation parameters were found by computer simulation in order to obtain the highest microwave frequency stability of the atomic clocks. An experiment was carried out employing these optimum parameters, and a short-term frequency stability as high as σy(τ) = 7.9 × 10−13τ−1/2 was obtained, where τ is an integration time of measurement.