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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

The Passive Optically Pumped Rb Frequency Standard: the Laser Approach

Jaques Vanier, C. Mandache

Published May 1, 2007• 4 citations
Publisher

Abstract

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.

DOI
10.1109/freq.2007.4319296

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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.
The /sup 87/Rb cell frequency standard, optically pumped by a laser diode, is of great interest in the development of high short-term stability oscillators. We report experiments performed on a rubidium cell prototype aiming at evaluate the transfer of the laser noise to the hyperfine clock transition via the light shift effect, which appears to be the main contribution to the observed short term frequency stability in this kind of standard. Pulsed optical pumping will also be examined in order to strongly reduce the light shift effect and to achieve the theoretical limit never approached up to now despite the strong detected microwave signals.
The paper summarizes the relative advantages and disadvantages of coherent population trapping (CPT) or intensity optical pumping (IOP) for the implementation of a passive atomic frequency standard using the isotope /sup 87/Rb. This paper outlines the basic principles common to both CPT and IOP when using laser optical pumping, and makes explicit their similarities and their differences. This paper describes experimental results obtained in the same cell on the characteristics of the CPT and IOP /sup 87/Rb-hyperfine-resonance line. The measurements showed that the signal contrast is larger in CPT than in IOP for the same resulting line width; the light shift is smaller in CPT than in IOP, and is easier to control; in principle, a passive frequency standard based on CPT has a smaller size than that based on IOP, due to the absence of a microwave cavity. Conclusions on overall expectations for the future of such frequency standards are drawn.
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 ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.
ln recent years, laser pumped Rb atomic clocks have been numerously studied and developed to reduce "light shift" and increase the accuracy and stability of the frequency. Previously, we reoorted on the measurement of the linewidths and S/N of the optical-microwave double resonance signal and the light shift in a Rb atomic clock pumped by a stabilized diode laser. In this paper, the light shift was numerically calculated by using the theory proposed by Cohen-Tannoudji & Barrat. Furthermore, contributions of the laser power and frequency detuning to the light shift were also estimated to attain the microwave frequency stability as high as 10^<-12>.