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Physical Review A

Parametric Frequency Conversion of Resonance Radiation in Optically Pumped Rb87 Vapor

Henry Tang

Published Jun 1, 1973• 3 citations
Publisher

Abstract

This paper reports an investigation of parametric frequency conversion in a vapor of ${\mathrm{Rb}}^{87}$ atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of ${\mathrm{Rb}}^{87}$ by the nonlinear susceptibilities of ${\mathrm{Rb}}^{87}$ vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of ${\mathrm{Rb}}^{87}$ and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of ${\mathrm{Rb}}^{87}$ (6.835 GHz). These sidebands have been directly observed in the spectral profiles of ${\mathrm{Rb}}^{85}$ resonance light which had passed through ${\mathrm{Rb}}^{87}$ vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.

DOI
10.1103/physreva.7.2010

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This paper reports an investigation of parametric frequency conversion in a vapor of Rb87{\mathrm{Rb}}^{87}Rb87 atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of Rb87{\mathrm{Rb}}^{87}Rb87 by the nonlinear susceptibilities of Rb87{\mathrm{Rb}}^{87}Rb87 vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of Rb87{\mathrm{Rb}}^{87}Rb87 and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of Rb87{\mathrm{Rb}}^{87}Rb87 (6.835 GHz). These sidebands have been directly observed in the spectral profiles of Rb85{\mathrm{Rb}}^{85}Rb85 resonance light which had passed through Rb87{\mathrm{Rb}}^{87}Rb87 vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.
We have observed appreciable light modulation at the 6.835-GHz hfs transition frequency of optically pumped Rb87{\mathrm{Rb}}^{87}Rb87 vapor. The frequency separation between the levels involved in the transition exceeded the total spectral width of the initial lamp profile. These observations indicate that persistent doubts as to the feasibility of a transmission-light-modulation experiment under such conditions are groundless.
Parametric frequency conversion of resonance radiation in an optically pumped atomic vapor has been observed for the first time. Conversion efficiencies of ${10}^{\ensuremath{-}3}$ have already been observed in Rb87{\mathrm{Rb}}^{87}Rb87 vapor, and considerably higher conversion efficiencies should be attainable.
A study was made of the dependences of the efficiency of resonant parametric frequency conversion in sodium vapor on the infrared radiation wavelength, vapor density, and detuning from two-photon pump resonance. It was found in this conversion system that for each infrared wave the conversion efficiency had three maxima on tuning the frequency of two-photon pumping over the region of a forbidden transition. The principal maximum was realized for accurate two-photon resonance, and the two other maxima resulted from a rise in the cubic susceptibility close to single-photon sum-frequency resonances. A quantum efficiency of 35% was achieved for a 9.26 μ infrared wave.
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 ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.