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Canadian Journal of Physics

Some Aspects of the Theory of Passive Rubidium Frequency Standards

Gilles Missout, Jacques Vanier

Published Jun 1, 1975• 16 citations
Publisher

Abstract

This paper gives a theory of the signal strength in rubidium vapor frequency standards for various situations encountered in practice. The density matrix formalism is used and the signal strength is given as a function of light intensity, rubidium density, absorption cell length, and applied microwave power. The results obtained are found to be in good agreement with published data.A theory is also developed giving the strength and the phase of the signal as a function of the modulation frequency and of the frequency excursion amplitude. This theory uses a model of a simple harmonic oscillator. The results are similar to those obtained by previous authors using a more complex model.

DOI
10.1139/p75-131

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This paper gives a theory of the signal strength in rubidium vapor frequency standards for various situations encountered in practice. The density matrix formalism is used and the signal strength is given as a function of light intensity, rubidium density, absorption cell length, and applied microwave power. The results obtained are found to be in good agreement with published data.A theory is also developed giving the strength and the phase of the signal as a function of the modulation frequency and of the frequency excursion amplitude. This theory uses a model of a simple harmonic oscillator. The results are similar to those obtained by previous authors using a more complex model.
The error signal which is used to control the frequency of the quartz crystal oscillator of a passive rubidium cell frequency standard is considered. The value of the slope of this signal, for an interrogation frequency close to the atomic transition frequency is calculated and measured for various phase (or frequency) modulation waveforms, and for several values of the modulation frequency. A theoretical analysis is made using a model which applies to a system in which the optical pumping rate, the relaxation rates and the RF field are homogeneous. Results are given for sine-wave phase modulation, square-wave frequency modulation and square-wave phase modulation. The influence of the modulation frequency on the slope of the error signal is specified. It is shown that the modulation frequency can be chosen as large as twice the non-saturated full-width at half-maximum without a drastic loss of the sensitivity to an offset of the interrogation frequency from center line, provided that the power saturation factor and the amplitude of modulation are properly adjusted.
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.
Abstract : Results of calculation and measurements on the light shift and buffer gas shift in passive rubidium frequency standards are reported. The light shift was measured for two configurations: the separated filter and the integrated filter approaches. A phenomenological analysis, which describes well the results obtained, is presented. Measurements of the frequency shifts created by various buffer gases-pure or mixture- are reported. A nonlinear dependence of frequency versus temperature is observed. The results are compared to already published data and a simple analysis using an equation quadratic in temperature is used to explain those results. (Author)
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.
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.
The need for a dynamical analysis of the atomic system response in square wave frequency modulated vapor cell passive frequency standards was recently recognized in connection with the problem of characterizing the mechanism by which frequency noise of the local oscillator (LO) is partially transferred onto the output frequency of the standard. In this paper, waveforms calculated with a dynamic analysis based on the density matrix formalism are reported and successfully compared with experimental ones obtained at NIST in a Rb cell standard. A theoretical description of how the dynamical response affects the noise transfer mechanism is briefly sketched and preliminary conclusions are drawn.