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IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control

A dynamic analysis of the LO noise transfer mechanism in a Rb-cell frequency standard

Massimo Ortolano, N. Beverini, Andrea De Marchi

Published Mar 1, 2000• 3 citations
Publisher

Abstract

Frequency noise of the local oscillator at even harmonics of the modulation frequency is known to contribute to the short-term instability of passive frequency standards. The mechanism by which this noise transfer takes place in Rb-cell standards is described here in a comprehensive approach that includes both signal theory methods and a time-dependent quantum mechanical analysis. The resulting calculated transfer coefficients for the various even harmonics are discussed in relationship with measured coefficients in an actual experiment.

DOI
10.1109/58.827438

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Frequency noise of the local oscillator at even harmonics of the modulation frequency is known to contribute to the short-term instability of passive frequency standards. The mechanism by which this noise transfer takes place in Rb-cell standards is described here in a comprehensive approach that includes both signal theory methods and a time-dependent quantum mechanical analysis. The resulting calculated transfer coefficients for the various even harmonics are discussed in relationship with measured coefficients in an actual experiment.
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.
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.
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 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.
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 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.