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Influence of modulation frequency in rubidium cell frequency standards

C. Audoin, Jacques Viennet, Normand Cyr, Jaques Vanier

Published Feb 1, 1983• 3 citations
OpenAlex

Abstract

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.

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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 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.
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.
Rubidium maser and passive frequency standards performances rely on the efficiency of the optical pumping scheme. When using a semiconductor laser as the pumping source in such experiments, one found that the sharpness of the laser spectrum allows only the excitation of a small class of atomic velocities. The use of a frequency-modulated laser has shown great promise by largely increasing the overall pumping efficiency.1 Broadening of the narrow laser spectrum ensures the contribution of all classes of atomic velocities present in the vapor.2 Different modulation waveforms, amplitudes and frequencies have very important effects in overall optical pumping efficiency. We theoretically evaluate the efficiency of a frequency-modulated laser pumping source by studying deterministic as well as random modulation. Important considerations are obtained regarding the optimal conditions concerning the magnitude and the bandwidth of the modulation signal. Moreover a deterministic modulation must be used to lock the laser frequency by interrogating an atomic cell and synchronously detecting the transmitted intensity. Experiments conducted on a rubidium 87 maser optically pumped with a semiconductor laser confirm the predictions. In fact the oscillation of the maser was only possible with the help of the laser frequency modulation.
We investigate a novel method to suppress the light-shift effect in laser-pumped passive rubidium frequency standards. The reduction of the light-shift due to additional frequency components in the pumping light is studied theoretically and compared to experimental results obtained with a frequency-modulated DBR laser diode as a pumping light source. In this way, a reduction of the light shift by a factor of 55 was successfully demonstrated. Complete cancellation of the light shift can be reached with a suitably adjusted modulation index and frequency.
Rubidium electrodeless lamp is one of the core components of rubidium atomic frequency standard. It plays the role of optical pumping and quantum state preparation, and realizes the particle number inversion between two ground states of rubidium atoms. The RF excitation frequency affects the effective light spectral distribution of rubidium electrodeless lamp, and then determines the pumping efficiency and the limiting frequency stability of rubidium atomic frequency standard. In this paper, the influence of RF excitation frequency on the spectral characteristics of rubidium electrodeless lamp can be optimized based on power compensation. It is found that there is a sensitive dependence between the heating rate and the excitation frequency of the rubidium electrodeless lamp, and the excitation frequency range corresponding to the turning point of the maximum heating rate was given experimentally. When the input power and the bubble wall temperature remain unchanged and the rubidium electrodeless lamp is in the ring-mode state, the spectral characteristics have a depression at the optimum resonance frequency. Therefore, the excitation frequency of the rubidium electrodeless lamp should be properly pulled to 5~9 MHz from the optimum resonant point, which can optimize the spectral characteristics of the rubidium electrodeless lamp and can improve the frequency stability of the rubidium atomic clock.