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Le Journal de Physique Colloques

MODULATION EFFECTS IN PASSIVE Rb FREQUENCY STANDARDS

P. Thomann, Giovanni Busca

Published Dec 1, 1981• 0 citations
Publisher

Abstract

The lineshape of a microwave resonance is studied theoretically and experimentally in the case of a phase-modulated RF-field and optical detection of the resonance. The calculation allows to optimize the error signal in a Rb frequency standard with respect to the modulation parameters. Sine-wave and square-wave modulation are examined in some detail.

DOI
10.1051/jphyscol:1981822

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The lineshape of a microwave resonance is studied theoretically and experimentally in the case of a phase-modulated RF-field and optical detection of the resonance. The calculation allows to optimize the error signal in a Rb frequency standard with respect to the modulation parameters. Sine-wave and square-wave modulation are examined in some detail.
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.
In this paper we characterized the lineshapes of Rabi resonances for microwave (MW) magnetic field with cesium vapor cell in free space. The relation between resonance lineshapes and phase modulation frequency under different experimental parameters are investigated. Based on the obtained lineshapes, the evaluation of Rabi frequency has been done in free space. Optimal laser intensity and cell temperature are obtained in our experiment, preliminary analysis of the experimental results is reported.
The effect of optical pumping on the lineshapes and the peak values of microwave absorption line is calculated by a density matrix method in the Doppler limit approximation. The calculated double resonance signal consists of two terms. One is proportional to the unperturbed population difference of the optical transition and has a Lorentzian lineshape at weak microwave saturation. In this term the two-photon processes cause broadening of the line. The other is proportional to the population difference of the microwave transition and gives the higher-order dynamic Stark effect. At moderate optical saturation the former term is much greater than the latter. At strong optical saturation the latter term becomes noticeable and lineshape anomaly occurs. The peak values of the double resonance signals are also calculated and compared with an experimental result.
We conducted a theoretical and experimental study of lineshape in modulation transfer spectroscopy for ⁸⁷Rb atoms. When a linearly polarized pump beam, modulated at an angular frequency of Ω, overlaps in parallel with an unmodulated linearly polarized probe beam, combined modulated probe beams are generated via nonlinear interaction with atoms. The detected modulation transfer signals are calculated by numerically solving the complete optical Bloch equations for the ⁸⁷Rb atoms without the use of any phenomenological parameters. We find that the calculated results are in good agreement with experimental results.
We consider the interaction of a three-level system with phase-modulated resonant fields in the \ensuremath{\Lambda} excitation scheme. We treat theoretically the case of a sinusoidal phase modulation, a phase step perturbation, and a stochastic phase modulation. The appearance of a Rabi resonance both in the spectrum of the optical transmitted signal (electromagnetically induced transparency) and in the spectrum of the microwave emission (coherent population trapping maser) is considered in detail. All the theoretical results are compared with the analogous ones reported for the two-level system and with our experimental observations obtained for the case of rubidium in a buffer gas.
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.