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Journal of the Optical Society of America B

Modulation transfer and optical Stark effect in a rubidium atomic clock pumped by a semiconductor laser

Minora Hashimoto, Motoichi Ohtsu

Published Oct 1, 1989• 27 citations

Abstract

Novel spectral line shapes of optical-microwave double resonance with an extremely narrow line width were observed in a rubidium atomic clock pumped by a semiconductor laser. It was confirmed that these novel spectral line shapes of double resonance were due to the modulation-transfer effect. These spectral line shapes were calculated by solving the equation of motion of the density matrix that describes the modulation-transfer process. The calculated results agree with the experimental results. By using the calculated results of the influence of the optical Stark effect on these spectral line shapes, characteristics of the inhomogeneous light shift were evaluated quantitatively for the frequency-modulated microwave. Furthermore, optimum values of modulation parameters were found by computer simulation in order to obtain the highest microwave frequency stability of the atomic clocks. An experiment was carried out employing these optimum parameters, and a short-term frequency stability as high as σy(τ) = 7.9 × 10−13τ−1/2 was obtained, where τ is an integration time of measurement.

DOI: 10.1364/josab.6.001777

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ln recent years, laser pumped Rb atomic clocks have been numerously studied and developed to reduce "light shift" and increase the accuracy and stability of the frequency. Previously, we reoorted on the measurement of the linewidths and S/N of the optical-microwave double resonance signal and the light shift in a Rb atomic clock pumped by a stabilized diode laser. In this paper, the light shift was numerically calculated by using the theory proposed by Cohen-Tannoudji & Barrat. Furthermore, contributions of the laser power and frequency detuning to the light shift were also estimated to attain the microwave frequency stability as high as 10^<-12>.

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Novel spectral line shapes of optical-microwave double resonance with an extremely narrow line width were observed in a rubidium atomic clock pumped by a semiconductor laser. It was confirmed that these novel spectral line shapes of double resonance were due to the modulation-transfer effect. These spectral line shapes were calculated by solving the equation of motion of the density matrix that describes the modulation-transfer process. The calculated results agree with the experimental results. By using the calculated results of the influence of the optical Stark effect on these spectral line shapes, characteristics of the inhomogeneous light shift were evaluated quantitatively for the frequency-modulated microwave. Furthermore, optimum values of modulation parameters were found by computer simulation in order to obtain the highest microwave frequency stability of the atomic clocks. An experiment was carried out employing these optimum parameters, and a short-term frequency stability as high as σy(τ) = 7.9 × 10−13τ−1/2 was obtained, where τ is an integration time of measurement.

Precise measurement of the shift (i.e. microwave frequency shift induced by the electric field of the pumping light) in a rubidium atomic clock pumped by a semiconductor laser is discussed. The spectral lineshape of the microwave resonance, which is used as a frequency discriminator for the atomic clock in the optical microwave double resonance experiment, depends strongly on the spatial distribution of the laser beam intensity, laser frequency detuning, and modulation parameters of the microwave frequency. Based on measurements of the deformation of the resonance lineshape, a self-tuning system was built to compensate for the effect of light shift. As a result of controlling the laser frequency with this system, long-term drift of the microwave frequency as low as 6.3*10/sup -13//h was obtained.>

Experiments were carried out to evaluate the performances of a semiconductor laser pumped rubidium (87Rb) atomic clock. Two kinds of Rb gas cells were used and their performances were compared [gas cell A (natural rubidium (87Rb/85Rb =\frac{3}{7}) and buffer gases) and gas cell B (87Rb and buffer gases)]. The highest microwave frequency stabilities were estimated as3.4 \times 10^{-12} \tau^{-1/2}and2.7 \times 10^{-12} \tau^{-1/2}at the optimal gas cell temperatures of 60°C and 48°C for the gas cellsAandB, respectively (τ: integration time). The light shift, i.e., microwave frequency shift induced by laser light, was measured as -0.50 Hz/MHz and -0.11 Hz/MHz for the gas cellsAandBat their optimal operating conditions given above. As an improved experiment by utilizing high temporal coherence of the laser, a novel double resonance spectral line shape with a drastically narrower linewidth was demonstrated. A technique, similar to FM laser spectroscopy, was employed for this purpose by utilizing laser FM sidebands which are induced by microwave frequency modulation and nonlinear susceptibility of three-level87Rb atoms. The minimum linewidth obtained was 20 Hz, which can be used as a sensitive frequency discriminator for an improved87Rb atomic clock.

In order to eliminate the light shifts and to increase the stability of gas-cell atomic clocks using optical pumping of the alkali atoms, the detection of a microwave pulse-induced coherent emission is used as the correction signal to lock a crystal oscillator to the atomic transition. Also, the line width of the O-O hyperfine transition is artificially narrowed by subjecting the atoms in the cell to two phase-coherent microwave pulses. In this case the resonance line has a width characteristic of the pulse-repetition frequency which can be made several times smaller than the natural line width in the cell. Proper timing of the sequence of microwave pulses and light pulses for optical pumping is necessary to conserve phase coherence and to obtain a well-defined Ramsey pattern. Results of the tests on a laboratory model using Rubidium-87 atoms show the elimination of the light shifts and an improvement of the short-term stability of the crystal oscillator by one order of magnitude.

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.

ln recent years, laser pumped Rb atomic clocks have been numerously studied and developed to reduce "light shift" and increase the accuracy and stability of the frequency. Previously, we reoorted on the measurement of the linewidths and S/N of the optical-microwave double resonance signal and the light shift in a Rb atomic clock pumped by a stabilized diode laser. In this paper, the light shift was numerically calculated by using the theory proposed by Cohen-Tannoudji & Barrat. Furthermore, contributions of the laser power and frequency detuning to the light shift were also estimated to attain the microwave frequency stability as high as 10^<-12>.