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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Theoretical and experimental study of Rb coherent population trapping atomic clock with phase modulation detection

Yuichiro Yano, Motoaki Hara, Masatoshi Kajita, T. Ido

Published Jul 1, 2017• 0 citations
Publisher

Abstract

We theoretically and experimentally study Coherent Population Trapping (CPT) resonance with phase modulation detection. We measured the time response behavior of CPT resonance using an87Rb gas cell and the D1-line vertical-cavity surface-emitting laser(VCSEL) and calculated the periodic behavior of the density matrix based on eigenvector algorithm. Experiment results are good agreement with calculation results.

DOI
10.1109/fcs.2017.8088866

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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•May 1, 2008•2 citations
We theoretically and experimentally study Coherent Population Trapping (CPT) resonance with phase modulation detection. We measured the time response behavior of CPT resonance using an87Rb gas cell and the D1-line vertical-cavity surface-emitting laser(VCSEL) and calculated the periodic behavior of the density matrix based on eigenvector algorithm. Experiment results are good agreement with calculation results.
A method of detecting Coherent Population Trapping resonance by phase modulation (PM) was studied to expand the frequency locking range (LR). We calculated error signals by density matrix analysis using an eigenvector algorithm and verified the calculated result using an 87Rb vapor cell and a Rb-D1 vertical cavity surface-emitting laser. By comparing the error signal for PM with that for conventional frequency modulation (FM), it was found that the LR with PM is one order of magnitude wider than that with FM without degrading the frequency stability.
We investigated, theoretically and experimentally, the influence of the laser spectrum (in particular the linewidth) on the coherent population trapping (CPT) resonance in87Rb buffer gas cell. We investigated the case of linearly polarized laser fields. The experiments have been performed by using either a current-modulated vertical cavity surface emitting laser (VCSEL) or a phase-locked-laser (PLL) system. A model based on the density matrix approach has been used for the data interpretation. We found that, under experimental conditions suitable for compact clock applications, the fact that VCSELs have a broader spectrum than PLLs does not influence significantly the CPT signal amplitude. We demonstrate that a not negligible role is played by the destructive interference between different CPT excitation channels and propose further investigations to evaluate this contribution with respect to the other causes. Finally, we discuss the application of this scheme in compact atomic clocks.
We report on the performance of the first table-top prototype atomic clock based on coherent population trapping (CPT) resonances with parallel linearly polarized optical fields (lin‖lin configuration). Our apparatus uses a vertical-cavity surface-emitting laser (VCSEL) tuned to the D1 line of 87Rb with the current modulation at the 87Rb hyperfine frequency. We demonstrate cancellation of the first-order light shift by the proper choice of rf modulation power and further improve our prototype clock stability by optimizing the parameters of the microwave lock loop. Operating in these optimal conditions, we measured a short-term fractional frequency stability (Allan deviation) 2×10−11τ−1/2 for observation times 1 s ≤ τ ≤ 20 s. This value is limited by large VCSEL phase noise and environmental temperature fluctuation. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated lin‖lin CPT resonance clock with environmental impacts minimized.
A 85Rb D1-line coherent-population-trapping (CPT) atomic clock with a natural-mixture Rb gas cell is demonstrated. D1-line excitation can generate a larger CPT resonance amplitude, and the choice of 85Rb rather than conventional 87Rb is because of its lower ground-state hyperfine-splitting frequency. The frequency deviation for the D1 line was measured using the same experimental setup as that for the D2 line except for the vertical-cavity surface-emitting laser (VCSEL) wavelength and RF power. In the case of D1-line excitation, the CPT resonance amplitude was 1.5 times that for the D2 line, and the light shift sensitivity was one-half that for the D2 line. The Allan standard deviations for the 85Rb D1 line, estimated from the frequency deviations, are <2.5×10-12 per day. In addition, the required RF is 1.5 GHz and its power is only -8.0 dBm.
A new source of two diode laser beams, spatially separated but optically phase-locked with each other, is used to study the modulation transfer spectroscopy of coherent population trapping resonance (CPT). The spectrum for the (87)Rb D2 line is obtained with narrow linewidth and high signal-to-noise ratio, and analyzed with different experimental parameters. A theoretical analysis of the CPT modulation transfer spectra is deduced from the density matrix equation of motion, and found to be in good agreement with the experimental results.
This paper outlines the features of the85Rb vapor cell atomic clock, the coherent population trapping (CPT) resonance in an85Rb/87Rb mixed vapor cell, and the results of the frequency stabilities of a pilot system. The experiments were performed with a sealed vapor cell containing a natural mixture of Rb isotopes and a buffer gas. Excitation of the CPT resonance was accomplished using a vertical-cavity surface-emitting laser modulated at 1.5, 3.0, 3.4 and 6.8 GHz, which corresponded to the full- and half-ground-state hyperfine frequencies of85Rb and87Rb. The results show that the CPT resonances at both85Rb and87Rb can be observed separately. The frequency stabilities of the output signals for each CPT resonance were ≪ 10x10−12/day for85Rb and ≪ 6x10−12/day for87Rb. In addition, the RF modulation signal power for85Rb was 1.1 dB less than that of87Rb, which was 3.4GHz.