The influence of the frequency modulation parameters on the stability of CPT based atomic clock.
In recent years, many groups around the world have been actively studying the effect of coherent population trapping (CPT) in alkali metals and the related to its effect of electromagnetically-induced transparency (EIT). The effect of CPT consists in the studied medium atoms falling into the so-called ‘dark’ resonant state when pumped with a bi-chromatic optical field with the frequency difference close to that of the hyperfine splitting. Atoms occupying this state cease to interact with the optical field, leading to observation of EIT. CPT resonances occurring in alkali metal atoms are known for their high quality factor of ~10^8, thus allowing their application as a quantum discriminator in frequency standards and magnetometers. For locking in the frequency of a quartz oscillator to the reference CPT resonance, the frequency difference of the bi-chromatic field around the resonance is modulated and a feed-back system with a lock-in amplifier is used. One of the advantages of this method is the possibility of noise filtering in the measurement system at frequencies not immediately adjacent to the modulation frequency. Given the fact that the noise intensity is reduced as the frequency rises, selection of higher modulation frequency leads to lower noise level in the feedback system, thus improving the device performance. However, higher frequencies introduce a number of effects related to a finite time of excitation and relaxation of the coherent ‘dark state’.
This paper describes an experimental optimization of the feedback system in a 87Rb CPT based clock which employs a small cube glass cell with and without antirelaxation coating. The feedback loop is implemented by superimposing low rate frequency modulation (FM) on the microwave drive signal to the diode laser thereby enabling to probe the atomic vapor using the FM spectroscopy scheme. Classical FM spectroscopy employs only one FM modulated field. The properties of the demodulated signal for this case have been analyzed and measured. However when FM spectroscopy is used in CPT based clocks (where the interacting fields are the side bands of a directly modulated diode laser), each spectral component carries its corresponding FM side bands. The signature of the CPT process on the demodulated signal is consequently different than in the classical case. This difference which may be subtle has nevertheless a profound effect on the sensitivity and SNR of the error signal feeding the feedback loop. This is demonstrated in the experiments we describe here on which yield sets of FM parameters (FM modulation frequency and amplitude) that ensure optimum. Our experimental studies of the optimal FM parameters for CPT resonance formation were conducted on the installation schematically depicted in Fig. 1.
Fig. 1. Diagram of the experimental installation.
The injection current of a single-frequency vertical-cavity semiconductor laser pump was modulated at the frequency of 3.417 GHz generated with a frequency synthesiser Phase Matrix 10 GHz. This led to emergence of two side components in the laser radiation spectrum detuned from the central peak by ± 3.417 GHz. A 10- MHz reference signal was provided by a rubidium atomic clock with relative instability of 10^–12/t. The frequency difference between the side components of the laser radiation corresponded to the frequency of the transition between the levels of hyperfine splitting of the fundamental state of 87Rb. To create a CPT resonance, the frequency difference between the side modes was modulated at a frequency that could be adjusted in the range of 300–2000 Hz, the modulation amplitude was adjusted in the range of 500–3000 Hz . The pumping radiation was then guided into an optical cell filled with 87Rb vapour. The intensity of the laser radiation passed through the cell was registered by a photo-detector with a 100-kHz bandwidth. In order to eliminate any external magnetic field, the optical cell was placed inside a three-layer magnetic shield. Both the pump laser and the optical cell were thermo-stabilised and their temperature instability did not exceed 10–3 °С. The power of the laser radiation entering the optical cell was 50 uW.
For each set of parameters measured by the change of the error signal at 10 Hz offset from the resonance. It was found that the error signal values are normally distributed. The magnitude of the standard deviation of the error signal was used as the amplitude of the noise
The result of this study is obtained according to the sensitivity of the feedback system for different cells. The dependency of the feedback loop sensitivity on modulation parameters for both cells shown in Fig. 2
Fig. 2. Measured feedback system sensitivity for coated and uncoated cells
It was found that despite the large difference in the width of the resonances best stability is achieved for all cells at approximately the same modulation parameters: amplitude and frequency of 1 kHz to 2 kHz. The best stability achieved at the maximum sensitivity of the feedback system is as follows: the coated cell - 3 x 10^-11 ; uncoated cell - 1.5 * 10^-10.
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 D. Radnatarov, S. Khripunov, S. Kobtsev, A. Taichenachev, V. Yudin, M. Basalaev, I. Popkov, V. Andryushkov // Proc. of SPIE – 2016. – Vol. 9763. - 97630A