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Chinese Physics Letters

Dick Effect in a Microwave Frequency Standard Based on Laser-Cooled 113 Cd+ Ions

Jianwei Zhang, K. Miao, Lijun Wang

Published Jan 1, 2015• 13 citations
Publisher

Abstract

The Dick effect is one of the main limits to the frequency stability of a passive frequency standard, especially for the fountain clock and ion clock operated in pulsed mode which require unavoidable dead time during interrogation. Here we measure the phase noise of the interrogation oscillator applied in the microwave frequency standard based on laser-cooled 113 Cd + ions, and analyze the Allan deviation limited by the Dick effect. The results indicate that the Dick effect is one of the key issues for the cadmium ion clock to reach expected frequency stability. This problem can be resolved by interrogating the local oscillator continuously with two ion traps.

DOI
10.1088/0256-307x/32/1/010601

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The Dick effect is one of the main limits to the frequency stability of a passive frequency standard, especially for the fountain clock and ion clock operated in pulsed mode which require unavoidable dead time during interrogation. Here we measure the phase noise of the interrogation oscillator applied in the microwave frequency standard based on laser-cooled 113 Cd + ions, and analyze the Allan deviation limited by the Dick effect. The results indicate that the Dick effect is one of the key issues for the cadmium ion clock to reach expected frequency stability. This problem can be resolved by interrogating the local oscillator continuously with two ion traps.
In the microwave 199 Hg + trapped-ion clock, the frequency instability degradation caused by the Dick effect is unavoidable because of the periodical interrogating field. In this paper, the general expression of the sensitivity function g ( t ) to the frequency fluctuation of the interrogating field with Nπ -pulse ( N is odd) is derived. According to the measured phase noise of the 40.5-GHz microwave synthesizer, the Dick-effect limited Allan deviation of our 199 Hg + trapped-ion clock is worked out. The results indicate that the limited Allan deviations are about and respectively in the linear ion trap and in the two-segment extended linear ion trap under our present experimental parameters.
We present an analysis of the frequency stability degradation of an optical atomic frequency standard which is operated sequentially, and that is caused by the frequency noise of the laser used to interrogate the clock transition. This is an extension to optical frequencies of the 'Dick effect' already studied in atomic microwave frequency standards. It is shown that the simple concept of laser linewidth is not the relevant parameter to estimate the frequency stability degradation. Rather, the details of the laser frequency noise spectral density must be accounted for together with the parameters of the interrogation method. We compute the optical Dick effect in the case of a four pulse Ramsey–Bordé interferometer. We show that it may be minimized by optimizing the time sequence so that only the Fourier frequencies with minimum laser noise are sampled. Finally, we evaluate the degradation which would be obtained with one of our lasers used as an interrogation oscillator. This laser reaches a white noise floor S ν ( f ) = 10 −2 Hz 2 /Hz at a Fourier frequency of 100 Hz. We show that with this particular laser, a relative frequency stability of the order of 10 −16 in a 1 s averaging time can be reached using realistic experimental parameters.
For most pulsed atomic clocks, the Dick effect is one of the main limits to reach its frequency stability limitation due to quantum projection noise. In this paper, we measure the phase noise of the local oscillator in the Ramsey-CPT atomic clock and calculate the Dick effect induced Allan deviation based on a three-level atomic model, which is quite different from typical atomic clocks. We further present a detailed analysis of optimizing the sensitivity function and minimizing the Dick effect by interleaving lock. By optimizing the duty circle of laser pulses, average time during detection and optical intensity of laser beam, the Dick effect induced Allan deviation can be reduced to the level of .
The ion microwave frequency standard is a candidate for the next generation of microwave frequency standard with the potential for very wide applications. The Dick effect and second-order Doppler frequency shift (SODFS) limit the performance of ion microwave frequency standards. The introduction of sympathetic cooling technology can suppress the Dick effect and SODFS and improve the stability and accuracy of the frequency standard. However, the sympathetically cooled ion microwave frequency standard has seldom been studied before. This paper reports a high-performance sympathetically cooled ion microwave frequency standard in a Paul trap. Using laser-cooled 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ as coolant ions, 113Cd+{}^{113}{\mathrm{Cd}}^{+}113Cd+ ion crystal is cooled to below 100 mK and has a coherence lifetime of over 40 s. The short-term frequency stability reached $3.48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/{\ensuremath{\tau}}^{1/2}$, which is comparable to that of the mercury ion frequency standard. Its uncertainty is $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$, which is better than that of directly laser-cooled cadmium ion frequency standard.
The Dick effect can be a limitation of the achievable frequency stability of a passive atomic frequency standard when the ancillary frequency source is only periodically sampled. Here, we analyze the Dick effect for a pulsed vapor cell clock using coherent population trapping (CPT). Because of its specific interrogation process without atomic preparation nor detection outside of the Ramsey pulses, it exhibits an original shape of the sensitivity function to phase noise of the oscillator. Numerical calculations using a three-level atom model are successfully compared with measurements; an approximate formula of the sensitivity function is given as an easy-to-use tool. A comparison of our CPT clock sensitivity to phase noise with a clock of the same duty cycle using a two-level system reveals a higher sensitivity in the CPT case. The influence of a free-evolution time variation and of a detection duration lengthening on this sensitivity is studied. Finally, this study permitted the choice of an adapted quartz oscillator and allowed an improvement of the clock fractional frequency stability at the level of 3.2 x 10-13at 1 s.