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Chinese Physics B

Evaluation of the frequency instability limited by Dick effect in the microwave 199 Hg + trapped-ion clock

Yi-He Chen, Lei She, Man Wang, Zhihui Yang, Hao Liu, Jiaomei Li

Published Nov 29, 2016• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/25/12/120601

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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.
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.
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.
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.
We report the development of a fieldable frequency standard based on 199Hg+ ions confined in a hybrid r.f./dc linear ion trap. This trap permits storage of large numbers of ions with reduced susceptibility to the second-order Doppler effect caused by the r.f. confining fields. A 160 mHz wide atomic resonance line for the 40·5 GHz clock transition is used to steer the output of a 5 MHz crystal oscillator to obtain a stability of 2 × 10−15 for 24 000 s averaging times. For longer averaging intervals, measurements are limited by instabilities in available hydrogen maser frequency standards. Measurements with 37 mHz linewidth for the Hg+ clock transition demonstrate that the inherent stability for this frequency standard is at least as good as 1 × 10−15.
A high-performance frequency standard based on (199)Hg(+) ions confined in a hybrid radio frequency (RF)/dc linear ion trap is demonstrated. This trap permits storage of large numbers of ions with reduced susceptibility to the second-order Doppler effect caused by the RF confining fields. A 160-mHz-wide atomic resonance line for the 40.5-GHz clock transition is used to steer the output of a 5-mHz crystal oscillator to obtain a stability of 2 x 10(exp -15) for 24,000-second averaging times. Measurements with a 37-mHz line width for the Hg(+) clock transition demonstrate that the inherent stability for this frequency standard is better than 1 x 10(exp -15) at 10,000-second averaging times.