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Journal of Optics B Quantum and Semiclassical Optics

The Dick effect for an optical frequency standard

Audrey Quessada, Richard P. Kovacich, I. Courtillot, Andr Clairon, Giorgio Santarelli, P. Lemonde

Published Apr 1, 2003• 104 citations

Abstract

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.

DOI: 10.1088/1464-4266/5/2/373

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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.

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.

We discuss the minimization of the Dick effect in an optical lattice clock. We show that optimizing the time sequence of operation of the clock can lead to a significant reduction of the clock stability degradation by the frequency noise of the interrogation laser. By using a nondestructive detection of the atoms, we are able to recycle most of the atoms between cycles and consequently to strongly reduce the time spent capturing the atoms in each cycle. With optimized parameters, we expect a fractional Allan deviation better than 2 x 10(-16tau-1/2) for the lattice clock.

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 .

We discuss the optimization of the Dick effect in an optical lattice clock. We show that optimizing the time sequence of operation of the clock can lead to a significant reduction of the clock stability degradation by the frequency noise of the interrogation laser. By using a non-destructive detection of the atoms, we are able to recycle most of the atoms between cycles and consequently to strongly reduce the time spent capturing the atoms in each cycle. With optimized parameters, we expect a fractional Allan deviation better than 2 middot 10-16tau-1/2for the lattice clock.

Optical atomic clocks play a crucial role in fundamental physics, relativistic geodesy, and the future redefinition of the Systeme International second. Standard operation relies on cyclic interrogation sequences, which alternate between atomic interrogation and dead time used for state preparation and readout. This approach introduces the Dick effect, where laser frequency noise aliases onto the atomic transition frequency. Although reducing laser noise improves clock stability, the Dick effect remains a key limitation. In this Letter, we demonstrate a zero-dead-time optical clock based on two interleaved ensembles of cold ^{87}Sr atoms. Our system significantly suppresses this noise and achieves a fractional frequency instability at the 10^{-19} level between 10 000 and 20 000 s over repeated measurements, with a best value of 2.9×10^{-19} at τ=20000 s. The estimated long-term stability based on the combined data of these measurements reaches 2.5×10^{-19} at 1 day. These results represent a more than ninefold improvement over a conventional single-ensemble clock, highlighting its potential for next-generation timekeeping applications.