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Journal of the Optical Society of America B

Estimation of instability induced by probe laser frequency noise in cold-atom microwave clocks

Bowen Yang, Haojie Zhao, Ling Xiao, Xiaolin Li, Jianliao Deng, Hua-Dong Cheng

Published May 16, 2023• 2 citations
Publisher

Abstract

The influence of laser frequency noise on the stability of a compact cold-atom microwave clock was investigated theoretically in this study. The phase-noisy laser was characterized by a phase-diffusion field. Given the laser linewidth, the analytical expressions of the atomic covariance function and the noise power spectral density of the relative intensity noise transferred from the frequency noise were derived based on stochastic differential equations. Our results provide an effective method to estimate the impact of laser frequency noise on the stability of an integrating sphere cold atomic clock. This method can be extended to other cold atom detection cases.

DOI
10.1364/josab.476894

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The influence of laser frequency noise on the stability of a compact cold-atom microwave clock was investigated theoretically in this study. The phase-noisy laser was characterized by a phase-diffusion field. Given the laser linewidth, the analytical expressions of the atomic covariance function and the noise power spectral density of the relative intensity noise transferred from the frequency noise were derived based on stochastic differential equations. Our results provide an effective method to estimate the impact of laser frequency noise on the stability of an integrating sphere cold atomic clock. This method can be extended to other cold atom detection cases.
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The medium long-term frequency stability of the integrating sphere cold atom clock was improved. During the clock operation, Rb87 atoms were cooled and manipulated using cooling light diffusely reflected by the inner surface of a microwave cavity in the clock. This light heated the cavity and caused a frequency drift from the resonant frequency of the cavity. Power fluctuations of the cooling light led to atomic density variations in the cavity’s central area, which increased the clock frequency instability through the cavity pulling effect. We overcame these limitations with appropriate solutions. A frequency stability of 3.5×10−15 was achieved when the integrating time τ increased to 2×104 s.
We present the long-term stability of the integrating sphere cold atom clock (ISCAC) and analyze its systematic limitations. The relative frequency instability of 2.6×10−15 is reached for an averaging time of 2×105  s. The second-order Zeeman effect and the cavity pulling effect in ISCAC, which would induce the frequency drift from the clock transition, are analyzed. The analytical and experimental results indicate that the cavity pulling effect is the main contribution to the long-term frequency instability of the ISCAC. Further technical improvements to the microwave cavity are also discussed.
We present a compact cold-atom clock configuration where isotropic laser cooling, microwave interrogation, and clock signal detection are successively performed inside a spherical microwave cavity. For ground operation, a typical Ramsey fringe width of 20 Hz has been demonstrated, limited by the atom cloud's free fall in the cavity. The isotropic cooling light's disordered properties provide a large and stable number of cold atoms, leading to a high signal-to-noise ratio limited by atomic shot noise. A relative frequency stability of $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ has been achieved, averaged down to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ after $5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ s of integration. Development of such a high-performance compact clock is of major relevance for on-board applications, such as satellite-positioning systems. As a cesium clock, it opens the door to a new generation of compact primary standards and timekeeping devices.
We use a probability-theory approach to study the laser noise's effects on laser-atom interactions. We consider the case where the atom is described by a two-level system without spontaneous emission and the laser has both intensity and frequency noises. A stochastic differential equation is established based on the Schr\"odinger equation of the laser-atom interaction in the semiclassical picture. We then analyze the equation using the path-integral technique to the first order of a perturbation approach. Because of the presence of laser noises, the atom wave function at a given time is a random variable. Therefore we construct a stochastic process characterizing its time evolution. We also provide the theoretical description for the experimental realization of measuring the laser linewidth by driving a narrow atomic transition, and establish the connection between the laser noise's roles in the laser-atom interaction and laser linewidth measurement by beat signal.
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.