We report the uncertainty evaluation of the Swiss continuous primary frequency standard FoCS-2 (Fontaine Continue Suisse). Unlike other primary frequency standards which are working with clouds of cold atoms, this fountain uses a continuous beam of cold caesium atoms bringing a series of metrological advantages and specific techniques for the evaluation of the uncertainty budget. Recent improvements of FoCS-2 have made possible the evaluation of the frequency shifts and of their uncertainties in the order of 1 × 10 −15. When operating in an optimal regime a relative frequency instability of 8 × 10 −14 (τ /s) −1/2 is obtained. The relative standard uncertainty reported in this article, 1.99 × 10 −15 , is strongly dominated by the statistics of the frequency measurements.

Dense cold atomic clouds have been shown to be similar to plasmas. Previous studies showed that such clouds exhibit instabilities induced by long-range interactions. However they did not describe the spatial properties of the dynamics. In this Letter, we study experimentally the spatial nature of stochastic instabilities and find out that the dynamics is localized. Data are analyzed both in the spectral domain and in the spatial domain (principal component analysis). Both methods fail to describe the dynamics in terms of eigenmodes, showing that space and time are not separable.PACS numbers: 37.10. Gh, 37.10.Vz, During the last decades, cold atoms have proven to be more than an extraordinary tool for studying the physics of dilute matter. Many spectacular results concern the field of condensed matter, as e.g. the direct observation of the Anderson localization [1], or that of the BEC-BCS crossover [2]. But even in the field of dilute matter, cold atoms are thought to be a good model system for plasmas, in particular because experiments are considered to be relatively simple and well controlled. Although cold atoms in a Magneto-Optical Trap (MOT) are neutral, it has been demonstrated that a coulombian-like repulsive force appears in the multiple scattering regime [3]. Based on this analogy, fluid-dynamical models used in plasma physics have been adapted to cold atoms physics [4][5][6]. On the other hand, it has been demonstrated that the dynamics of cold atoms in a MOT can be described through the Vlasov-Fokker-Planck equations [7], as e.g. the plasma dynamics in the inertial confinement fusion [8], the stellar dynamics [9] or the electron dynamics in storage rings [10].Most of these systems are known to exhibit instabilities under appropriate parameter sets. Numerous types of instabilities have been observed, with very different properties and signatures. Although plasmas are governed by long-range interactions, instabilities appear not only at large spatial scales, but also at smaller scales. Some examples of local instabilities are the microbunching instability in the storage rings [10], drift wave microinstabilities in plasmas confined by a magnetic field [11], or microinstabilities of the solar corona [12].Instabilities in MOTs have been observed for several decades, and have been studied for 15 years. Mainly two types of instabilities have been reported through experiments. Self-sustained instabilities are periodic oscillations [13,14], while stochastic instabilities exhibit random characteristics [15]. In all cases, the experimental characterization is done through the temporal evolution of global variables, such as the fluorescence of the cloud or the location of its center of mass. The spatial properties of the instabilities, in particular their location in the cloud, is not known. However, most simplified models allowing to reproduce these instabilities have considered they are global [16,17]. On the other hand, taking formally into account the different processes involved in the MOTs leads to the Vlaso...

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Abstract. We report the evaluation of the second order Zeeman shift in the continuous atomic fountain clock FoCS-2. Because of the continuous operation and of its geometrical constraints, the methods used in pulsed fountains are not applicable. We use here time-resolved Zeeman spectroscopy to probe the magnetic field profile in the clock. The pulses of ac magnetic excitation allow us to spatially resolve the Zeeman frequency and to evaluate the Zeeman shift with a relative uncertainty smaller than 1 × 10 −16 .

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