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The present definition of the unit of time, the second, is based on the frequency of the microwave transition between two hyperfine levels of the Cs atom. Recently, it has been realized that the accuracy and stability of atomic clocks can be substantially improved by trapping atoms in optical lattices operated at a certain “magic” wavelength [1, 2]. At this magic wavelength, both clock levels experience the same AC Stark shift; the clock frequency becomes essentially independent on trapping laser intensity.

This paper reports our works on the 3 LNE- SYRTE fountains and their frequency comparisons. We have performed new experiments on the frequency shifts related to the microwave synthesis and to the blackbody radiation interaction. We have also refined the accuracy budget of the 87Rb hyperfine splitting and obtained a new measurement of the frequency comparison between cesium and rubidium.

We report the operation of LNE-SYRTE FO2 fountain with rubidium 87 after several substantial improvements. With these improvements, FO2-Rb fountain reaches a similar level of performance as LNE-SYRTE cesium fountains with an accuracy of 4.5 parts in 1016. This Rb fountain has been compared to LNE-SYRTE FOM transportable fountain for more than 50 days, down to a resolution

We present a new evaluation of an 87Sr optical lattice clock using spin polarized atoms. The frequency of the 1S0→3P0 clock transition is found to be 429 228 004 229 873.6 Hz with a fractional uncertainty of 2.6×10-15, a value that is comparable to the frequency difference between the various primary standards throughout the world. This measurement is in excellent agreement with a previous one of similar accuracy [Phys. Rev. Lett. 98, 083002 (2007)].

Comparisons between three Cs fountains are described. All three LNE-SYRTE fountain clocks are now using a cryogenic sapphire oscillator as a starting point to generate the microwave probe signal. As a result, all three fountains have a fractional frequency instability in the 10-14 range at 1 s. All three fountains are also using a recently developed generation of microwave synthesizers allowing to switch the microwave probe signal without introducing detrimental phase transient. Several series of measurements have been made totalizing more than 80 days of simultaneous operation under optimized conditions of a pair of either fountains. Results of these measurements are presented. Finally, modifications of the FO2 fountain has been completed to allow simultaneous operation with Rb and Cs. Operation with Rb leads to a fractional frequency instability of 6.3 × 10-14τ-1/2.

International audience; We propose a novel and robust technique to realize a beam splitter for trapped Bose–Einstein condensates (BECs). The scheme relies on the possibility of producing different potentials simultaneously for two internal atomic states. The atoms are coherently transferred, via a Rabi coupling between the two long-lived internal states, from a single well potential to a double-well. We present numerical simulations supporting our proposal and confirming excellent efficiency and fidelity of the transfer process with realistic numbers for a BEC of 87 Rb. We discuss the experimental implementation by suggesting state-selective microwave (MW) potentials as an ideal tool to be exploited for magnetically trapped atoms. The working principles of this technique are tested on our atom chip device which features an integrated coplanar MW guide. In particular, the first realization of a double-well potential by using a MW dressing field is reported. Experimental results are presented together with numerical simulations, showing good agreement. Simultaneous and independent control on the external potentials is also demonstrated in the two Rubidium clock states. The transfer between the two states, featuring respectively a single and a double-well, is characterized and it is used to measure the energy spectrum of the atoms in the double-well. Our results show that the spatial overlap between the two states is crucial to ensure the functioning of the beamsplitter. Even though this condition could not be achieved in our current setup, the proposed technique can be realized with current state-of-the-art devices being particularly well suited for atom chip experiments. We anticipate applications in quantum enhanced interferometry.

We present a comparison between SYRTE's Cs fountain FO1 and Cs-Rb fountain FO2 using a cryogenic sapphire oscillator (CSO) to generate an ultra-stable interrogation signal. A description of the experimental setup is given and the clock accuracies are discussed. For the first time, a frequency resolution in the low 10/sup -16/ is achieved in the comparison between two primary standards. The paper also summarizes recent contributions of these fountains to research activities such as test of the stability of fundamental constants, timekeeping and test of sub-systems of the PHARAO space clock.

This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the $^{133}$Cs and $^{87}$Rb atomic fountains are described. Thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference, a fountain frequency instability of $1.6\times 10^{-14}\tau^{-1/2}$ where $\tau $ is the measurement time in seconds is measured. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of $2\times 10^{-16}$ at $50,000s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of $7\times 10^{-16}$, one order of magnitude below that of uncooled devices. In a second part, we describe tests of possible variations of fundamental constants using $^{87}$Rb and $^{133}$Cs fountains. Finally we give an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which is scheduled to fly on board the International Space Station in 2008, enabling a new generation of relativity tests., Comment: 30 pages, 11 figures

International audience; We report a test of the stability of fundamental constants based on laboratory experiments. This test relies on high-precision comparisons of atomic frequencies. The ground state hyperfine frequencies of 87Rb and 133Cs are compared over five years using atomic fountains. These measurements lead to the following constraint {d / {dt}} ln ( {(g{C} {s} /g{Rb} )alpha 0.44 } ; ) = (0.2 ± 7.0) × 10{ - 16} {yr}{ - 1} (1sigma uncertainty) where g is the nuclear g-factor and alpha the fine structure constant.

To date atomic fountain clocks using laser cooled Cs atoms prove to be the most accurate frequency standards. Among the three set-ups at BNM-SYRTE, the historically first Cs fountain clock, FO1, has recently undergone substantial changes. The cold atom preparation and selection have been rebuilt. Selection of the F = 3, mF = 0 state can be carried out by adiabatic passage allowing the preparation of 100% or 50% of the atom density with a precision of 10-3. Thereby, we can quantify the collisional frequency shift at a level of 10-16. Furthermore, a cryogenic sapphire oscillator is used for the synthesis of the microwave interrogation signal. With these improvements FO1 is currently operating at a stability of 2.8 x 10-14s-1/2 and an accuracy of a few 10-16.

We study the two transverse quadrupole modes of a cigar-shaped Bose-Einstein condensate with a single centered vortex. We show that the counterrotating mode is more strongly damped than in the absence of a vortex, whereas the corotating mode is not affected appreciably by the vortex. We interpret this result as a decay of the counterrotating quadrupole mode into two excitations of the vortex line, the so-called Kelvin modes. This is supported by direct observation of the vortex line.

A scissors mode of a rotating Bose-Einstein condensate is investigated both theoretically and experimentally. The condensate is confined in an axi-symmetric harmonic trap, superimposed with a small rotating deformation. For angular velocities larger than $\omega_\perp/\sqrt2 $, where $\omega_\perp$ is the radial trap frequency, the frequency of the scissors mode is predicted to vanish like the square root of the deformation, due to the tendency of the system to exhibit spontaneous rotational symmetry breaking. Measurements of the frequency confirm the predictions of theory. Accompanying characteristic oscillations of the internal shape of the condensate are also calculated and observed experimentally., Comment: 4 pages, 4 figures, submitted to PRA Rapid Communication

We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 seconds. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis., 4 pages, 4 figures, submitted to PRL

We study experimentally and theoretically a cold trapped Bose gas under critical rotation, i.e. with a rotation frequency close to the frequency of the radial confinement. We identify two regimes: the regime of explosion where the cloud expands to infinity in one direction, and the regime where the condensate spirals out of the trap as a rigid body. The former is realized for a dilute cloud, and the latter for a Bose-Einstein condensate with the interparticle interaction exceeding a critical value. This constitutes a novel system in which repulsive interactions help in maintaining particles together., Comment: 4 pages, 4 figures, submitted to PRL

We study experimentally the transverse monopole mode of an elongated rubidium condensate. Due to the scaling invariance of the non-linear Schr\"odinger (Gross-Pitaevski) equation, the oscillation is monochromatic and sinusoidal at short times, even under strong excitation. For ultra-low temperatures, the quality factor $Q=\omega_0/\gamma_0$ can exceed 2000, where $\omega_0$ and $\gamma_0$ are the mode angular frequency and damping rate. This value is much larger than any previously reported for other eigenmodes of a condensate. We also present the temperature variation of $\omega_0$ and $\gamma_0$., Comment: 4 pages, 4 figures, submitted to PRL

Systematic measurements of the magnetic moment per Ni atom in Cu/Ni/Cu/Si(001) structures have been made using polarized neutron reflection (PNR) for Ni thicknesses in the range 30Å, , perpendicular anisotropy strength, and surface in-plane Ni lattice constant, respectively, during epitaxial growth. RHEED measurements show that the in-plane lattice constant falls by 1.7% in the Ni thickness range 30 Å, , and total moment per atom versus Ni thickness as found for the total moment by PNR. Polar MOKE measurements confirmed the transition from a perpendicular easy axis towards an in-plane magnetic easy axis as has already been extensively studied in the literature. Comparison of the PNR results with RHEED measurements reveal a striking correlation between the increase of in-plane strain and reduction in magnetic moment per atom with decreasing Ni thickness. While a direct strain-induced variation of the moment based on bulk phase calculations cannot account for the magnitude of the moment variations we observe, we show that the results cannot be attributed to sample contamination, interdiffusion, or a reduction of the Curie temperature with decreasing Ni thickness. Furthermore, the presence of a magnetically dead layer in the samples is not consistent with the PNR results. The strong moment variation partially explains the large thickness range for which perpendicular anisotropy is observed in this system.

National audience; Cet article présente les derniers résultats des horloges en fontaine du BNM-SYRTE avec leurs stabilités et exactitudes respectives (FOM : 1,7.10-13tau -1/2, 0,8.10-15 ; DF{Cs} : 3,5.10-14tau -1/2, 0,8.10-15 ; DF{Rb} : 1,4.10-14tau -1/2, 0,7.10-15). Pour la détermination du déplacement collisionel une nouvelle méthode de mesure différentielle des densités a été mis en place. La méthode de passage adiabatique permet la préparation des atomes avec 50% ou 100% de la densité maximale. Les comparaisons entre les fontaines ont abouti à un test de la variation éventuelle de la constante de structure fine alpha. En supposant que seule alpha varie la variation relative est (-0,4 ± 16).10-16 an-1.

This paper presents the achievement of the dual atom clock operation of the FO2 double fountain at LNE-SYRTE with both Cs and Rb atoms launched simultaneously. We describe how it works, metrological characteristics and results of the first Rb/Cs frequency measurement campaign performed with FO2 as a dual atom clock, among which a new absolute frequency determination of the 87Rb hyperfine frequency.

International audience; The transfer of ultra-stable frequencies between distant laboratories is required by many applications from fundamental metrology to high-precision measurements. For that purpose, optical fibre links have been intensively studied over the last decade. They have demonstrated impressive results far beyond the GPS capabilities on distances up to 2000 km, thanks to an active compensation of the fiber propagation noise.Up to now, optical links has been mainly implemented between two labs, when future applications will require the development of metrological fiber networks. Towards this goal, we have developed a few techniques which allow us to distribute the ultrastable optical signal to many users simultaneously. We have designed repeater laser stations, which can be used to build a cascaded link or to distribute the ultrastable signal among two optical links [1]. These stations allow us also to compare the output end signals of two optical links. These versatile stations will be a key-component of the national metrological network currently being developed in France within the Refimeve+ project. To complete the network, we have demonstrated the extraction of the ultrastable signal from a main link and its seeding to a secondary link [2].Optical links are already been successfully used for clocks comparison. Recently we were able to compare the atomic clocks of the French and German National Metrology Institutes through two connected optical links of total length 1415-km [3]. We found that the two fully independent Sr lattice optical clocks at the two sites agreed to better than 5x10-17 limited only by the clocks uncertainties. A fractional statistical uncertainty of 3x10-17 was reached after only 1000 s averaging time, which is 10 times better, and more than four orders of magnitude faster than with any other existing frequency transfer method. The atomic fountain primary frequency standards from the two institutes were also compared and they were found to agree well within their combined uncertainties of a few 10-16 [4].

We describe two experimental tests of the Equivalence Principle that are based on frequency measurements between precision oscillators and/or highly accurate atomic frequency standards. Based on comparisons between the hyperfine frequencies of 8 7 Rb and 1 3 3 Cs in atomic fountains, the first experiment constrains the variability of fundamental constant. The second experiment is based on a comparison between a cryogenic sapphire oscillator and a hydrogen maser. It tests Local Lorentz Invariance. In both cases, we report recent results which improve significantly over previous experiments.

We will report on the work performed with LNE-SYRTE fountain ensemble, focusing on characterization of the distributed cavity phase shift and on extensive comparison between the three fountains FO1, FO2 and FOM.

We report recent experiments performed with our Sr optical lattice clock. With the fermionic isotope 87Sr, the clock accuracy approaches 10-15 using spin-polarized atoms. We also report the first accuracy evaluation of an optical lattice clock with bosonic atoms, here 88Sr.

This thesis describes the conception and construction of an “entanglement-enhanced” trapped atom clock on an atom chip (TACC). The key feature of this new experiment is the integration of two optical Fabry-Pérot micro resonators which enable generation of spin-squeezed states of the atomic ensemble via atom-light interactions and non-destructive detection of the atomic state. It has been shown before that spin-squeezed states can enhance the metrological performance of atomic clocks, but existing proof-of-principle experiments have not yet reached a metrologically relevant level of precision. This is the first goal of the new setup. To retain the compactness and stability of our setup, we chose the optical resonator to be a fiber Fabry-Pérot (FFP) resonator where the resonator mirrors are realized on the tip of optical fibers. To meet the requirements of our experiment, a new generation of FFP resonators was developed in the context of this thesis, demonstrating the longest FFP resonators to date. For this purpose, we developed a “dot milling” procedure using a focused CO2-laser that allows shaping of fused silica surfaces with unprecedented precision and versatility. Incorporating optical resonators in the TACC system requires a new atom chip design, allowing transportation of the atom cloud into the resonator. We present the design and the fabrication of this atom chip. The completed setup will enable investigations of the interplay of spin-dynamics in presence of light mediated correlations and spin-squeezing at a metrologically relevant stability level of 10⁻¹³ at 1 s., L’objet de cette thèse de doctorat est la conception et la construction d’une horloge atomique réalisée sur un microcircuit à atomes (TACC) et améliorée par l’intrication. L’élément principal de cette nouvelle expérience est un micro-résonateur Fabry Pérot qui permet la génération d’états de spin comprimés de l'ensemble atomique grâce aux interactions entre la lumière et les atomes. Il a déjà été montré que ces états peuvent améliorer les performances métrologiques des horloges atomiques. Cependant, les expériences ayant permis cette démonstration de principe n'ont pas encore atteint un niveau de précision présentant un intérêt métrologique. C’est précisément l'objectif de la nouvelle configuration expérimentale que nous proposons ici. Afin de conserver la compacité et la stabilité de notre installation, nous avons choisi d’utiliser une cavité Fabry-Pérot fibrée (fibered Fabry-Pérot, FFP) comme résonateur optique, dans lequel les miroirs du résonateur sont réalisés sur la pointe de fibres optiques. Pour répondre aux exigences de notre expérience, une nouvelle génération de résonateurs FFP a été développée au cours de cette thèse, les plus longs réalisés à ce jour. A cette fin, nous avons développé une procédure d’ablation par tirs multiples à l'aide d'un laser CO2 focalisé, qui permet la mise en forme des surfaces de silice fondue avec une précision et une polyvalence sans précédent.L'intégration du résonateur optique au dispositif expérimental TACC nécessite une conception nouvelle du microcircuit à atomes, qui doit permettre le transport du nuage atomique jusqu’au résonateur. Nous présenterons donc la conception et la fabrication de ce microcircuit à atomes.

This thesis reports the development of two original tools for atom interferometry.The first is a high finesse optical cavity for the manipulation of 87Rb cold atoms. This cavity isfirstly used to enhance the intensity of an optical dipole trap. Thus, by realizing an evaporativecooling on the atomic sample, we reached Bose-Einstein condensation. Furthermore, the nondegeneratecavity allows the injection of different transverse electromagnetic modes. In thisway, we have demonstrated the generation and the manipulation of arrays of atomic ensemblesusing these modes. Successive measurements of these atomic ensembles in an atominterferometric sequence would increase the interrogation time and thus the sensitivity of thesensor.Secondly, the use of weak nondestructive measurements on the atoms allows to extractinformation from the system with negligible perturbation of the ensemble. Applying feedbackafter the measurement, we were able to control the quantum state of the system. Using amodified Ramsey sequence with weak nondestructive measurements and phase corrections, werealized a phase lock loop between a local oscillator and the atomic state. We have thendemonstrated that this protocol leads to a stability enhancement of an atomic clock byovercoming the limit set by the local oscillator.We also contributed to the development of the commercial laser platform EYLSA fromQuantel, testing its performances on two laser cooling experiments.; Cette thèse décrit le développement de deux outils originaux pour l’interférométrie atomique. Le premier est une cavité optique à haute finesse pour la manipulation d’atomes ultra-froids de 87Rb. Cette cavité est d’abord utilisée pour augmenter l’intensité d’un piège dipolaire optique qui permet de piéger et refroidir les atomes. Ainsi, en procédant à un refroidissement par évaporation de l’échantillon atomique, nous avons atteint le régime de condensation de Bose-Einstein. La cavité étant non dégénérée, elle permet également l’injection de différents modes transverses électromagnétiques. Nous avons alors démontré la création et la manipulation de réseau d’ensembles atomiques en utilisant ces modes. La mesure successive de ces ensembles atomiques au cours d’une séquence d’interférométrie atomique permettrait d’augmenter le temps de mesure et ainsi d‘améliorer la sensibilité de l’instrument. Deuxièmement, l’utilisation d’une mesure faible non destructive sur les atomes permet de soutirer de l’information du système sans le perturber. En appliquant une rétroaction après ces mesures, l’état quantique peut être contrôlé. Par l’utilisation d’une séquence de Ramsey adaptée avec des mesures faibles et des corrections de phase, nous avons ainsi démontré la réalisation d’une boucle à verrouillage de phase entre un oscillateur local et l’état atomique. Nous avons ensuite démontré que ce protocole améliore la stabilité d’une horloge atomique en surpassant la limite de stabilité de l’oscillateur local. Nous avons également validé l’utilisation de la plate-forme laser commercial EYLSA de Quantel sur deux expériences de refroidissement d’atomes par laser.