Measurement of the Blackbody Radiation Shift of the 133Cs Hyperfine Transition in an Atomic Fountain

We used a Cs atomic fountain frequency standard to measure the Stark shift on the ground state hyperfine transiton frequency in cesium (9.2 GHz) due to the electric field generated by the blackbody radiation. The measures relative shift at 300 K is -1.43(11)e-14 and agrees with our theoretical evaluation -1.49(07)e-14. This value differs from the currently accepted one -1.69(04)e-14. The difference has a significant implication on the accuracy of frequency standards, in clocks comparison, and in a variety of high precision physics tests such as the time stability of fundamental constants.Comment: 4 pages, 2 figures, 2 table

A cryogenic Strontium lattice clock

Optical clocks have moved to the forefront of frequency metrology. Their outstanding performances enable the exploration of new fields of research such as the search for dark matter and dark energy [1, 2], temporal drifts of the fine structure constant alpha [3, 5], violations of the Einstein equivalence principle (EEP) [6], and new applications such as chronometric leveling [7]. State-of-the-art optical clocks outperform the current realization of the SI-unit "Second" by the 133cesium fountain clocks, by two orders magnitude or more in instability and accuracy which triggers a discussion on a re-definition of the second. In 2016 the Consultative Committee for Time and Frequency (CCTF) of the International Bureau of Weights and Measures (BIPM) released a roadmap towards a redefinition of the SI second. One of the requests is the characterization of the systematic uncertainty of at least three independent clocks at the level of 10^-18. In this work, PTB's new cryogenic strontium lattice clock, Sr3, operating on the 1S0 - 3P0 clock transition in neutral 87Sr is described. Its systematic uncertainty has is evaluated to 2.7 x 10^-18 in fractional frequency units. This represents an improvement of more than a factor of 5 compared to its predecessor system Sr1 [8]. In Sr1 the dominant contribution of frequency uncertainty was about 1.4 x 10^-17 from the uncertainty of the black-body radiation (BBR) frequency shift. It arose from temperature gradients across the in-vacuum magnetic field coils that are placed close to the atoms. Reducing the gradients was not possible which ultimately limited the systems achievable systematic uncertainty. Sr3 features an in-vacuum dual-layer environment, the cryostat, that provides a very homogeneous temperature distribution for the atoms. This translates to a lower BBR frequency shift uncertainty as Sr1 at room temperature operation. The corresponding total systematic uncertainty for room temperature operation was evaluated to about 3.5 x 10^-18. Furthermore Sr3 features a closed-cycle pulse tube cooler that allows to operate the cryostat at any temperature ranging from room temperature to about 80K to further reduce the BBR frequency shift and uncertainty where the systematic uncertainty reaches the value of 2.7 x 10^-18 as mentioned above. Sr3 also features an arrangement of electrodes that allow the characterization of the dc-Stark frequency shift in three dimensional space. In this work the characterization of the electrode arrangement is described and the determination of the dc Stark shift. In Sr1 the this capability was limited to one direction that was pointing along the quantization magnetic field axis. During clock operation of Sr1, several high-accuracy comparisons to other atomic clocks have been performed. This includes many absolute frequency measurements yielding in a new record uncertainty in the transition frequency. An absolute frequency of Sr1 of f(Sr1) = 429 228 004 229 873.00(7)Hz [8] was measured that is in agreement withe the one measured of Sr3 of f(Sr3) = 429 228 004 229 872:94(19)Hz. The statistical uncertainty the measurements was significantly improved by using a H-Maser as a flywheel oscillator toeither extend the dataset or to bridge downtimes of the Sr-clocks [9]. Optical frequency ratio measurements between either of the two strontium clocks and the on-campus 171Yb+ single-ion clock have been carried out [10] for direct determination of their frequency ratio beyond the limitation of the primary frequency standards represented by Cs fountain clocks. The ratio measurements involving Sr1 span over a period of more than seven years and more than half a year with Sr3. The measurements have also revealed that the frequency ratio of the clocks, are reproducible within their uncertainties on short time scales but exhibits unexpected large scatter in the long term. The observed variations are on the order of several 10^-17 which is beyond any of the clocks reported systematic uncertainty. Despite an excessive search no uncontrolled frequency shifts were found. In the near future the in-vacuum cryostat is supposed to be updated with rotatable shutters. They will allow to minimize the BBR shift uncertainty during cryogenic operation. Prospectively a BBR shift uncertainty at the low 10^-19 level can be expected which paves the way for the system to reach a total systematic uncertainty of below 1 x 10^-18

First Accuracy Evaluation of NIST-F2

We report the first accuracy evaluation of NIST-F2, a second-generation laser-cooled Cesium fountain primary standard developed at the National Institute of Standards and Technology (NIST) with a cryogenic (Liquid Nitrogen) microwave cavity and flight region. The 80 K atom interrogation environment reduces the uncertainty due to the Blackbody Radiation (BBR) shift by more than a factor of 50. Also, the Ramsey microwave cavity exhibits a high Q (>50,000) at this low temperature, resulting in a reduced distributed cavity phase shift. NIST-F2 has undergone many tests and improvements since we first began operation in 2008. In the last few years NIST-F2 has been compared against a NIST maser time scale and NIST-F1 (the US primary frequency standard) as part of in-house accuracy evaluations. We report the results of nine in-house comparisons since 2010 with a focus on the most recent accuracy evaluation. This paper discusses the design of the physics package, the laser and optics systems, and the accuracy evaluation methods. The Type B fractional uncertainty of NIST-F2 is shown to be 0.11 × 10-15 and is dominated by microwave amplitude dependent effects. The most recent evaluation (August 2013) had a statistical (Type A) fractional uncertainty of 0.44 × 10-15

Fortschrittliche Mikrowellensynthesizer für Caesium-Fontänenuhren

Time interval and frequency can be measured with lower uncertainty and greater resolution than any other physical quantity. Using caesium fountain clocks, the SI-second can be realized with uncertainties of several parts in 10^16. In a fountain clock, microwave fields are used to manipulate the atomic states. These fields are driven by dedicated microwave signals. The generation of microwave signals is a key aspect for the operation of fountain clocks, as it can significantly contribute to the clocks statistical as well as the systematic uncertainty. This thesis discusses the contributions of the microwave signal generation to the uncertainty of a caesium fountain. Several methods aimed at the reduction of the statistical as well as the systematic uncertainty were implemented and assessed. A modular microwave synthesizer has been designed, ensuring high reliability and high availability. By utilizing a high stability local oscillator, the contribution of the microwave signal generation to the statistical uncertainty of the fountain clock could be reduced to an insignificant level. The synthesizer has been augmented with a modulation scheme to implement the method of Rapid Adiabatic Passage for collisional frequency shift measurements. Application of this method in the fountain clock CSF2 lead to a significant reduction of the collisional shift uncertainty and enabled fountain operation with high atom numbers. Phase perturbations in the microwave fields during the state manipulation can lead to shifts of the fountain frequency if they are synchronous with the fountain cycle. To facilitate a detailed analysis of cyclic perturbations on the micro-radian level, a dedicated phase transient analyzer was developed. With this system, the effect of cyclic phase perturbations can be evaluated at the low 10^-17 level. Uncontrolled interactions between the caesium atoms and resonant microwave fields can also be a source of frequency shifts. A method for the suppression of such shifts has been developed, relying upon a precise control of the field's frequency detuning. By using this scheme, the uncertainty contributions due to such interactions at CSF2 could be limited to few parts in 10^17.Von allen physikalischen Größen können Frequenz und Zeitintervall mit den geringsten Unsicherheiten bestimmt werden. Für die Realisierung der SI-Sekunde werden Caesium-Fontänenuhren eingesetzt, dabei werden relative Unsicherheiten von wenigen 10-16 erreicht. In Fontänenuhren nutzt man Mikrowellenfelder, um die atomaren Zustände der Caesium-Atome zu manipulieren, die Felder werden mit eigens entwickelten Mikrowellen-Signalgeneratoren erzeugt. Im Rahmen dieser Arbeit wurde der Einfluss der Mikrowellenerzeugung auf die Gesamtunsicherheit der Fontäne untersucht und Methoden zu deren Reduzierung entwickelt und bewertet. Der Fontänenbetrieb stellt hohe Anforderungen an die Zuverlässigkeit und Verfügbarkeit der verwendeten Elektronik. Im Rahmen dieser Arbeit wurde ein modularer Mikrowellensynthesizer aufgebaut. Als Referenzsignal wurde eine optisch stabilisierte Mikrowellenquelle verwendet. Damit konnte der Beitrag der Mikrowellensynthese zur statistischen Unsicherheit der Fontäne deutlich reduziert werden. Bei dem Synthesizer wurde die Rapid Adiabatic Passage Methode implementiert um die Unsicherheit in der Bestimmung der Stoßverschiebung zu reduzieren. Die Methode wird an der Fontänenuhr CSF2 eingesetzt und erlaubt den Fontänenbetrieb mit deutlich höheren Atomzahlen und damit einer geringeren statistischen Unsicherheit. Wenn während der Manipulation der Atome Störungen in der Phase der Mikrowellenfelder auftreten, kann die Frequenzbestimmung beeinflusst werden. Sind diese Störungen synchron zum Abfragezyklus der Fontänenuhr, kann es zu einer Verschiebung der Fontänenfrequenz kommen. Im Rahmen dieser Arbeit wurde ein Phasentransienten-Analysator entwickelt mit dem die Auswirkungen von zyklus-synchronen Phasentransienten auf wenige 10^-17 genau bestimmt werden können. Eine weitere mögliche Quelle für Frequenzverschiebungen ist die Interaktion von Caesium-Atomen während der wechselwirkungsfreien Zeit. Eine Verstimmung des Mikrowellenfeldes während dieser Zeit kann diesen Effekt und die damit verbundenen systematischen Unsicherheiten deutlich reduzieren. Im Rahmen dieser Arbeit wurde ein System zur präzisen Steuerung der Frequenz des Mikrowellenfeldes entwickelt und charakterisiert. Damit konnte sichergestellt werden, daß Unsicherheitsbeiträge durch diesen Effekt bei CSF2 im niedrigen 10^-17 Bereich liegen

Cold atom Clocks and Applications

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 figure

A 920 km optical fiber link for frequency metrology at the 19th decimal place

With residual uncertainties at the 10^-18 level, modern atomic frequency standards constitute extremely precise measurement devices. Besides frequency and time metrology, they provide valuable tools to investigate the validity of Einstein's theory of general relativity, to test a possible time variation of the fundamental constants, and to verify predictions of quantum electrodynamics. Furthermore, applications as diverse as geodesy, satellite navigation, and very long base-line interferometry may benefit from steadily improving precision of both microwave and optical atomic clocks. Clocks ticking at optical frequencies slice time into much finer intervals than microwave clocks and thus provide increased stability. It is expected that this will result in a redefinition of the second in the International System of Units (SI). However, any frequency measurement is based on a comparison to a second, ideally more precise frequency. A single clock, as highly developed as it may be, is useless if it is not accessible for applications. Unfortunately, the most precise optical clocks or frequency standards can not be readily transported. Hence, in order to link the increasing number of world-wide precision laboratories engaged in state-of-the-art optical frequency standards, a suitable infrastructure is of crucial importance. Today, the stabilities of current satellite based dissemination techniques using global satellite navigation systems (such as GPS, GLONASS) or two way satellite time and frequency transfer reach an uncertainty level of 10^-15 after one day of comparison . While this is sufficient for the comparison of most microwave clock systems, the exploitation of the full potential of optical clocks requires more advanced techniques. This work demonstrates that the transmission of an optical carrier phase via telecommunication fiber links can provide a highly accurate means for clock comparisons reaching continental scales: Two 920 km long fibers are used to connect MPQ (Max-Planck- Institut für Quantenoptik, Garching, Germany) and PTB (Physikalisch-Technische Bundesanstalt, Braunschweig, Germany) separated by a geographical distance of 600 km. The fibers run in a cable duct next to a gas pipeline and are actively compensated for fluctuations of their optical path length that lead to frequency offsets via the Doppler effect. Together with specially designed and remotely controllable in-line amplication this enables the transfer of an ultra-stable optical signal across a large part of Germany with a stability of 5 x 10^-15 after one second, reaching 10^-18 after less than 1000 seconds of integration time. Any frequency deviation induced by the transmission can be constrained to be smaller than 4 x 10^-19. As a first application, the fiber link was used to measure the 1S-2S two photon transition frequency in atomic hydrogen at MPQ referenced to PTB's primary Cs-fountain clock (CSF1). Hydrogen allows for precise theoretical analysis and the named transition possesses a narrow natural line width of 1.3 Hz. Hence, this experiment constitutes a very accurate test bed for quantum electrodynamics and has been performed at MPQ with ever increasing accuracy. The latest measurement has reached a level of precision at which satellite-based referencing to a remote primary clock is limiting the experiment. Using the fiber link, a frequency measurement can be carried out directly since the transmission via the optical carrier phase provides orders of magnitude better stability than state-of-the-art microwave clocks. The achieved results demonstrate that high-precision optical frequency dissemination via optical fibers can be employed in real world applications. Embedded in an existing telecommunication network and passing several urban agglomerations the fiber link now permanently connects MPQ and PTB and is operated routinely. It represents far more than a proof-of-principle experiment conducted under optimized laboratory conditions. Rather it constitutes a solution for the topical issue of remote optical clock comparison. This opens a variety of applications in fundamental physics such as tests of general and special relativity as well as quantum electrodynamics. Beyond that, such a link will enable clock-based, relativistic geodesy at the sub-decimeter level. Further applications in navigation, geology, dynamic ocean topography and seismology are currently being discussed. In the future, this link will serve as a backbone of a Europe-wide optical frequency dissemination network

Evaluating and Minimizing Distributed Cavity Phase Errors in Atomic Clocks

We perform 3D finite element calculations of the fields in microwave cavities and analyze the distributed cavity phase errors of atomic clocks that they produce. The fields of cylindrical cavities are treated as an azimuthal Fourier series. Each of the lowest components produces clock errors with unique characteristics that must be assessed to establish a clock's accuracy. We describe the errors and how to evaluate them. We prove that sharp structures in the cavity do not produce large frequency errors, even at moderately high powers, provided the atomic density varies slowly. We model the amplitude and phase imbalances of the feeds. For larger couplings, these can lead to increased phase errors. We show that phase imbalances produce a novel distributed cavity phase error that depends on the cavity detuning. We also design improved cavities by optimizing the geometry and tuning the mode spectrum so that there are negligible phase variations, allowing this source of systematic error to be dramatically reduced.Comment: To appear in Metrologi

Realization and characterization of optical frequency standards

During the Ph.D. Course I worked on the realization and the characterization of an ytterbium optical frequency standard. Since year 2000, it is possible using optical frequency comb to directly and reliably scale a frequency measurement in the optical domain to a measurement in the microwave domain. This possibility allows the realization of high accuracy and high stability optical frequency standards, whose atomic quality factors are several orders of magnitude higher than the best microwave ones. Among others, the alkaline earth atoms are very promising and, once trapped in an optical lattice, are capable of a short term stability approaching 10−15 at 1 s. A ytterbium optical clock is currently being developed in the laboratories of the Optics Division of Istituto Nazionale di Ricerca Metrologica (INRIM) The experiment aims to cool and trap ytterbium atoms in a two stage magneto-optical trap (MOT) (at 399 nm and 556 nm) and to probe them in an optical lattice with a ultrastable laser at 578 nm. This thesis presents the realization of the required laser sources, the stabilization of the clock laser, the development of the cooling and trapping stages and the design of a new experimental setup. The blue and green radiations for the two-stage MOT at 399 nm and 556 nm are obtained by second harmonic generation in non-linear crystals. The yellow clock laser at 578 nm is generated by sum of frequency in non-linear crystal. The clock laser is stabilized with the Pound-Drever-Hall technique on a high-finesse Fabry-Pérot cavity. The temperature stabilization of the cavity is implemented with a novel Active Disturbance Rejection Control scheme. The frequency noise of the laser is characterized with a stability 3 × 10−15 at 1 s. Atoms are trapped in the blue magneto-optical trap at 399 nm and transferred in the green trap at 556 nm. A new experimental setup is designed, studying the vacuum chamber, the MOT coils and the atomic source. I have been guest researcher at National Institute of Standards and Technology (NIST) for six months in 2011. I will describe development of NIST ytterbium optical clocks during my visi