Singly ionized ytterbium, with ultranarrow optical clock transitions at 467 and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the first direct measurement of the frequency ratio of these two clock transitions, without reference to a cesium primary standard, and using the same single ion of 171Yb+. The absolute frequencies of both transitions are also presented, each with a relative standard uncertainty of 6 × 10 -16. Combining our results with those from other experiments, we report a threefold improvement in the constraint on the time variation of the proton-to-electron mass ratio, mu-dot/mu = 0.2(1.1) × 10-16 yr-1, along with an improved constraint on time variation of the fine structure constant, alpha-dot/alpha = -0.7(2.1) x 10-17 yr-1.

Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants.

We give an overview of the work done with the Laboratoire National de Metrologie et d'Essais-Systemes de Reference Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the 87Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.

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Progress in atomic fountains at LNE-SYRTE

We report the first accuracy evaluation of NIST-F2, a second-generation laser-cooled caesium 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 shift by more than a factor of 50. Also, the Ramsey microwave cavity exhibits a high quality factor (>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.

/pdf/first-accuracy-evaluation-of-nist-f2-1v4posrss7.pdf

First accuracy evaluation of NIST-F2

We have measured the absolute frequency of the optical lattice clock based on $^{87}$Sr at PTB with an uncertainty of $3.9\times 10^{-16}$ using two caesium fountain clocks. This is close to the accuracy of today's best realizations of the SI second. The absolute frequency of the 5s$^2$ $^1$S$_0$-5s5p $^3$P$_0$ transition in $^{87}$Sr is 429,228,004,229,873.13(17) Hz. Our result is in excellent agreement with recent measurements performed in different laboratories worldwide. We improved the total systematic uncertainty of our Sr frequency standard by a factor of five and reach $3\times 10^{-17}$, opening new prospects for frequency ratio measurements between optical clocks for fundamental research, geodesy, or optical clock evaluation.

A strontium lattice clock with $3 \times 10^{-17}$ inaccuracy and its frequency

We have measured the absolute frequency of the optical lattice clock based on 87Sr at PTB with an uncertainty of 3.9 × 10−16 using two caesium fountain clocks. This is close to the accuracy of todayʼs best realizations of the SI second. The absolute frequency of the 5 s2 1S0 – 5s5p 3P0 transition in 87Sr is 429 228 004 229 873.13(17) Hz. Our result is in excellent agreement with recent measurements performed in different laboratories worldwide. We improved the total systematic uncertainty of our Sr frequency standard by a factor of five and reach 3 × 10−17, opening new prospects for frequency ratio measurements between optical clocks for fundamental research, geodesy or optical clock evaluation.

https://iopscience.iop.org/article/10.1088/1367-2630/16/7/073023/pdf

A strontium lattice clock with 3 × 10−17 inaccuracy and its frequency

We evaluate the distributed cavity phase and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 cesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the distributed cavity phase uncertainty to $1.1 \times 10^{-16}$. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of $6.2 \times 10^{-17}$. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to $2.3 \times 10^{-16}$, nearly a factor of two lower than its most recent complete evaluation.

Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts

We evaluate the distributed cavity phase (DCP) and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 caesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the DCP uncertainty to 1.1 ? 10?16. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of 6.2 ? 10?17. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to 2.3 ? 10?16, nearly a factor of two lower than its most recent complete evaluation.

https://iopscience.iop.org/article/10.1088/0026-1394/48/5/007/pdf

We perform 3D finite element calculations of the fields in microwave cavities and analyse the distributed cavity phase (DCP) 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 DCP 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.

http://iopscience.iop.org/article/10.1088/0026-1394/47/5/004/pdf

Evaluating and minimizing distributed cavity phase errors in atomic clocks

Examines cylindrical TE/sub 011/ microwave cavities and finds large phase shifts of the microwave field near the edges of the cut-off waveguide apertures, where there are nodes in the field. The phase shifts lead to a potential distributed cavity phase shift for atomic clocks. Using an additional larger diameter cut-off waveguide section can effectively exclude the nodes and the large phase shifts from the atomic trajectories. It has been suggested that recoils from the absorption of microwave photons lead to frequency shift and also a loss of fringe contrast. We present measurements of the contrast for up to 2 19/spl pi//2 pulses and find no loss of contrast beyond that expected from measuring microwave field inhomogeneities with up to 19/spl pi/ Rabi pulses.

Ruoxin Li

Papers

Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts

Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts

Evaluating and minimizing distributed cavity phase errors in atomic clocks

Distributed cavity phase shifts and microwave photon recoils