A detailed analysis of the most relevant sources of phase noise in an atomic interferometer is carried out, both theoretically and experimentally. Even a short interrogation time of 100 ms allows our cold atom gravimeter to reach an excellent short term sensitivity to acceleration of $1.4\times 10^{-8}$g at 1s. This result relies on the combination of a low phase noise laser system, efficient detection scheme and good shielding from vibrations. In particular, we describe a simple and robust technique of vibration compensation, which is based on correcting the interferometer signal by using the AC acceleration signal measured by a low noise seismometer.Comment: 30 pages, 14 figure

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Ultracold atoms at temperatures close to the recoil limit have been achieved by extending Doppler cooling to forbidden transitions. A cloud of (40)Ca atoms has been cooled and trapped to a temperature as low as 6 microK by operating a magnetooptical trap on the spin-forbidden intercombination transition. Quenching the long-lived excited state with an additional laser enhanced the scattering rate by a factor of 15, while a high selectivity in velocity was preserved. With this method, more than 10% of precooled atoms from a standard magnetooptical trap have been transferred to the ultracold trap. Monte Carlo simulations of the cooling process are in good agreement with the experiments.

We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10 −18 , we propose 115 In + ions sympathetically cooled by 172 Yb + . We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding secondorder Doppler shift contributes less than 10 −18 to the relative uncertainty of the frequency standard.

We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.

As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low 10 −18 range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in the commonly encountered regime where the transition linewidth is comparable to the rf drive frequency. We show that a fractional frequency uncertainty due to the 2nd-order Doppler shift below |∆ν/ν| = 1 × 10 −20 can be achieved. The quantitative evaluation is verified in an interleaved measurement with the conceptually simpler resolved sideband method. If not performed deep within the Lamb-Dicke regime, a temperature-dependent offset at the level of 10 −19 is observed in resolved sideband measurements due to sampling of intrinsic micromotion. By direct comparison with photoncorrelation measurements, we show that the simple to implement parametric heating method is sensitive to micromotion at the level of |∆ν/ν| = 1 × 10 −20 as well.

We present an experiment to characterize our new linear ion trap designed for the operation of a many-ion optical clock using 115 In + as clock ions. For the characterization of the trap as well as the sympathetic cooling of the clock ions we use 172 Yb + . The trap design has been derived from finite element method (FEM) calculations and a first prototype based on glass-reinforced thermoset laminates was built. This paper details on the trap manufacturing process and micromotion measurement. Excess micromotion is measured using photon-correlation spectroscopy with a resolution of 1.1 nm in motional amplitude, and residual axial rf fields in this trap are compared to FEM calculations. With this method, we demonstrate a sensitivity to systematic clock shifts due to excess micromotion of |(∆ν/ν) mm | = 8.5 × 10 −20 . Based on the measurement of axial rf fields of our trap, we estimate a number of twelve ions that can be stored per trapping segment and used as an optical frequency standard with a fractional inaccuracy of ≤ 1 × 10 −18 due to micromotion.Submitted to: New J. Phys.

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