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 10-17, 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 10-18, 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.

https://iopscience.iop.org/article/10.1088/1361-6633/aab409/pdf

Atomic clocks for geodesy

Atomic Clocks for Geodesy

The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a limit is set by the measurement process, which returns not the phase, but its projection in terms of population difference on two energetic levels. The phase interval over which the relation can be inverted is thus limited to the interval [−π/2, π/2]; going beyond it introduces an ambiguity in the read out, hence a sensitivity loss. Here, we extend the unambiguous interval to probe the phase evolution of an atomic ensemble using coherence preserving measurements and phase corrections, and demonstrate the phase lock of the clock oscillator to an atomic superposition state. We propose a protocol based on the phase lock to improve atomic clocks under local oscillator noise, and foresee the application to other atomic interferometers such as inertial sensors.

https://hal.archives-ouvertes.fr/hal-01098353/document

Phase Locking a Clock Oscillator to a Coherent Atomic Ensemble

The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a limit is set by the measurement process, which returns not the phase, but its projection in terms of population difference on two energetic levels. The phase interval over which the relation can be inverted is thus limited to the interval $[-\pi/2,\pi/2]$; going beyond it introduces an ambiguity in the read out, hence a sensitivity loss. Here, we extend the unambiguous interval to probe the phase evolution of an atomic ensemble using coherence preserving measurements and phase corrections, and demonstrate the phase lock of the clock oscillator to an atomic superposition state. We propose a protocol based on the phase lock to improve atomic clocks under local oscillator noise, and foresee the application to other atomic interferometers such as inertial sensors.

/pdf/phase-locking-a-clock-oscillator-to-a-coherent-atomic-umr289qsfm.pdf

Phase locking a clock oscillator to a coherent atomic ensemble

We give an overview of recent changes to the collinear laser spectroscopy beamline in the IGISOL laboratory. We present a new data acquisition system, commissioning of a newly installed charge exchange cell, and cooler-voltage calibration measurements. Currently ongoing modifications to the RFQ cooler-buncher are also discussed.

Upgrades to the collinear laser spectroscopy experiment at the IGISOL

$$^{171}\hbox {Yb}^+$$
 ions confined within a linear quadrupole trap were laser cooled to below 1 K. The microwave frequency of the hyperfine splitting of the ground state was continuously measured over 6 h. Frequency was corrected by evaluating the systematic shifts in each clock measurement. The absolute microwave frequency was determined as 12 642 812 118.468 2(4) Hz, in strong agreement with previously reported measurements.

Determination of the absolute microwave frequency of laser-cooled $$^{171}\hbox {Yb}^+$$ 171 Yb +

We experimentally demonstrated that the stability of an atomic clock improves at its fastest rate ? ?1 (where ? is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (an atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over three measurement cycles, and thereby improved the stability scaling from to ? ?1 during the three measurement cycles. This simple method provides a path by which atomic clocks can approach a quantum projection noise limit, even when the measurement noise is dominated by the technical noise.

https://iopscience.iop.org/article/10.1088/1367-2630/16/7/073029/pdf

Accelerating the averaging rate of atomic ensemble clock stability using atomic phase lock

We experimentally demonstrated that the stability of an atomic clock improves at fastest rate $\tau^{-1}$ (where $\tau$ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over 3 measurement cycles, and thereby improved the stability scaling from $\tau^{-1/2}$ to $\tau^{-1}$ during the 3 measurement cycles. 
%Compared with the standard method that initialize phase during each measurement cycle, the long term stability was improved by a factor of $\sqrt{n_{cp}}$ (where $n_{cp}$ is the number of continuous phase measurements). 
This simple method provides a path by which atomic clocks can approach a quantum projection noise limit, even when the measurement noise is dominated by the technical noise.

Piyaphat Phoonthong

Papers

Determination of the absolute microwave frequency of laser-cooled $$^{171}\hbox {Yb}^+$$ 171 Yb +

Accelerating the averaging rate of atomic ensemble clock stability using atomic phase lock

Accelerating the Averaging Rate of Atomic Ensemble Clock Stability using Atomic Phase Lock