High Performance Clocks and Gravity Field Determination

Abstract

Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their accuracy and stability over the last decade that approached the level of 10$^{-18}$. Based on a fully relativistic description of the background gravitational physics, we discuss the impact of those highly-precise clocks on the realization of reference frames and time scales used in geodesy. We discuss the current definitions of basic geodetic concepts and come to the conclusion that the advances in clocks and other metrological technologies will soon require the re-definition of time scales or, at least, clarification to ensure their continuity and consistent use in practice. The relative frequency shift between two clocks is directly related to the difference in the values of the gravity potential at the points of clock's localization. According to general relativity the relative accuracy of clocks in 10$^{-18}$ is equivalent to measuring the gravitational red shift effect between two clocks with the height difference amounting to 1 cm. We show how clock measurements can provide geopotential numbers for the realization of gravity-field-related height systems and can resolve discrepancies in classically-determined height systems as well as between national height systems. Another application of clocks is the direct use of observed potential differences for the improved recovery of regional gravity field solutions. Finally, clock measurements for space-borne gravimetry are analyzed along with closely-related deficiencies of this method like an extra-ordinary knowledge of the spacecraft velocity, etc. For all these applications besides the near-future prospects, we also discuss the challenges that are related to using those novel clock data in geodesy.Comment: Will be published in Space Science Reviews as special issue on High Performance Clocks which is organized by ISS

Robust optical clock transitions in trapped ions using dynamical decoupling

“…Optical clocks based on neutral atoms trapped in optical lattices and single trapped ions have reached estimated systematic uncertainties of a few parts in 10 −18 [1][2][3][4] or even below [5]. Taking advantage of these record uncertainties for applications ranging from relativistic geodesy [6][7][8][9] over fundamental physics [10][11][12] to frequency metrology [13][14][15][16][17] requires achieving statistical measurement uncertainties of the same level within practical averaging times τ (given in seconds). This has been achieved with single-ensemble optical lattice clocks in self-comparison experiments up to a level of 1.6 10 16 t - [18] and by implementing an effectively deadtime-free clock consisting of two independent clocks probed in an interleaved fashion [19,20], reaching a statistical uncertainty in the range of 5 10 17 t -.…”

Relativistic geoid: Gravity potential and relativistic effects

“…Two possibilities are, e.g., 4 Note that in this limit the indices are raised and lowered with the Kronecker delta δ µ ν . 5 In all the equations above, ∇ is the flat space operator.…”

“…On the one hand, high-precision satellite missions such as GRACE/GRACE-FO allow to deduce properties of the Earth's gravity field, its changes on various time scales, and the investigation of underlying phenomena [1][2][3]. On the other hand, Earth-bound clock comparison networks or portable optical atomic clocks are used in the framework of chronometric geodesy [4][5][6][7]. One of the central notions that is to be determined by such geodetic measurements is the Earth's geoid -its mathematical figure as the German mathematician C.F.…”

Improving Our Knowledge on the 229mThorium Isomer: Toward a Test Bench for Time Variations of Fundamental Constants

“…Thus, even a future ultraprecise nuclear clock will not be sensitive enough to give access to higher-order terms in the above indicated 1/c 2 expansion of relative frequency shifts. [61] On a global scale, consistency could be achieved only on the decimeter level, which is not accurate enough for a unified world height system. More precisely, the relativistic geoid is the reference surface for global clock comparison, where precise clocks run with the same speed and the surface is nearest to mean sea level.…”