Geodetic methods to determine the relativistic redshift at the level of 10 $$^{-18}$$ - 18 in the context of international timescales: a review and practical results

Abstract

The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1 m 2 s −2 , equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 −18 .

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 -.…”

Direct comparisons of European primary and secondary frequency standards via satellite techniques

“…All relevant values are provided in table 3, where the underlying coordinate reference frame is ITRF2008 with the epoch 2005.0, and the zero reference potential (consistent with the IAU recommendations from the year 2000 and with the resolution 2 of the 26 th CGPM 2018) for the geopotential numbers is W 0 = 62 636 856.00 m 2 s −2 . The uncertainties of the differential redshift determinations for the distant clocks are less than 4 × 10 −18 , corresponding to less than 4 cm uncertainty in height [30][31][32].…”

Chronometric Geodesy: Methods and Applications

“…For applications on the Earth, such as (ground) clock syntonization (section 3.4) and the realization of a worldwide coordinate time (section 3.5), a natural choice of a relativistic reference system is the spatial part of the geocentric celestial reference system (GCRS) together with the terrestrial time (TT) as a coordinate time (see section 2.3). Following [80,81], the coordinate to proper time transformation can be written down to a relative accuracy of 10 −18 as:…”

“…Fortunately, such a data situation exists for most of the metrology institutes with optical clock laboratories -at least in Europe. Furthermore, the perspective exists to improve the uncertainty of the calculated quasigeoid heights [81]. Now, once the disturbing potential values T are computed, either from a global geopotential model by equation (47), or from a regional solution by equation (50) based on Molodensky's theory, the gravity potential W , needed for the relativistic redshift corrections, can be computed most straightforwardly from eq.…”

“…The uncertainty of the quasigeoid heights (height anomalies) is discussed in the previous subsection, showing that a standard deviation of 1.9 cm is possible in a best-case scenario. Moreover, the values are nearly uncorrelated over longer distances, with a correlation of less than 10 % beyond a distance of about 180 km [81]. Aiming at the determination of the absolute gravity potential W according to equations (51) or (52), which is the main advantage of the GNSS/geoid technique over the geometric levelling approach, both the uncertainties of GNSS and the quasigeoid have to be considered.…”