McGrew et al. (2018) demonstrated two ytterbium optical lattice clocks whose systematic uncertainty (1.4×10−181.4\times10^{-18}), instability and mutual reproducibility surpass the ability to correct for gravity itself: transforming each clock's frequency to Terrestrial Time (TT) carried 6×10−186\times10^{-18} of uncertainty, limited by several-centimetre-level geodetic knowledge of the gravity potential, so that sub-centimetre clock-based geodesy 'remains at best an optimistic goal'. The 2019-2026 literature shows the geodetic core remains open: the best demonstrated remote or transportable-clock determinations of geopotential differences stand at 1.9-4 cm, intercontinental comparison links remain at 6.3×10−156.3\times10^{-15}, satellite-only gravity models resolve no better than about 200 km, and the 2024 CCTF redefinition roadmap still lists clock-site geopotential knowledge at 10−1810^{-18} among unmet challenges. Component strands were narrowed but not closed: the Yb blackbody-radiation dynamic-correction coefficient was directly measured in 2025 (30% uncertainty reduction, and a cryogenic clock reaching 1.7×10−201.7\times10^{-20} BBR uncertainty), and multipolar lattice-shift compensation exists only as a proposal. The open problem is to make remote optical-clock comparisons and clock-based geodesy limited by the clocks, not by gravitational, environmental or link knowledge, at the 1 cm / 1×10−181\times10^{-18} level.

Background

An optical lattice clock traps thousands of neutral atoms at the nodes of a laser standing wave tuned to a 'magic wavelength' where the AC Stark light shift of the two clock states cancels, and interrogates an ultra-narrow optical transition; its accuracy is quantified by the systematic uncertainty (the fractional frequency error budget from residual perturbations such as blackbody radiation and lattice light shifts) and its averaging speed by the measurement instability. General relativity makes such clocks gravimeters: near Earth's surface a clock runs faster than a reference 1 cm below it by a fractional gravitational redshift of about 1.1×10−181.1\times10^{-18} (Δν/ν≈gh/c2\Delta\nu/\nu\approx gh/c^{2}). Comparing clocks at different sites therefore measures differences of the gravity potential WW ('chronometric levelling', or relativistic geodesy); conversely, to compare distant clocks or contribute to time scales, each clock's proper frequency must be transformed to the coordinate time scale Terrestrial Time (TT), realized by International Atomic Time (TAI) and referred to the conventional geoid potential W0W_0, using the imperfectly known potential at its site. Before 2018, Takano et al. (2016) determined a geopotential difference between two synchronously linked strontium lattice clocks 15 km apart with 5 cm height-equivalent resolution, Grotti et al. (2018) performed the first transportable-clock geodesy campaign, and the geodetic state of the art (Pavlis and Weiss 2017; Denker et al. 2018) established that Global Navigation Satellite System (GNSS) positioning combined with gravimetric geoid models (models of the geoid, the equipotential surface of Earth's gravity field approximating mean sea level) delivers potential differences with roughly 2 cm (few-10−1810^{-18}) uncertainty, with systematic errors that grow over long baselines, while spirit levelling reaches millimetres locally but accumulates decimetre-level systematics over continents. McGrew et al. (2018, at the US National Institute of Standards and Technology, NIST) then reported two 171^{171}Yb optical lattice clocks, each with 1.4×10−181.4\times10^{-18} total systematic uncertainty, measurement instability enabling 3.2×10−193.2\times10^{-19} resolution in one hour, and ten blinded inter-clock comparisons consistent at [−7±(5)stat±(8)sys]×10−19[-7\pm(5)_{\mathrm{stat}}\pm(8)_{\mathrm{sys}}]\times10^{-19} - performance sufficient for centimetre-level geodesy if the gravity correction were known. The paper's central open problem is that this correction is not known: the redshift transformation to the TT reference frame carried 6×10−186\times10^{-18} of uncertainty, 'limited by the several-centimetre-level state-of-the-art geodetic determination', so height determinations at or below 1 cm (fractional frequency uncertainties below 1×10−181\times10^{-18}) 'remain at best an optimistic goal'. The paper identifies two subsidiary systematic limitations for clocks used outside a common environment: the blackbody-radiation (BBR) Stark shift, whose 'dynamic correction' (the frequency-dependent part of the atomic response across the thermal spectrum, dominated in Yb by the poorly known 6s5d 3D16s5d\ ^{3}D_{1} state and inferred from its lifetime and branching ratio to 3P0^{3}P_{0}) contributed 8.5×10−198.5\times10^{-19} of uncertainty; and higher-order lattice polarizabilities (magnetic-dipole M1, electric-quadrupole E2 and two-photon E1 light shifts) that were controlled operationally, with a cubic model accurate to 3×10−193\times10^{-19} at the operating trap depth, and largely common-mode between the two co-located clocks. The paper also noted that its one-dimensional, room-temperature lattice operation constitutes 'useful traits for future portable apparatus'. Remote comparisons at 10−1810^{-18} are the backbone of the planned redefinition of the SI second (Dimarcq et al. 2024) and of a proposed unified centimetre-level global height system.

Problem Statement

Close the gap, identified by McGrew et al. 2018, between optical-clock performance (10−1810^{-18}-level systematic uncertainty and reproducibility) and the gravitational and environmental knowledge needed to exploit it: make remote (non-co-located) comparisons of optical clocks and clock-based geodesy limited by the clocks themselves rather than by auxiliary knowledge, by determining and correcting gravity-potential differences between clock sites - in the Terrestrial Time (W0W_{0}-referenced) frame - at or below 1 cm height equivalent, i.e. fractional frequency at or below 1×10−181\times10^{-18}, over baselines beyond a single laboratory, with every other contribution to the comparison (link noise, clock systematics, time-variable gravity) also below that level. As necessary components of this single objective: (a) geodetic determination of the gravity potential at remote clock sites to about 0.1 m2/s20.1\ \mathrm{m^{2}/s^{2}} (~1 cm), beyond the several-centimetre state of the art in satellite positioning (GNSS) and geoid modelling, including reduction of time-variable signals (tides, loading, vertical land motion) in a consistent reference frame; and (b) clock systematic uncertainties below 1×10−181\times10^{-18} in comparisons where shifts no longer cancel as common-mode, including the room-temperature blackbody-radiation dynamic correction and the higher-order M1/E2/two-photon lattice polarizabilities across realistic operating conditions.

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