Source-linked AI summary
Geodesy and metrology with a transportable optical clock
Jacopo Grotti, Silvio Koller, Stefan Vogt, Sebastian Häfner, Uwe Sterr, Christian Lisdat, Heiner Denker, Christian Voigt, Ludger Timmen, Antoine Rolland, Fred N. Baynes, Helen S. Margolis, Michel Zampaolo, Pierre Thoumany, Marco Pizzocaro, Benjamin Rauf, Filippo Bregolin, Anna Tampellini, Piero Barbieri, Massimo Zucco, Giovanni A. Costanzo, Cecilia Clivati, Filippo Levi, Davide Calonico
TL;DR
Determining gravity potential differences requires accounting for each clock site’s local gravity influence. The study reports 10 032.1(16) m2/s2 between the Sr clock positions at LSM and INRIM, although local height determination limited uncertainty.
Problem
Determining gravity potential requires estimating the potential at each clock site with the best possible uncertainty while accounting for local spatial influences.
Method
The study determines gravity potential differences using clock-site potential estimates and corrections for local spatial gravity influences.
Results
10 032.1(16) m2/s2 was obtained between the positions of the Sr clocks at LSM and INRIM.
Takeaways & Limitations
The measurement campaign contributed data for evaluating an existing gravity database and filling coverage gaps.
Takeaways & Limitations
The clock results have larger uncertainty because local height differences between the clocks and reference markers were determined using a simple method.
Abstract
from arXiv · showhide
The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a revision of the International System of units (SI). However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy, a major challenge remains. This is their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations. Here we report the first field measurement campaign performed with a ubiquitously applicable $^{87}$Sr optical lattice clock. We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km apart, exploiting both local and remote clock comparisons to eliminate potential clock errors. A local comparison with a $^{171}$Yb lattice clock also serves as an important check on the international consistency of independently developed optical clocks. This campaign demonstrates the exciting prospects for transportable optical clocks.
Methods · Operation of lattice clocks
The Yb and Sr lattice clocks use similar operation: laser cooling, magic-wavelength one-dimensional lattice trapping, and state preparation for precision spectroscopy. Optical pumping reduces cold-collision and line-pulling shifts, while alternating Zeeman-sensitive transitions removes the linear Zeeman shift.
- Operation of lattice clocks: Yb and Sr atoms are cooled to microkelvin temperatures in two-stage magneto-optical traps using strong and weak transitions [16,13,30].The cooling transitions are at 399 and 556 nm for Yb, and 461 and 689 nm for Sr.
- Operation of lattice clocks: The cooled atoms are trapped in one-dimensional optical lattices operating near the magic wavelengths λ_Ybmagic ≈ 759 nm and λ_Srmagic ≈ 813 nm [31].
- Operation of lattice clocks: Atoms are optically pumped into a single magnetic sublevel mf before spectroscopy.This preparation reduces shifts from cold collisions and line pulling.
- Operation of lattice clocks: The Yb clock probes π-transitions from mf = ±1/2 sublevels, while the Sr clock uses mf = ±9/2 sublevels.
- Operation of lattice clocks: The two transitions are probed alternately at approximately halfwidth detunings to lock the interrogation laser to their average transition frequency.
- Operation of lattice clocks: Locking to the average of the alternately probed transitions effectively removes the linear Zeeman shift.
Uncertainties of lattice clocks
The section evaluates key uncertainty contributions in the Yb and Sr lattice clocks, including lattice light shifts, density shifts, and blackbody-radiation shifts. A deeper Sr lattice produced no significant variation in the measured frequency ratio R, while maser noise was modeled for Sr/Cs ratio transfer.
- Lattice light shifts: The Yb lattice operated at ν_l = 394 798.238 GHz and U_0 = 196(4) Er, with the linear shift measured near the magic wavelength and nonlinear shifts calculated from prior data.The atomic temperature was 7(3) µK, determined by sideband spectroscopy.
- Lattice light shifts: No significant variation in the measured frequency ratio R was observed with a deeper Sr lattice, despite linear and higher-order light-shift uncertainties of 29×10^-17 and 1×10^-17.Three measurements used a lattice depth of about 160 Er.
- Density shift: Density shifts were evaluated by varying the interrogated atom number in both lattice clocks, with Sr corrections applied for changes in atomic temperature.
- Blackbody radiation (BBR) shift: Blackbody-radiation uncertainty was mainly associated with temperature inhomogeneity, with atomic-environment temperatures measured using calibrated platinum resistance thermometers.
- Frequency-ratio transfer: For Sr/Cs frequency-ratio transfer, an H-maser extended averaging between the Sr lattice clock and Cs primary clock, with maser noise modeled using characterized noise components.The ratio νSr/νCs was determined from νSr/νH and νH/νCs datasets of different lengths, and the resulting additional uncertainty can be calculated when maser noise is well characterized.
Gravity potential determination
The gravity potential difference was determined by combining GNSS heights, spirit levelling, and a geoid model refined with local gravity measurements. The resulting difference between the Sr-clock positions was 10 032.1(16) m2/s2, with larger clock uncertainty arising from simple local height-difference measurements.
- Gravity potential determination: Separate gravity surveys added 36 points around INRIM and 123 around LSM, including absolute observations at both sites and relative measurements elsewhere.Eleven points were located inside the Fréjus tunnel near LSM; the new data checked the existing database and filled coverage gaps.
- Gravity potential determination: The determination combined GNSS-based ellipsoidal heights, spirit levelling, and a geoid model refined by local gravity measurements.Uncertainties included contributions from the Alpine geoid model, GNSS, and levelling measurements.
- Gravity potential determination: 10 032.1(16) m2/s2 was the determined gravity potential difference between the Sr-clock positions at LSM and INRIM.The corresponding difference between nearby reference markers was 10 029.7(6) m2/s2.
- Gravity potential determination: The clock-position uncertainty was larger because local height differences between the clocks and reference markers were determined using a simple method.The gravity-potential determination also accounted for local spatial influences and global and temporal gravity-potential variations.
Supplement:
The supplement details the fibre-based remote clock comparison and reports transportable Sr-clock frequency results, including an absolute frequency and a Yb/Sr frequency ratio.
- Supplement:: The remote comparison used a 1542.14 nm link laser, fibre frequency combs, transfer-oscillator processing, and Doppler-noise cancellation over the telecom fibre.Two bidirectional erbium-doped fibre amplifiers generated a phase-stable signal at LSM.
- Supplement:: Eight optical frequency-ratio measurements totaling 15 h over one week were combined using generalized least squares with correlated systematic uncertainties.The analysis treated clock systematic uncertainties as fully correlated and duration-related statistics separately.