[Paper Review] Frequency comparison of ${}^{171}$Yb${}^+$ ion optical clocks at PTB and NPL via GPS PPP

J. Leute, Nils Huntemann+12 more|arXiv (Cornell University)|Jul 15, 2015

Advanced Frequency and Time Standards4 citations

TL;DR

This study presents the first direct remote comparison of two 171Yb+ ion optical clocks at PTB (Germany) and NPL (UK) using GPS Precise Point Positioning (PPP) for frequency transfer. By employing hydrogen masers as flywheel oscillators and applying numerical extrapolation to handle data gaps, the authors achieved a fractional frequency difference of −1.3(1.2)×10⁻¹⁵ over 67 hours, demonstrating sub-10⁻¹⁵ uncertainty despite fragmented optical clock data.

ABSTRACT

We used Precise Point Positioning, a well-established GPS carrier-phase frequency transfer method to perform a direct remote comparison of two optical frequency standards based on single laser-cooled $^{171}$Yb$^+$ ions operated at NPL, UK and PTB, Germany. At both institutes an active hydrogen maser serves as a flywheel oscillator; it is connected to a GPS receiver as an external frequency reference and compared simultaneously to a realization of the unperturbed frequency of the ${{}^2S_{1/2}(F=0)-{}^2D_{3/2}(F=2)}$ electric quadrupole transition in ${}^{171}$Yb${}^+$ via an optical femtosecond frequency comb. To profit from long coherent GPS link measurements we extrapolate over the various data gaps in the optical clock to maser comparisons which introduces maser noise to the frequency comparison but improves the uncertainty from the GPS link. We determined the total statistical uncertainty consisting of the GPS link uncertainty and the extrapolation uncertainties for several extrapolation schemes. Using the extrapolation scheme with the smallest combined uncertainty, we find a fractional frequency difference $y(\mathrm{PTB})-y(\mathrm{NPL})$ of $-1.3(1.2) imes 10^{-15}$ for a total measurement time of 67 h. This result is consistent with an agreement of both optical clocks and with recent absolute frequency measurements against caesium fountain clocks.

Motivation & Objective

• To enable direct remote comparison of two state-of-the-art 171Yb+ ion optical clocks located at different continents.
• To overcome the challenge of intermittent data availability in optical clock measurements using GPS PPP frequency transfer.
• To develop and apply a numerical extrapolation method that minimizes uncertainty from data gaps while leveraging long coherent GPS links.
• To achieve a statistical uncertainty below 1.2×10⁻¹⁵ in the frequency comparison, validating the consistency of the two clocks.

Proposed method

• Utilized GPS Precise Point Positioning (PPP) to transfer time and frequency between PTB and NPL via carrier-phase measurements.
• Employed active hydrogen masers as flywheel oscillators to stabilize the frequency reference between optical clock measurements.
• Connected both masers and GPS receivers to a frequency comb to compare the maser frequency to the 171Yb+ E2 transition frequency.
• Applied numerical extrapolation techniques to estimate missing optical clock data points, reducing uncertainty from data gaps.
• Combined GPS PPP uncertainty with extrapolation uncertainty using multiple schemes to identify the optimal combination.
• Corrected for gravitational redshift using a height difference of 66.7(4) m between the two laboratories.

Experimental results

Research questions

• RQ1 Can GPS PPP be used to achieve a stable and accurate remote comparison of two 171Yb+ ion optical clocks with minimal data gaps?
• RQ2 What is the optimal extrapolation strategy for handling intermittent optical clock data while minimizing total uncertainty in the frequency comparison?
• RQ3 How does the use of a flywheel oscillator (hydrogen maser) affect the stability and uncertainty of the frequency comparison over long periods with data gaps?
• RQ4 To what extent can long coherent GPS links compensate for short data collection intervals in optical clock systems?
• RQ5 How does the combined uncertainty of GPS PPP and data extrapolation compare to absolute frequency measurements against caesium fountain clocks?

Key findings

• The fractional frequency difference between the PTB and NPL 171Yb+ clocks was measured as −1.3(1.2)×10⁻¹⁵ over a 67-hour measurement period, with the uncertainty dominated by statistical contributions.
• The smallest combined uncertainty of 1.2×10⁻¹⁵ was achieved using an extrapolation scheme that covered the entire data availability period, including gaps during which no optical clock data was collected.
• The GPS PPP link alone contributed a statistical uncertainty of 2×10⁻¹⁵ in the optimal case, but the use of extrapolation significantly reduced the overall uncertainty by enabling longer coherent averaging.
• The result is in excellent agreement with recent absolute frequency measurements against caesium fountain clocks, which yielded a difference of −0.87(75)×10⁻¹⁵.
• The systematic uncertainty from the GPS PPP link was negligible, confirming its reliability for optical clock comparisons.
• The study demonstrates that high-precision remote optical clock comparisons are feasible even with highly fragmented data, provided appropriate extrapolation and stable flywheel oscillators are used.