Optical two-way time and frequency transfer over free space

Journal name:
Nature Photonics
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Published online


The transfer of high-quality time–frequency signals between remote locations underpins many applications, including precision navigation and timing, clock-based geodesy, long-baseline interferometry, coherent radar arrays, tests of general relativity and fundamental constants, and future redefinition of the second1, 2, 3, 4, 5, 6, 7. However, present microwave-based time–frequency transfer8, 9, 10 is inadequate for state-of-the-art optical clocks and oscillators1, 11, 12, 13, 14, 15, 16 that have femtosecond-level timing jitter and accuracies below 1 × 10−17. Commensurate optically based transfer methods are therefore needed. Here we demonstrate optical time–frequency transfer over free space via two-way exchange between coherent frequency combs, each phase-locked to the local optical oscillator. We achieve 1 fs timing deviation, residual instability below 1 × 10−18 at 1,000 s and systematic offsets below 4 × 10−19, despite frequent signal fading due to atmospheric turbulence or obstructions across the 2 km link. This free-space transfer can enable terrestrial links to support clock-based geodesy. Combined with satellite-based optical communications, it provides a path towards global-scale geodesy, high-accuracy time–frequency distribution and satellite-based relativity experiments.

At a glance


  1. Optical two-way time-frequency transfer.
    Figure 1: Optical two-way time–frequency transfer.

    a, Transfer takes place between two co-located sites A and B sharing a common optical oscillator or ‘clock’, allowing evaluation of the residual timing deviation. The sites are linked by 385 m and 115 m optical fibre paths (black lines) from the laboratory to each free-space launch for the 2 km air path (grey line). b, A comb, consisting of a femtosecond fibre laser phase-locked to the common clock, generates a pulse train that is coherent (that is, ‘ticks’ synchronously) with the clock at a repetition rate of fr  100 MHz for Site A and fr + Δfr  100.003 MHz for Site B. These pulse trains are exchanged between sites. c, LOS detects the arrival of the received pulses in analogy with sampling oscilloscopes. The local comb pulse train (blue) optically samples the received comb pulses (red) at varying delays to generate an interferogram (black trace, measured data) with an equivalent time step of ~Δfr/fr2 per point. d, The set-up is implemented using commercial fibre-optic components. The comb output is amplified (grey triangle) and bandpass-filtered (BPF) to 0.9 THz (7 nm) to generate an ~4 mW pulse train near 193 THz. The superposed received and local comb pulses are detected, low-pass filtered (LPF), digitized with an analogue-to-digital converter (ADC), and the resulting interferogram processed to find ΔTA(B) (see Methods and Supplementary Discussion). e, Measured interferograms (black) at τ = 0 and 4,354 s (1.2 h). The grey traces indicate the interferogram expected in the absence of path length or timing variations. For the case shown, the one-way delay increased by 11 ps (3.3 mm) in 1.2 h.

  2. Example data.
    Figure 2: Example data.

    a, The detected intensity at site A exhibits the strong fluctuations and fading characteristic of coherent links over turbulent paths. b, Variation in the one-way time-of-flight ΔTA (blue, left axis) and air temperature (green, right axis). The reset in ΔTA at 13:45 is a consequence of a phase slip between the clock and one comb. c, Residual timing difference ΔTAB acquired at τ0 = 300 μs intervals and averaged over 100 ms time intervals. The slow ripple (standard deviation of 2.5 fs) is attributed to temperature-induced path-length fluctuations within the transceiver and not the reciprocal free-space link.

  3. Power spectral densities.
    Figure 3: Power spectral densities.

    The PSD for the time-of-flight SA(f) across 2 km of air and 500 m of optical fibre (dark blue line) has contributions from the 500 m optical fibre (light blue line) at intermediate frequencies and the atmospheric piston effect SP(f) (dashed blue line) at low frequencies, calculated for 1 m s−1 wind speed and Cn2 = 2.5 × 10−14 m−2/3. In contrast, the PSD for the two-way timing difference SAB(f) (dark purple line) has negligible contribution from atmospheric turbulence or fibre noise and lies directly on top of the two-way PSD measured over a shorted path (red line).

  4. Precision (residual Allan deviation) and offset of the optical TWTFT, evaluated over multiple data sets covering 24 h of acquisition.
    Figure 4: Precision (residual Allan deviation) and offset of the optical TWTFT, evaluated over multiple data sets covering 24 h of acquisition.

    a, Residual modified Allan deviation MDEV for optical TWTFT (solid squares), calculated from ΔTAB, is well below the instabilities of state-of-the-art optical clocks (shaded region)1, 11, 12, 13, 14, 15, 17 and lies directly on the modified Allan deviation for a shorted path (red dashed line). The overlapping Allan deviation at 100 ms averaging (open squares) corresponds to two isolated 100 ms measurements at the start and end of the time interval and exhibits similar performance. In contrast, the modified Allan deviation for one-way transfer (open triangles), calculated from ΔTA, is significantly higher and limited by path-length fluctuations. b, Timing deviation of optical TWTFT. c, The fractional offset, or bias, across 11 data sets (squares labelled by start time and duration) has a weighted average (solid line) of 1.8 × 10−19 ± 2.1 × 10−19, consistent with zero as expected for the common clock (and well below the accuracy of the best optical clocks). The uncertainty per point is estimated at 7 × 10−19 assuming a flat Allan deviation at integration times beyond 2,000 s.


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  1. National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA

    • Fabrizio R. Giorgetta,
    • William C. Swann,
    • Laura C. Sinclair,
    • Esther Baumann,
    • Ian Coddington &
    • Nathan R. Newbury


W.C.S., L.C.S., I.C., E.B., F.R.G. and N.R.N. set up and operated the measurement system. F.R.G. and N.R.N. analysed the TWTF data. L.C.S. and N.R.N. analysed the turbulence data. N.R.N., F.R.G., L.C.S., W.C.S., E.B. and I.C. prepared the manuscript.

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