Abstract
The combination of optical time transfer and optical clocks opens up the possibility of large-scale free-space networks that connect both ground-based optical clocks and future space-based optical clocks. Such networks promise better tests of general relativity1,2,3, dark-matter searches4 and gravitational-wave detection5. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry6,7, advanced satellite navigation8, clock-based geodesy2,9,10 and thousandfold improvements in intercontinental time dissemination11,12. Thus far, only optical clocks have pushed towards quantum-limited performance13. By contrast, optical time transfer has not operated at the analogous quantum limit set by the number of received photons. Here we demonstrate time transfer with near quantum-limited acquisition and timing at 10,000 times lower received power than previous approaches14,15,16,17,18,19,20,21,22,23,24. Over 300 km between mountaintops in Hawaii with launched powers as low as 40 µW, distant sites are synchronized to 320 attoseconds. This nearly quantum-limited operation is critical for long-distance free-space links in which photons are few and amplification costly: at 4.0 mW transmit power, this approach can support 102 dB link loss, more than sufficient for future time transfer to geosynchronous orbits.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
All data for the figures in this manuscript are available at https://data.nist.gov/od/id/mds2-2967.
Code availability
The algorithms necessary to perform this experiment are described between the main text and the Methods.
References
Derevianko, A. et al. Fundamental physics with a state-of-the-art optical clock in space. Quantum Sci. Technol. 7, 044002 (2022).
Mehlstäubler, T. E., Grosche, G., Lisdat, C., Schmidt, P. O. & Denker, H. Atomic clocks for geodesy. Rep. Prog. Phys. 81, 064401 (2018).
Altschul, B. et al. Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission. Adv. Space Res. 55, 501–524 (2015).
Derevianko, A. & Pospelov, M. Hunting for topological dark matter with atomic clocks. Nat. Phys. 10, 933–936 (2014).
Kolkowitz, S. et al. Gravitational wave detection with optical lattice atomic clocks. Phys. Rev. D 94, 124043 (2016).
The Event Horizon Telescope Collaboration. First M87 event horizon telescope results. II. Array and instrumentation. Astrophys. J. Lett. 875, L2 (2019).
Kurczynski, P. et al. The Event Horizon Explorer mission concept. In Proc. Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave (eds Coyle, L. E. et al.) Vol. 12180, 215–224 (SPIE, 2022).
Warren, Z. & Fields, R. Optical crosslinks and satellite synchronization for GNSS, communications, and beyond. GPS Solut. 26, 64 (2022).
Takamoto, M. et al. Test of general relativity by a pair of transportable optical lattice clocks. Nat. Photonics https://doi.org/10.1038/s41566-020-0619-8 (2020).
Lisdat, C. et al. A clock network for geodesy and fundamental science. Nat. Commun. 7, 12443 (2016).
Riehle, F. Towards a redefinition of the second based on optical atomic clocks. C.R. Phys. 16, 506–515 (2015).
Bize, S. The unit of time: present and future directions. C.R. Phys. 20, 153–168 (2019).
Itano, W. M. et al. Quantum projection noise: population fluctuations in two-level systems. Phys. Rev. A 47, 3554–3570 (1993).
Giorgetta, F. R. et al. Optical two-way time and frequency transfer over free space. Nat. Photonics 7, 434–438 (2013).
Deschênes, J.-D. et al. Synchronization of distant optical clocks at the femtosecond level. Phys. Rev. X 6, 021016 (2016).
Bergeron, H. et al. Tight real-time synchronization of a microwave clock to an optical clock across a turbulent air path. Optica 3, 441 (2016).
Sinclair, L. C. et al. Synchronization of clocks through 12 km of strongly turbulent air over a city. Appl. Phys. Lett. 109, 151104 (2016).
Sinclair, L. C. et al. Comparing optical oscillators across the air to milliradians in phase and 10-17 in frequency. Phys. Rev. Lett. 120, 050801 (2018).
Bergeron, H. et al. Femtosecond time synchronization of optical clocks off of a flying quadcopter. Nat. Commun. 10, 1819 (2019).
Bodine, M. I. et al. Optical time-frequency transfer across a free-space, three-node network. APL Photonics 5, 076113 (2020).
Boulder Atomic Clock Optical Network (BACON) Collaboration. et al. Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564–569 (2021).
Ellis, J. L. et al. Scaling up frequency-comb-based optical time transfer to long terrestrial distances. Phys. Rev. Appl. 15, 034002 (2021).
Shen, Q. et al. Experimental simulation of time and frequency transfer via an optical satellite–ground link at 10-18 instability. Optica 8, 471–476 (2021).
Shen, Q. et al. Free-space dissemination of time and frequency with 10−19 instability over 113 km. Nature 610, 661–666 (2022).
Fujieda, M. et al. Carrier-phase two-way satellite frequency transfer over a very long baseline. Metrologia 51, 253 (2014).
Djerroud, K. et al. Coherent optical link through the turbulent atmosphere. Opt. Lett. 35, 1479–1481 (2010).
Kang, H. J. et al. Free-space transfer of comb-rooted optical frequencies over an 18 km open-air link. Nat. Commun. 10, 4438 (2019).
Gozzard, D. R. et al. Ultrastable free-space laser links for a global network of optical atomic clocks. Phys. Rev. Lett. 128, 020801 (2022).
Caldwell, E. D., Sinclair, L. C., Newbury, N. R. & Deschenes, J.-D. The time-programmable frequency comb and its use in quantum-limited ranging. Nature 610, 667–673 (2022).
Shapiro, J. H. Reciprocity of the turbulent atmosphere. J. Opt. Soc. Am. 61, 492–495 (1971).
Andrews, L. C. & Phillips, R. L. Laser Beam Propagation through Random Media (SPIE, 2005).
Sinclair, L. C. et al. Optical phase noise from atmospheric fluctuations and its impact on optical time-frequency transfer. Phys. Rev. A 89, 023805 (2014).
Liu, C. H. & Yeh, K. C. Pulse spreading and wandering in random media. Radio Sci. 14, 925–931 (1979).
Young, C. Y. in Free-Space Laser Communication and Laser Imaging II Vol. 4821 (eds Ricklin, J. & Voelz, D. G.) 74–81 (SPIE, 2002).
Stahl, H. P., Stephens, K. R., Henrichs, T., Smart, C. & Prince, F. A. Single-variable parametric cost models for space telescopes. OE 49, 073006 (2010).
Abich, K. et al. In-orbit performance of the GRACE follow-on laser ranging interferometer. Phys. Rev. Lett. 123, 031101 (2019).
Świerad, D. et al. Ultra-stable clock laser system development towards space applications. Sci. Rep. 6, 33973 (2016).
Numata, K. et al. Progress and plans for a U.S. laser system for the LISA mission. In Proc. International Conference on Space Optics—ICSO 2018(eds Cugny, B. et al.) Vol. 11180, 152–159 (SPIE, 2019).
Swann, W. C. et al. Measurement of the impact of turbulence anisoplanatism on precision free-space optical time transfer. Phys. Rev. A 99, 023855 (2019).
Robert, C., Conan, J.-M. & Wolf, P. Impact of turbulence on high-precision ground-satellite frequency transfer with two-way coherent optical links. Phys. Rev. A 93, 033860 (2016).
Stuhl, B. K. Atmospheric refraction corrections in ground-to-satellite optical time transfer. Opt. Express 29, 13706 (2021).
Francis, S. P. et al. Weak-light phase tracking with a low cycle slip rate. Opt. Lett., OL 39, 5251–5254 (2014).
Tønnes, M. B. K. et al. Coherent fiber links operated for years: effect of missing data. Metrologia 59, 065004 (2022).
Kuwahara, T. et al. Laser data downlink system of micro-satellite RISESAT. In Proc. Small Satellite Conference https://digitalcommons.usu.edu/smallsat/2013/all2013/57 (2013).
Kolev, D. et al. Status update on laser communication activities in NICT. In Proc. 2022 IEEE International Conference on Space Optical Systems and Applications (ICSOS) 36–39 (IEEE, 2022).
Carrasco-Casado, A. & Mata-Calvo, R. in Springer Handbook of Optical Networks (eds. Mukherjee, B. et al.) 1057–1103 (Springer, 2020).
Robinson, B. S. et al. TeraByte InfraRed Delivery (TBIRD): a demonstration of large-volume direct-to-Earth data transfer from low-Earth orbit. In Proc. Free-Space Laser Communication and Atmospheric Propagation XXX (eds Boroson, D. M. & Hemmati, H.) Vol. 10524, 253–258 (SPIE, 2018).
Wright, M. W., Kovalik, J., Morris, J., Abrahamson, M. & Biswas, A. LEO-to-ground optical communications link using adaptive optics correction on the OPALS downlink. In Proc. Free-Space Laser Communication and Atmospheric Propagation XXVIII (eds Boroson, D. M. & Hemmati, H.) Vol. 9739, 973904 (International Society for Optics and Photonics, 2016).
Gregory, M. et al. Commercial optical inter-satellite communication at high data rates. Opt. Eng. 51, 031202 (2012).
Swann, W. C. et al. Low-loss reciprocal optical terminals for two-way time-frequency transfer. Appl. Opt. 56, 9406–9413 (2017).
Acknowledgements
We acknowledge comments from T. Bothwell, F. Giorgetta and B. Washburn. We acknowledge technical assistance from S. Syed, M. Bodine, H. Leopardi, T. Wright, M. Martinsen, D. Kuniyuki, S. Baumann, the NOAA Mauna Loa Observatory and the Haleakala MEES Observatory. We acknowledge the Air Force Office of Scientific Research (grant no. MIPR F4FGA02152G001), Air Force Research Laboratory (grant no. FA9453-16-D-0004), NSF QLCI Award (grant no. OMA – 2016244), NSF GRFP (grant no. DGE 1650115), OSD and DARPA DSO through a CRADA with Vector Atomic and NIST for funding. Approved for public release; distribution is unlimited. Approval no. AFRL-2022-5993.
Author information
Authors and Affiliations
Contributions
J.-D.D., L.C.S. and N.R.N. conceived the experiment. E.D.C., J.-D.D., L.C.S. and N.R.N. acquired and analysed the synchronization data from Hawaii, and wrote the paper. J.-D.D. and H.B. developed the signal acquisition processing. J.E., E.D.C. and L.C.S. constructed the optical system and acquired 2 km data. W.C.S. and B.K.S. designed and built the free-space optical terminals and contributed to the writing.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature thanks David Gozzard and Jungwon Kim and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Extended Data Fig. 1 Free space optical terminal design.
Each terminal transmits both the comb light (at a few mW) and a beacon laser signal at similar low power (~2 mW at the aperture) through a 10 cm aperture with an 8 cm 1/e2 beam diameter. To avoid sacrificing comb light to active tip/tilt stabilization, a separate beacon beam at 1532 nm or 1542 nm is polarization multiplexed directly onto the comb beam. (The beacon wavelengths differ for the two terminals, allowing wavelength demultiplexing of the transmitted and received beacon beams). A terminal’s transmitted beacon beam, originating from a polarization maintaining fiber-coupled laser, is collimated through a fiber collimator, reflected off the face of an interference filter (which acts as a mirror), and directed to the polarization coupler. The combined, ~3.3-mm diameter beam is directed to a galvo mirror that provides tip/tilt control, and then passes through a 24:1, 10 cm aperture beam expander. The beacon light is detected at the far end by a focal plane array. The images are processed, and the beam position fed back to adjust the tip/tilt of the outgoing combined comb light and beacon light. This corrects for atmospheric turbulence and optimizes coupling of the incoming frequency comb light into the polarization maintaining single-mode optical fiber.
Extended Data Fig. 2 Total link loss.
(a) Diagram of link loss. The aperture-to-aperture link loss, which includes the channel loss \({{\ell }}_{channel}\), is reciprocal as is any excess loss from coupling into single-mode fiber, \({{\ell }}_{smf}\), whereas the transceiver-specific losses \({{\ell }}_{rcv}\) and \({{\ell }}_{xmit}\) are not. While \({{\ell }}_{smf}\) is reciprocal for both sites, the loss is unidirectional, that is it only occurs when the incoming light is coupled into the fiber. (b) Measured median total loss over different runs plotted against the integrated turbulence, as measured by the piston noise and assuming a wind velocity of 10 m/s. The mean loss across runs is 91 dB giving 11-dB margin over the tolerable loss of 102 dB.
Extended Data Fig. 3 System diagram emphasizing signal processing.
Each site has a local reference oscillator (cavity stabilized laser), to which both the clock comb and tracking comb are self-referenced. As shown for site A, after both the clock and tracking combs are phase-locked to the reference oscillator, they have an arbitrary local time offset between each other. This local time offset is directly zeroed by digitally adjusting the tracking comb timing until there is a maximum heterodyne overlap with the clock comb pulses. Subsequent timing values for the local tracking comb are then referenced to the local clock comb. After acquisition, the timing discriminator measures the (small) time offset δta between the incoming clock comb and local tracking comb. This timing difference is summed with the tracking comb time offset, to generate an estimate of the incoming clock comb pulse time, ta. This estimate, along with the corresponding measured incoming power, is input to the Kalman filter, whose output provides an optimized, filtered estimate of the incoming clock comb pulse time, \({t}_{a}^{KF}\). This value is fed into a final feedback controller for the tracking comb, GLO. Due to the feedback loop, the tracking comb output itself (both the physical optical pulse time and the corresponding digital value), is now a filtered, estimated value of the incoming clock comb pulse timing with respect to the local clock comb pulse time. This value is transmitted over a communication link from site A to site B, where it is combined with the corresponding local value of tb to generate an error signal for the site B clock comb. When both sites have acquired their lock onto the incoming clock comb pulses, the final synchronization feedback controller Gsy is activated and the site B clock comb is actively synchronized to the site A clock comb, at their local reference point. The effective bandwidth of the Kalman Filter depends on the input power, and ranges from 10 Hz to 25 Hz. The bandwidth of the subsequent lock of the tracking comb (Htrack) is ~450 Hz. The bandwidth of the synchronization lock (Hsynch) is ~15 Hz. The communication link is over rf coaxial cable here. For a future point-to-point link, it would be over free space by either rf or optical as in ref. 15. The message rate (for update of ta) is 400 Hz and the total bit rate is 26 kbps. red solid lines: optical comb pulses, red dashed line: CW optical laser light, black lines: digital values, P: input optical power.
Extended Data Fig. 4 Tracking comb timing measurement using an optical timing discriminator.
(a) Subset of system diagram from Extended Data Fig. 4 showing how the timing of the incoming clock comb is measured with the local tracking comb. (b) System diagram of the optical timing discriminator and subsequent signal processing. The optical timing discriminator generates two measurement channels with the lead and lag positions between the two combs switched between channels. After measuring these channels on balanced photodiodes (BPD), the heterodyne output voltages are demodulated to generate IQ (complex) signals, which are then low pass filtered (LPF). The phase of one signal is used in a phase-locked loop to adjust the demodulation frequency, fDDS, and centre the baseband signals at DC. The magnitudes of the signals are combined to generate an estimate of the power (from their mean squared values) and a timing offset value, δtb, from their normalized difference. BS, beam splitter; ADC, analog to digital converter; NCO, numerically controlled oscillator. (c) Absolute value of the timing discriminator output voltages, |V1| and |V2|, as a function of the time offset between the local tracking comb and incoming clock comb. (d) The error signal generated from the two channels along with the polynomial fit used in the digital processing to generate the timing error value based on the normalized error signal, E.
Extended Data Fig. 5 Optical time transfer transceiver design for a single site.
This transceiver routes the local clock comb to the FSO terminals and the incoming remote clock comb to the optical timing discriminator for mixing and detection with the local tracking comb. To minimize excess fiber optic delays, the transceiver also includes the necessary fiber optic components to generate the RF optical beat signals, fopt, used for locking the two clock and tracking combs to the local cavity stabilized laser (CW in) reference, and the out-of-loop verification beat signals. The reference plane for the out-of-loop verification is defined by the point at which the two clock combs overlap within the 50:50 splitter. A calibration step with a fiber-shorted link determines the time offset for the two clock combs due to path delays in the transceivers. This time offset is included in the overall synchronization loop so that the clock pulses remain overlapped when the system is operated over the link. All fiber is PM1550. 50:50, 50/50 splitter; 90:10, 90/10 splitter; BPF, band-pass filter; iso, isolator; DWDM, dense wavelength division multiplexer at the cavity-stabilized laser wavelength; 45° BS, polarization beam splitter with the input fiber rotated 45°.
Extended Data Fig. 6 Out-of-loop verification.
Calibration curve of heterodyne voltage vs time offset between the two clock combs used for out-of-loop verification. A fifth order polynomial is fit to the curve to generate a mapping from the measured demodulated heterodyne voltage to the time offset.
Extended Data Fig. 7 Traces for synchronization over 300 km for 4.0 mW of comb power at site B (left, blue traces) and for reduced, 40 μW comb power at site B (right, green curves).
(a) Time trace of received power, Prec, measured at the output of the timing discriminator for site A with the applied threshold shown as a dashed black line. (b) The control effort, ΔTcntrl, applied on site B to maintain synchronization between the two site’s clock combs. As such, it is also a measurement of the time offset between the two cavity-stabilized reference lasers. (c) Changes in the time-of-flight. These changes are due to temperature drifts in the 300 km of air and in the fiber paths up to the terminals, atmospheric turbulence, and mechanical movement in the terminals. (d) The out-of-loop timing verification or ‘Truth’ data indicates constant temporal overlap between the clock combs at both sites despite 100’s of ps changes in the time-of-flight and 100’s of ns changes in ΔTcntrl. This truth data is used to generate the instability deviations of Fig. 3.
Extended Data Fig. 8 Additional fractional frequency instabilities.
Modified Allan deviations of the out-of-loop verification data (‘truth’ data) for 4 different days across the 300 km link. Data from June 27th and early on June 28th (purple and pink curves) have an elevated MDEV at long averaging times due to a malfunctioning temperature controller on the out-of-loop verification fiber and both transceivers. The data from June 29th (blue curve) also appears in Fig. 3 of the main text.
Extended Data Fig. 9 Received power and fade statistics over the 300 km link at site A for 4.0 mW of comb power from site B.
(a–c) Received power over 600-seconds, 6 s, and 0.06 s. Red line indicates the 270 fW detection threshold. (d) Normalized histogram (i.e., probability density function, PDF) of the received power for the 600-second segment. (e) PDF of the fade durations. For the 4.0 mW comb power sent from site B, no fades exceeded a duration of 10 ms – a direct consequence of the low detection threshold at site A.
Extended Data Fig. 10 Received power and fade statistics over the 300 km link at site A for 40 µW of comb power from site B.
(a–c) Received power over 600-seconds, 6 s, and 0.06 s. Red line indicates the 270 fW detection threshold. (d) Normalized histogram (i.e., probability density function, PDF) of the received power for the 600-second segment. (e) PDF of the fade durations. For the greatly reduced launch power, fades are more frequency and of longer duration than the data of Extended Data Fig. 9.
Supplementary information
Supplementary Information
This file contains Supplementary Figs.1–2 and Discussion.
Rights and permissions
About this article
Cite this article
Caldwell, E.D., Deschenes, JD., Ellis, J. et al. Quantum-limited optical time transfer for future geosynchronous links. Nature 618, 721–726 (2023). https://doi.org/10.1038/s41586-023-06032-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-023-06032-5
This article is cited by
-
Clocks synchronized at the quantum limit
Nature (2023)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
