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The time-programmable frequency comb and its use in quantum-limited ranging

Abstract

Two decades after its invention, the classic self-referenced frequency comb laser is an unrivalled ruler for frequency, time and distance metrology owing to the rigid spacing of its optical output1,2. As a consequence, it is now used in numerous sensing applications that require a combination of high bandwidth and high precision3,4,5. Many of these applications, however, are limited by the trade-offs inherent in the rigidity of the comb output and operate far from quantum-limited sensitivity. Here we demonstrate an agile programmable frequency comb where the pulse time and phase are digitally controlled with ±2-attosecond accuracy. This agility enables quantum-limited sensitivity in sensing applications as the programmable comb can be configured to coherently track weak returning pulse trains at the shot-noise limit. To highlight its capabilities, we use this programmable comb in a ranging system, reducing the required power to reach a given precision by about 5,000-fold compared with a conventional dual-comb system. This enables ranging at a mean photon per pulse number of 1/77 while retaining the full accuracy and precision of a rigid frequency comb. Beyond ranging and imaging6,7,8,9,10,11,12, applications in time and frequency metrology1,2,5,13,14,15,16,17,18,19,20,21,22,23, comb-based spectroscopy24,25,26,27,28,29,30,31,32, pump–probe experiments33 and compressive sensing34,35 should benefit from coherent control of the comb-pulse time and phase.

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Fig. 1: A time-programmable frequency comb.
Fig. 2: Illustration and characterization of the time programmability of the TPFC through LOS.
Fig. 3: Dual-comb ranging with a time-programmable frequency comb.
Fig. 4: Ranging and velocity data to a moving retroreflector.
Fig. 5: Comparison of conventional and tracking dual-comb ranging.

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Data availability

The data for the figures in this paper are available for download at https://data.nist.gov/od/id/mds2-2703.

Code availability

The mathematics and algorithms necessary to create a time-programmable frequency comb are described between the main text and Methods.

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Acknowledgements

We acknowledge J. Ellis, T. Fortier, K. Cossel, W. Swann, B. Stuhl and B. Washburn for discussions. We acknowledge funding from the National Institute of Standards and Technology.

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E.D.C., L.C.S., N.R.N. and J.-D.D. all contributed to the initial conception, the experiment design, the data acquisition, the analysis of the results and the writing of the manuscript.

Corresponding authors

Correspondence to Laura C. Sinclair or Nathan R. Newbury.

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Nature thanks Takuro Ideguchi, Xiaoxiao Xue and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Range deviation power comparison.

Range deviation (left axis) and time deviation (right axis) of dual-comb range measurements from a fixed reflection for signal-comb powers from 980 nW (bottom curve) down to 0.33 pW (top curve) with the following power levels ± 10%: 980 nW, 190 nW, 86 nW, 38 nW, 21 nW, 9.6 nW, 1.8 nW, 1.2 nW, 390 pW, 200 pW, 89 pW, 33 pW, 23 pW, 8.5 pW, 4.1 pW, 1.9 pW, 990 fW, 550 fW and 330 fW. The vertical dashed cyan line indicates the 200-ms averaging time for the data in Fig. 3c. Beyond 200-ms, the range deviation increases due to temperature-induced fluctuations in the fibre path up to the fixed reflection. In addition, the deviations for the difference between the absolute range from the tracking comb timing and the relative range from the unwrapped carrier phase shift, from Fig. 4, are shown for the time periods of 60 to 100 seconds at 3.2 pW (green squares) and 110 seconds to 150 seconds at 32 pW (green triangles). For these data, the differential chirp between the signal and TPFC pulses was larger, leading to an additional 1.5x penalty in C and thus lie slightly above the curves at the same power for ranging off the fixed reflection (solid circles). However, because the path-length variation is common mode, the difference continues to average down beyond 200 ms.

Extended Data Fig. 2 Range power spectral density.

Range power spectral density (PSD) for the data from Fig. 4 over the period of 60 s to 100 s at 3.2 pW return power for X(t) from the tracking comb (blue trace) and the unwrapped carrier phase \(\theta (t)\) (purple trace). Also shown is the noise floor for the unwrapped carrier phase (dark blue trace). The vibrations of the nominally immobile retroreflector can be clearly seen in the carrier-phase data. At the low average power of 3.2 pW, the tracking dual-comb range shot-noise limited noise floor lies just above the minimal vibrations seen here. The vertical magenta line indicates the maximum 10 Hz update rate of FMCW while the vertical dark green line indicates the 13 kHz cut-off imposed by the 26 kHz measurement rate for the range data.

Extended Data Table 1 Ranging modality comparison

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Caldwell, E.D., Sinclair, L.C., Newbury, N.R. et al. The time-programmable frequency comb and its use in quantum-limited ranging. Nature 610, 667–673 (2022). https://doi.org/10.1038/s41586-022-05225-8

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