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Optical flywheels with attosecond jitter

Abstract

It has been known for some time that the steady-state pulse propagating inside a mode-locked laser is the optical equivalent of a mechanical flywheel. By measuring the timing error spectrum between phase-locked optical pulse trains emitted from two nearly identical 10 fs Ti:sapphire lasers, we demonstrate a record low integrated timing error of less than 13 as, measured from d.c. to the Nyquist frequency of the pulse train, which is 41 MHz. This corresponds to the lowest high-frequency phase noise ever recorded of –203 dBc Hz–1 (assuming a 10 GHz carrier) for offset frequencies greater than 1 MHz. Such a highly uniform train of pulses will enable the synchronization of pump–probe experiments that measure the evolution dynamics of chemical1,2 and atomic processes3,4 evolving on femtosecond and attosecond timescales. The ultralow timing jitter of such pulse trains will also allow photonic analog-to-digital conversion of mid-infrared waveforms with a resolution of 6 bits5.

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Figure 1: Experimental apparatus.
Figure 2: Timing jitter spectral density and rescaled single-sideband phase noise between the phase-locked optical pulse trains from two mode-locked Ti:sapphire lasers, as measured by the optical cross-correlator.

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References

  1. Fritz, D. M. et al. Ultrafast bond softening in bismuth: mapping a solid's interatomic potential with X-rays. Science 315, 633–636 (2007).

    Article  ADS  Google Scholar 

  2. Lindenberg, A. M. et al. Atomic-scale visualization of inertial dynamics. Science 308, 392–395 (2005).

    Article  ADS  Google Scholar 

  3. Schotte, F. et al. Watching a protein as it functions with 150-ps time-resolved X-ray crystallography. Science 300, 1944–1947 (2003).

    Article  ADS  Google Scholar 

  4. Wöhri, A. B. et al. Light-induced structural changes in a photosynthetic reaction center caught by Laue diffraction. Science 328, 630–633 (2010).

    Article  ADS  Google Scholar 

  5. Valley, G. C. Photonic analog-to-digital converters. Opt. Express 15, 1955–1982 (2007).

    Article  ADS  Google Scholar 

  6. Udem, T., Holzwarth, R. & Hansch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).

    Article  ADS  Google Scholar 

  7. Li, C-H. et al. A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1. Nature 452, 610–612 (2008).

    Article  ADS  Google Scholar 

  8. Braje, D. A., Kirchner, M. S., Osterman, S., Fortier, T. & Diddams, S. A. Astronomical spectrograph calibration with broad-spectrum frequency combs. Eur. Phys. J. D 48, 57–66 (2008).

    Article  ADS  Google Scholar 

  9. Wilken, T. et al. High-precision calibration of spectrographs. Mon. Not. R. Astron. Soc. 405, L16–L20 (2010).

    Article  ADS  Google Scholar 

  10. Thorpe, M. J., Moll, K. D., Jones, R. J., Safdi, B. & Ye, J. Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection. Science 311, 1595–1599 (2006).

    Article  ADS  Google Scholar 

  11. Ozawa, A. et al. High harmonic frequency combs for high resolution spectroscopy. Phys. Rev. Lett. 100, 253901 (2008).

    Article  ADS  Google Scholar 

  12. Corkum, P. B. & Krausz, F. Attosecond science. Nature Phys. 3, 381–387 (2007).

    Article  ADS  Google Scholar 

  13. Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–172 (2009).

    Article  ADS  Google Scholar 

  14. Ludlow, A. D. et al. Sr lattice clock at 1×10−16 fractional uncertainty by remote optical evaluation with a Ca clock. Science 319, 1805–1808 (2008).

    Article  ADS  Google Scholar 

  15. Rosenband, T. et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place. Science 319, 1808–1812 (2008).

    Article  ADS  Google Scholar 

  16. Haus, H. A. & Mecozzi, A. Noise of mode-locked lasers. IEEE J. Quantum Electron. 29, 983–996 (1993).

    Article  ADS  Google Scholar 

  17. Ivanov, E. N. & Tobar, M. E. Low phase-noise sapphire crystal microwave oscillators: current status. IEEE Trans. Ultrason. Ferroelec. Freq. Control 56, 263–269 (2009).

    Article  Google Scholar 

  18. Ivanov, E. N., Mouneyrac, D., Le Floch, J-M., Tobar, M. E. & Cros, D. Precise phase synchronization of a cryogenic microwave oscillator. Rev. Sci. Instrum. 81, 064702 (2010).

    Article  ADS  Google Scholar 

  19. Haus, H. A. & Ippen, E. P. Group velocity of solitons. Opt. Lett. 26, 1654–1656 (2001).

    Article  ADS  Google Scholar 

  20. Gordon, J. P. & Haus, H. A. Random walk of coherently amplified solitons in optical fiber transmission. Opt. Lett. 11, 665–667 (1986).

    Article  ADS  Google Scholar 

  21. Paschotta, R. Noise of mode-locked lasers (Part II): timing jitter and other fluctuations. Appl. Phys. B 79, 163–173 (2004).

    Article  Google Scholar 

  22. Ivanov, E. N., Hollberg, L. & Diddams, S. A. Analysis of noise mechanisms limiting frequency stability of microwave signals generated with a femtosecond laser. Proceedings of the IEEE International Frequency Control Symposium and PDA Exhibition 2002, 435–441 (2002).

    Article  Google Scholar 

  23. Bartels, A. et al. Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references. Opt. Lett. 30, 667–669 (2005).

    Article  ADS  Google Scholar 

  24. Ivanov, E. N., McFerran, J. J., Diddams, S. A. & Hollberg, L. Noise properties of microwave signals synthesized with femtosecond lasers. Proceedings of the 2005 IEEE International Frequency Control Symposium and Exposition 2005. 932–936 (2005).

    Article  Google Scholar 

  25. Ivanov, E. N., Tobar, M. E. & Woode, R. A. Microwave interferometry: application to precision measurements and noise reduction techniques. IEEE Trans. Ultrason. Ferroelect. Freq. Control 45, 1526–1536 (1998).

    Article  Google Scholar 

  26. Schibli, T. R. et al. Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation. Opt. Lett. 28, 947–949 (2003).

    Article  ADS  Google Scholar 

  27. Bartels, A., Diddams, S. A., Ramond, T. M. & Hollberg, L. Mode-locked laser pulse trains with subfemtosecond timing jitter synchronized to an optical reference oscillator. Opt. Lett. 28, 663–665 (2003).

    Article  ADS  Google Scholar 

  28. Ma, X., Liu, L. & Tang, J. Timing jitter measurement of transmitted laser pulse relative to the reference using type II second harmonic generation in two nonlinear crystals. Opt. Express 17, 19102–19112 (2009).

    Article  ADS  Google Scholar 

  29. Fortier, T. M. et al. Generation of ultrastable microwaves via optical frequency division. Nature Photon. 5, 425–429 (2011).

    Article  ADS  Google Scholar 

  30. Cox, J. A., Nejadmalayeri, A. H., Kim, J. & Kärtner, F. X. Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers. Opt. Lett. 35, 3522–3524 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support from the Department of Energy (grant no. DE-SC0005262), the Defense Advanced Research Projects Agency (grant no. HR0011-05-C-0155), the National Science Foundation (grant no. ECCS-0900901) and the Air Force Office of Scientific Research (grant no. FA9550-10-1-0063). The authors are grateful for the loan of a pump laser by Coherent Inc and a Ti:sapphire laser from IdestaQE to pursue this study.

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Contributions

F.X.K. initiated the project. J.G.F. helped with the detection circuit. A.J.B. designed the experimental set-up, acquired the phase noise data and performed the initial data analysis. A.J.B., F.X.K. and J.G.F. interpreted the data.

Corresponding author

Correspondence to Franz X. Kärtner.

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The authors declare no competing financial interests.

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Benedick, A., Fujimoto, J. & Kärtner, F. Optical flywheels with attosecond jitter. Nature Photon 6, 97–100 (2012). https://doi.org/10.1038/nphoton.2011.326

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