Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity

Abstract

State-of-the-art laser frequency stabilization by high-finesse optical cavities is limited fundamentally by thermal noise-induced cavity length fluctuations. We present a novel design to reduce this thermal noise limit by an order of magnitude as well as an experimental realization of this new cavity system, demonstrating the most stable oscillator of any kind to date for averaging times of 0.1–10 s. The cavity spacer and the mirror substrates are both constructed from single-crystal silicon and are operated at 124 K, where the silicon thermal expansion coefficient is zero and the mechanical loss is small. The cavity is supported in a vibration-insensitive configuration, which, together with the superior stiffness of the silicon crystal, reduces the vibration-related noise. With rigorous analysis of heterodyne beat signals among three independent stable lasers, the silicon system demonstrates a fractional frequency instability of 1 × 10−16 at short timescales and supports a laser linewidth of <40 mHz at 1.5 µm.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Performance of a single-crystal silicon Fabry–Pérot interferometer.
Figure 2: Schematic of the vibration-reduced, nitrogen-gas-based cryostat, including the vacuum chamber and two heat shields centred around the silicon single-crystal cavity.
Figure 3: Traces of the three beats involved in the three-cornered hat comparison after offset and linear drift removal.
Figure 4
Figure 5: Optical heterodyne beat between the silicon cavity system and REF. 2.
Figure 6: Modified Allan deviation of each cavity-stabilized laser derived from a three-cornered hat analysis of the data in Fig. 3.

Similar content being viewed by others

References

  1. Chou, C. W., Hume, D. B., Koelemeij, J. C. J., Wineland, D. J. & Rosenband, T. Frequency comparison of two high-accuracy Al+ optical clocks. Phys. Rev. Lett. 104, 070802 (2010).

    Article  ADS  Google Scholar 

  2. 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 

  3. Tamm, C., Weyers, S., Lipphardt, B. & Peik, E. Stray-field induced quadrupole shift and absolute frequency of the 688 THz 171Yb+ single-ion optical frequency standard. Phys. Rev. A 80, 043403 (2009).

    Article  ADS  Google Scholar 

  4. Harry, G. M. et al. Thermal noise from optical coatings in gravitational wave detectors. Appl. Opt. 45, 1569–1574 (2006).

    Article  ADS  Google Scholar 

  5. Abbott, B. P. et al. LIGO: the laser interferometer gravitational-wave observatory. Rep. Prog. Phys. 72, 076901 (2009).

    Article  ADS  Google Scholar 

  6. Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005).

    Article  ADS  Google Scholar 

  7. Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  8. Abbott, B. et al. Observation of a kilogram-scale oscillator near its quantum ground state. New J. Phys. 11, 073032 (2009).

    Article  ADS  Google Scholar 

  9. Eisele, C., Nevsky, A. Y. & Schiller, S. Laboratory test of the isotropy of light propagation at the 10−17 level. Phys. Rev. Lett. 103, 090401 (2009).

    Article  ADS  Google Scholar 

  10. Numata, K., Kemery, A. & Camp, J. Thermal-noise limit in the frequency stabilization of lasers with rigid cavities. Phys. Rev. Lett. 93, 250602 (2004).

    Article  ADS  Google Scholar 

  11. Notcutt, M. et al. Contribution of thermal noise to frequency stability of rigid optical cavity via Hertz-linewidth lasers. Phys. Rev. A 73, 031804 (2006).

    Article  ADS  Google Scholar 

  12. Kessler, T., Legero, T. & Sterr, U. Thermal noise in optical cavities revisited. J. Opt. Soc. Am. B 29, 178–184 (2012).

    Article  ADS  Google Scholar 

  13. Ludlow, A. D. et al. Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10−15. Opt. Lett. 32, 641–643 (2007).

    Article  ADS  Google Scholar 

  14. Young, B. C., Cruz, F. C., Itano, W. M. & Bergquist, J. C. Visible lasers with subhertz linewidths. Phys. Rev. Lett. 82, 3799–3802 (1999).

    Article  ADS  Google Scholar 

  15. Jiang, Y. Y. et al. Making optical atomic clocks more stable with 10−16 level laser stabilization.Nature Photon. 5, 158–161 (2011).

    Article  ADS  Google Scholar 

  16. Kimble, H. J., Lev, B. L. & Ye, J. Optical interferometers with reduced sensitivity to thermal noise. Phys. Rev. Lett. 101, 260602 (2008).

    Article  ADS  Google Scholar 

  17. Millo, J. et al. Ultrastable lasers based on vibration insensitive cavities. Phys. Rev. A 79, 053829 (2009).

    Article  ADS  Google Scholar 

  18. Legero, T., Kessler, T. & Sterr, U. Tuning the thermal expansion properties of optical reference cavities with fused silica mirrors. J. Opt. Soc. Am. B 27, 914–919 (2010).

    Article  ADS  Google Scholar 

  19. Storz, R., Braxmaier, C., Jäck, K., Pradl, O. & Schiller, S. Ultrahigh long-term dimensional stability of a sapphire cryogenic optical resonator. Opt. Lett. 23, 1031–1033 (1998).

    Article  ADS  Google Scholar 

  20. Seel, S., Storz, R., Ruoso, G., Mlynek, J. & Schiller, S. Cryogenic optical resonators: a new tool for laser frequency stabilization at the 1 Hz level. Phys. Rev. Lett. 78, 4741–4744 (1997).

    Article  ADS  Google Scholar 

  21. Nietzsche, S. et al. Cryogenic Q-factor measurement of optical substrates for optimization of gravitational wave detectors. Supercond. Sci. Technol. 19, S293–S296 (2006).

    Article  Google Scholar 

  22. Richard, J.-P. & Hamilton, J. J. Cryogenic monocrystalline silicon Fabry–Pérot cavity for the stabilization of laser frequency. Rev. Sci. Instrum. 62, 2375–2378 (1991).

    Article  ADS  Google Scholar 

  23. Schnabel, R. et al. Building blocks for future detectors: silicon test masses and 1550 nm laser light. J. Phys. Conf. Ser. 228, 012029 (2010).

    Article  Google Scholar 

  24. Petersen, K. E. Silicon as a mechanical material. Proc. IEEE 70, 420–457 (1982).

    Article  ADS  Google Scholar 

  25. Glassbrenner, C. J. & Slack, G. A. Thermal conductivity of silicon and germanium from 3 °K to the melting point. Phys. Rev. 134, A1058–A1069 (1964).

    Article  ADS  Google Scholar 

  26. Brantley, W. A. Calculated elastic constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44, 534–535 (1973).

    Article  ADS  Google Scholar 

  27. Nawrodt, R. et al. A new apparatus for mechanical Q-factor measurements between 5 and 300 K. Cryogenics 46, 718–723 (2006).

    Article  ADS  Google Scholar 

  28. Harry, G. M. et al. Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings. Class. Quantum Grav. 19, 897–917 (2002).

    Article  ADS  Google Scholar 

  29. Notcutt, M., Ma, L.-S., Ye, J. & Hall, J. L. Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity. Opt. Lett. 30, 1815–1817 (2005).

    Article  ADS  Google Scholar 

  30. Nazarova, T., Riehle, F. & Sterr, U. Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser. Appl. Phys. B 83, 531–536 (2006).

    Article  ADS  Google Scholar 

  31. Webster, S. A., Oxborrow, M. & Gill, P. Vibration insensitive optical cavity. Phys. Rev. A 75, 011801(R) (2007).

    Article  ADS  Google Scholar 

  32. Drever, R. W. P. et al. Laser phase and frequency stabilization using an optical resonator. Appl. Phys. B 31, 97–105 (1983).

    Article  ADS  Google Scholar 

  33. Glazov, V. & Pashinkin, A. The thermophysical properties (heat capacity and thermal expansion) of single-crystal silicon. High Temperature 39, 443–449 (2001).

    Google Scholar 

  34. Webster, S. & Gill, P. Force-insensitive optical cavity. Opt. Lett. 36, 3572–3574 (2011).

    Article  ADS  Google Scholar 

  35. Gray, J. E. & Allan, D. W. in Proc. 28th Frequency Control Symposium 243–246 (1974).

  36. Ma, L.-S., Jungner, P., Ye, J. & Hall, J. L. Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by optical fiber or other time-varying path. Opt. Lett. 19, 1777–1779 (1994).

    Article  ADS  Google Scholar 

  37. Rubiola, E. On the measurement of frequency and of its sample variance with high-resolution counters. Rev. Sci. Instrum. 76, 054703 (2005).

    Article  ADS  Google Scholar 

  38. Dawkins, S. T., McFerran, J. J. & Luiten, A. N. Considerations on the measurement of the stability of oscillators with frequency counters. IEEE Trans. Ultr. Ferr. Freq. Contr. 54, 918–925 (2007).

    Article  Google Scholar 

  39. Allan, D. W. & Barnes, J. in Proceedings of the 35th Annual Frequency Control Symposium, 470–475 (Electronic Industries Association, 1981).

  40. Greenhall, C. & Riley, W. in Proc. 2003 PTTI Meeting 267–280 (2003).

  41. Riley, W. & Greenhall, C. Power law noise identification using the lag 1 autocorrelation. IEEE Trans. Instrum. Meas. 2004, 576–580 (2004).

    Google Scholar 

  42. Premoli, A. & Tavella, P. A revisited three-cornered hat method for estimating frequency standard instability. IEEE Trans. Instrum. Meas. 42, 7–13 (1993).

    Article  Google Scholar 

  43. Swallows, M. D. et al. Suppression of collisional shifts in a strongly interacting lattice clock. Science 331, 1043–1046 (2011).

    Article  ADS  Google Scholar 

  44. Telle, H. R., Lipphardt, B. & Stenger, J. Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements. Appl. Phys. B 74, 1–6 (2002).

    Article  ADS  Google Scholar 

  45. Hartnett, J. G., Nand, N. R. & Lu, C. Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators. Appl. Phys. Lett. 100, 183501 (2012).

    Article  ADS  Google Scholar 

  46. Schibli, T. R. et al. Optical frequency comb with submillihertz linewidth and more than 10 W average power. Nature Photon. 2, 355–358 (2008).

    Article  ADS  Google Scholar 

  47. Brückner, F. et al. Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal. Phys. Rev. Lett. 104, 163903 (2010).

    Article  ADS  Google Scholar 

  48. Cole, G. D., Gröblacher, S., Gugler, K., Gigan, S. & Aspelmeyer, M. Monocrystalline AlxGa1– xAs heterostructures for high-reflectivity high-Q micromechanical resonators in the megahertz regime. Appl. Phys. Lett. 92, 261108 (2008).

    Article  ADS  Google Scholar 

  49. Chen, L. et al. Vibration-induced elastic deformation of Fabry–Pérot cavities. Phys. Rev. A 74, 053801 (2006).

    Article  ADS  Google Scholar 

  50. Wong, N. C. & Hall, J. L. Servo control of amplitude modulation in frequency-modulation spectroscopy: demonstration of shot-noise-limited detection. J. Opt. Soc. Am. B 2, 1527–1533 (1985).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This silicon cavity work was supported and developed jointly by the Centre for Quantum Engineering and Space-Time Research (QUEST), the Physikalisch-Technische Bundesanstalt (PTB), the JILA Physics Frontier Center (NSF) and the National Institute of Standards and Technology (NIST). The authors thank R. Lalezari of ATF for the coating of the silicon mirrors and Y. Lin of JILA for the initial finesse measurements. The authors also thank M. Notcutt and R. Fox for technical assistance with the construction of the second reference cavity. U. Kuetgens and D. Schulze are thanked for X-ray orientation of the spacer and mirrors, and G. Grosche for technical assistance with fibre noise cancellation. J. Ye thanks the Alexander von Humboldt Foundation for support.

Author information

Authors and Affiliations

Authors

Contributions

U.S., L.C., F.R. and J.Y. designed the silicon cavity. T.K., C.H., M.J.M., T.L., U.S., J.Y. and F.R. devised the measurements. T.K., C.H., M.J.M. and T.L. performed the experiments. T.K., C.H., M.J.M., T.L. and C.G. analysed and discussed the data. T.K., C.H., M.J.M., T.L., J.Y., U.S. and F.R. wrote the manuscript.

Corresponding authors

Correspondence to F. Riehle or J. Ye.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kessler, T., Hagemann, C., Grebing, C. et al. A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity. Nature Photon 6, 687–692 (2012). https://doi.org/10.1038/nphoton.2012.217

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2012.217

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing