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
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 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
References
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).
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).
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).
Harry, G. M. et al. Thermal noise from optical coatings in gravitational wave detectors. Appl. Opt. 45, 1569–1574 (2006).
Abbott, B. P. et al. LIGO: the laser interferometer gravitational-wave observatory. Rep. Prog. Phys. 72, 076901 (2009).
Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005).
Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).
Abbott, B. et al. Observation of a kilogram-scale oscillator near its quantum ground state. New J. Phys. 11, 073032 (2009).
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).
Numata, K., Kemery, A. & Camp, J. Thermal-noise limit in the frequency stabilization of lasers with rigid cavities. Phys. Rev. Lett. 93, 250602 (2004).
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).
Kessler, T., Legero, T. & Sterr, U. Thermal noise in optical cavities revisited. J. Opt. Soc. Am. B 29, 178–184 (2012).
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).
Young, B. C., Cruz, F. C., Itano, W. M. & Bergquist, J. C. Visible lasers with subhertz linewidths. Phys. Rev. Lett. 82, 3799–3802 (1999).
Jiang, Y. Y. et al. Making optical atomic clocks more stable with 10−16 level laser stabilization.Nature Photon. 5, 158–161 (2011).
Kimble, H. J., Lev, B. L. & Ye, J. Optical interferometers with reduced sensitivity to thermal noise. Phys. Rev. Lett. 101, 260602 (2008).
Millo, J. et al. Ultrastable lasers based on vibration insensitive cavities. Phys. Rev. A 79, 053829 (2009).
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).
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).
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).
Nietzsche, S. et al. Cryogenic Q-factor measurement of optical substrates for optimization of gravitational wave detectors. Supercond. Sci. Technol. 19, S293–S296 (2006).
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).
Schnabel, R. et al. Building blocks for future detectors: silicon test masses and 1550 nm laser light. J. Phys. Conf. Ser. 228, 012029 (2010).
Petersen, K. E. Silicon as a mechanical material. Proc. IEEE 70, 420–457 (1982).
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).
Brantley, W. A. Calculated elastic constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44, 534–535 (1973).
Nawrodt, R. et al. A new apparatus for mechanical Q-factor measurements between 5 and 300 K. Cryogenics 46, 718–723 (2006).
Harry, G. M. et al. Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings. Class. Quantum Grav. 19, 897–917 (2002).
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).
Nazarova, T., Riehle, F. & Sterr, U. Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser. Appl. Phys. B 83, 531–536 (2006).
Webster, S. A., Oxborrow, M. & Gill, P. Vibration insensitive optical cavity. Phys. Rev. A 75, 011801(R) (2007).
Drever, R. W. P. et al. Laser phase and frequency stabilization using an optical resonator. Appl. Phys. B 31, 97–105 (1983).
Glazov, V. & Pashinkin, A. The thermophysical properties (heat capacity and thermal expansion) of single-crystal silicon. High Temperature 39, 443–449 (2001).
Webster, S. & Gill, P. Force-insensitive optical cavity. Opt. Lett. 36, 3572–3574 (2011).
Gray, J. E. & Allan, D. W. in Proc. 28th Frequency Control Symposium 243–246 (1974).
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).
Rubiola, E. On the measurement of frequency and of its sample variance with high-resolution counters. Rev. Sci. Instrum. 76, 054703 (2005).
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).
Allan, D. W. & Barnes, J. in Proceedings of the 35th Annual Frequency Control Symposium, 470–475 (Electronic Industries Association, 1981).
Greenhall, C. & Riley, W. in Proc. 2003 PTTI Meeting 267–280 (2003).
Riley, W. & Greenhall, C. Power law noise identification using the lag 1 autocorrelation. IEEE Trans. Instrum. Meas. 2004, 576–580 (2004).
Premoli, A. & Tavella, P. A revisited three-cornered hat method for estimating frequency standard instability. IEEE Trans. Instrum. Meas. 42, 7–13 (1993).
Swallows, M. D. et al. Suppression of collisional shifts in a strongly interacting lattice clock. Science 331, 1043–1046 (2011).
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).
Hartnett, J. G., Nand, N. R. & Lu, C. Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators. Appl. Phys. Lett. 100, 183501 (2012).
Schibli, T. R. et al. Optical frequency comb with submillihertz linewidth and more than 10 W average power. Nature Photon. 2, 355–358 (2008).
Brückner, F. et al. Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal. Phys. Rev. Lett. 104, 163903 (2010).
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).
Chen, L. et al. Vibration-induced elastic deformation of Fabry–Pérot cavities. Phys. Rev. A 74, 053801 (2006).
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).
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
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
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2012.217
This article is cited by
-
Moderate-coherence sensing with optical cavities: ultra-high accuracy meets ultra-high measurement bandwidth and range
Communications Engineering (2024)
-
Experimental realization of a 12,000-finesse laser cavity based on a low-noise microstructured mirror
Communications Physics (2023)
-
A lab-based test of the gravitational redshift with a miniature clock network
Nature Communications (2023)
-
Red narrow-linewidth lasing and frequency comb from gain-switched self-injection-locked Fabry–Pérot laser diode
Scientific Reports (2023)
-
Temperature-dependent photo-elastic coefficient of silicon at 1550 nm
Scientific Reports (2023)