Thermal noise and mechanical loss of SiO2/Ta2O5 optical coatings at cryogenic temperatures
Open accessAbstract
Mechanical loss of dielectric mirror coatings sets fundamental limits for both gravitational wave detectors and cavity-stabilized optical local oscillators for atomic clocks. Two approaches are used to determine the mechanical loss: ringdown measurements of the coating quality factor and direct measurement of the coating thermal noise. Here we report a systematic study of the mirror thermal noise at 4, 16, 124, and 300 K by operating reference cavities at these temperatures. The directly measured thermal noise is used to extract the mechanical loss for S i O 2 / T a 2 O 5 coatings, which are compared with previously reported values.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Silicon dioxide (SiO2) is the most commonly used material to fabricate dielectric mirrors.
“The most commonly used material to fabricate dielectric mirrors is silicon dioxide (SiO2).”
From Metal Oxide Thin Films for Advanced Photonic Applications (2026) · cites this paper as [30]
The introduction (p. 1) says SiO2 and Ta2O5 are the most common choices for the low- and high-refractive-index layers of highly reflective optical coatings, respectively. This supports SiO2 as a common mirror-coating material, but not the claim that it alone is the most commonly used material for dielectric mirrors. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe SiO2/TiO2 pair offers the largest optical contrast, making it suitable for high-reflectance dielectric mirrors with a smaller number of pairs and sharper stopbands.
“However, the pair SiO2/TiO2 offers the largest optical contrast, rendering it perfect for high-reflectance dielectric mirrors with a smaller number of pairs and sharper stopbands.”
From Metal Oxide Thin Films for Advanced Photonic Applications (2026) · cites this paper as [30]
The introduction (p. 1) says highly reflective coatings stack materials with high and low refractive indices, but identifies SiO2/Ta2O5—not SiO2/TiO2—as the common pair. Searches for SiO2/TiO2, optical contrast, pair count, and stopbands found no passage assessing the claimed advantages of SiO2/TiO2. (LLM, conf=0.77)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Exploring the sensitivity of next generation gravitational wave detectors
Abbott, B. P., Abbott, R., Abbott, T. D., Abernathy, M. R., Ackley, K., Adams, C., Addesso, P., Adhikari, R. X., Adya, V. B., Affeldt, C., et al. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa51f4 · Cited by 1,228 · see citing works
Calculated elastic constants for stress problems associated with semiconductor devices
Brantley, W. A. (1973) · Journal of Applied Physics · doi:10.1063/1.1661935 · Cited by 1,204 · see citing works
A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity
Keßler, T., Hagemann, C., Grebing, C., Legero, T., Sterr, U., Riehle, F., Martin, M. J., Chen, L., & Ye, J. (2012) · Nature Photonics · doi:10.1038/nphoton.2012.217 · Cited by 755 · see citing works
Self-citation1.5 μ m Lasers with Sub-10 mHz Linewidth
Matei, D. G., Legero, T., Häfner, S., Grebing, C., Weyrich, R., Zhang, W., Sonderhouse, L., Robinson, J. M., Ye, J., Riehle, F., et al. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.263202 · Cited by 575 · see citing works
Self-citationThermal-Noise Limit in the Frequency Stabilization of Lasers with Rigid Cavities
Numata, K., Kemery, A., & Camp, J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.250602 · Cited by 556 · see citing works
Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks
Oelker, E., Hutson, R. B., Kennedy, C. J., Sonderhouse, L., Bothwell, T., Goban, A., Kedar, D., Sanner, C., Robinson, J. M., Marti, G. E., et al. (2019) · Nature Photonics · doi:10.1038/s41566-019-0493-4 · Cited by 475 · see citing works
Self-citationTenfold reduction of Brownian noise in high-reflectivity optical coatings
Cole, G. D., Zhang, W., Martin, M. J., Ye, J., & Aspelmeyer, M. (2013) · Nature Photonics · doi:10.1038/nphoton.2013.174 · Cited by 381 · see citing works
Self-citationThermal noise in interferometric gravitational wave detectors due to dielectric optical coatings
Harry, G. M., Gretarsson, A. M., Saulson, P. R., Kittelberger, S. E., Penn, S., Startin, W. J., Rowan, S., Fejer, M. M., Crooks, D. R. M., Gianpietro Cagnoli, C., et al. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/5/305 · Cited by 337 · see citing works
Bothwell, T., Kedar, D., Oelker, E., Robinson, J. M., Bromley, S. L., Tew, W. L., Ye, J., & Kennedy, C. J. (2019) · Metrologia · doi:10.1088/1681-7575/ab4089 · Cited by 324 · see citing works
Self-citationHigh-performance near- and mid-infrared crystalline coatings
Cole, G. D., Zhang, W., Bjork, B., Follman, D., Heu, P., Deutsch, C., Sonderhouse, L., Robinson, J. M., Franz, C., Alexandrovski, A. L., et al. (2016) · Optica · doi:10.1364/optica.3.000647 · Cited by 181 · see citing works
Self-citationCrystalline optical cavity at 4 K with thermal-noise-limited instability and ultralow drift
Robinson, J. M., Oelker, E. G., Milner, W. R., Zhang, W., Legero, T., Matei, D. G., Riehle, F., Sterr, U., & Ye, J. (2019) · Optica · doi:10.1364/optica.6.000240 · Cited by 170 · see citing works
Self-citationThermal noise from optical coatings in gravitational wave detectors
Harry, G. M., Armandula, H., Black, E. D., Crooks, D. R. M., Gianpietro Cagnoli, C., Hough, J., Murray, P. G., Reid, S. D., Rowan, S., Sneddon, P. H., et al. (2006) · Applied Optics · doi:10.1364/ao.45.001569 · Cited by 147 · see citing works
Ultrastable Silicon Cavity in a Continuously Operating Closed-Cycle Cryostat at 4 K
Zhang, W., Robinson, J. M., Sonderhouse, L., Oelker, E. G., Benko, C., Hall, J. L., Legero, T., Matei, D. G., Riehle, F., Sterr, U., et al. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.243601 · Cited by 131 · see citing works
Self-citationMeasurement of quantum back action in the audio band at room temperature
Cripe, J., Aggarwal, N., Lanza, R. K., Libson, A., Singh, R., Heu, P., Follman, D., Cole, G. D., Mavalvala, N., & Corbitt, T. R. (2019) · Nature · doi:10.1038/s41586-019-1051-4 · Cited by 90 · see citing works
Effect of heat treatment on mechanical dissipation in Ta 2 O 5 coatings
Martin, I. W., Bassiri, R., Nawrodt, R., Fejer, M. M., Gretarsson, A., Gustafson, E. K., Harry, G. M., Hough, J., MacLaren, I., Penn, S., et al. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/22/225020 · Cited by 84 · see citing works
Brownian thermal noise in multilayer coated mirrors
Hong, T. F., Yang, H., Gustafson, E. K., Adhikari, R. X., & Chen, Y. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.082001 · Cited by 81 · see citing works
High mechanical Q-factor measurements on silicon bulk samples
Nawrodt, R., Zimmer, A., Koettig, T., Schwarz, C. J., Heinert, D., Hudl, M., Neubert, R., Thürk, M., Nietzsche, S., Vodel, W., et al. (2008) · Journal of Physics Conference Series · doi:10.1088/1742-6596/122/1/012008 · Cited by 75 · see citing works
First cryogenic test operation of underground km-scale gravitational-wave observatory KAGRA
Akutsu, T., Ando, M., Arai, K., Arai, Y., Araki, S., Araya, A., Aritomi, N., Asada, H., Aso, Y., Atsuta, S., et al. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab28a9 · Cited by 63 · see citing works
Measurement of the mechanical loss of a cooled reflective coating for gravitational wave detection
Yamamoto, K., Miyoki, S., Uchiyama, T., Ishitsuka, H., Ohashi, M., Kuroda, K., Tomaru, T., Sato, N., Suzuki, T., Haruyama, T., et al. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.022002 · Cited by 59 · see citing works
Operating a 87 Sr optical lattice clock with high precision and at high density
Swallows, M. D., Martin, M. J., Bishof, M., Benko, C., Lin, Y., Blatt, S., Rey, A. M., & Ye, J. (2012) · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · doi:10.1109/tuffc.2012.2210 · Cited by 46 · see citing works
Self-citationDirect measurement of coating thermal noise in optical resonators
Gras, S., & Evans, M. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.122001 · Cited by 44 · see citing works
High-Reflection Coatings for Gravitational-Wave Detectors:State of The Art and Future Developments
Amato, A., Gianpietro Cagnoli, C., Canepa, M., Coillet, É., Degallaix, J., Dolique, V., Forest, D., Granata, M., Martinez, V., Michel, C., et al. (2018) · Journal of Physics Conference Series · doi:10.1088/1742-6596/957/1/012006 · Cited by 42 · see citing works
Mirror Coating Solution for the Cryogenic Einstein Telescope
Craig, K., Steinlechner, J., Murray, P. G., Bell, A. S., Birney, R., Haughian, K., Hough, J., MacLaren, I., Penn, S., Reid, S. D., et al. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.231102 · Cited by 42 · see citing works
Crooks, D. R. M., Gianpietro Cagnoli, C., Fejer, M. M., Harry, G. M., Hough, J., Khuri-Yakub, B. T., Penn, S., Route, R. K., Rowan, S., Sneddon, P. H., et al. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/15/014 · Cited by 41 · see citing works
Häfner, S., Herbers, S., Vogt, S., Lisdat, C., & Sterr, U. (2020) · Optics Express · doi:10.1364/oe.390105 · Cited by 37 · see citing works
Self-citationMeasurement of the intrinsic mechanical loss of low-loss samples using a nodal support
Numata, K., Bianc, G. B., Ohishi, N., Sekiya, A., Otsuka, S., Kawabe, K., Ando, M., & Tsubono, K. (2000) · Physics Letters A · doi:10.1016/s0375-9601(00)00646-0 · Cited by 35 · see citing works
Granata, M., Craig, K., Gianpietro Cagnoli, C., Carcy, C., Cunningham, W. R., Degallaix, J., Flaminio, R., Forest, D., Hart, M. J., Hennig, J., et al. (2013) · Optics Letters · doi:10.1364/ol.38.005268 · Cited by 35 · see citing works
A second generation of low thermal noise cryogenic silicon resonators
Matei, D. G., Legero, T., Grebing, C., Häfner, S., Lisdat, C., Weyrich, R., Zhang, W., Sonderhouse, L., Robinson, J. M., Riehle, F., et al. (2016) · Journal of Physics Conference Series · doi:10.1088/1742-6596/723/1/012031 · Cited by 32 · see citing works
Self-citationCryogenically cooled ultra low vibration silicon mirrors for gravitational wave observatories
Shapiro, B., Adhikari, R. X., Aguiar, O. D., Bonilla, E. C., Fan, D., Gan, L., Gomez, I., Khandelwal, S., Lantz, B. T., MacDonald, T., et al. (2016) · Cryogenics · doi:10.1016/j.cryogenics.2016.12.004 · Cited by 27 · see citing works
Broadband measurement of coating thermal noise in rigid Fabry–Pérot cavities
Chalermsongsak, T., Seifert, F., Hall, E. D., Arai, K., Gustafson, E. K., & Adhikari, R. X. (2014) · Metrologia · doi:10.1088/0026-1394/52/1/17 · Cited by 12 · see citing works
High-precision laser stabilization via optical cavities
Martin, M. J., & Ye, J. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9780511762314.017 · Cited by 7 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 5
- [18]18. M. D. Swallows, M. J. Martin, M. Bishof, C. Benko, Y. Lin, S. Blatt, A. M. Rey, and J. Ye, IEEE Transactions on Ultrason. Ferroelectr. Freq. Control. 59 , 416 (2012).
- [21]21. R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P . Seidel, and A. Tünnermann, J. Physics: Conf. Ser. 122 , 012008 (2008).
- [25]25. P. Klocek, Handbook of infrared optical materials (CRC Press, 1991).
- [28]28. A. Amato, G. Cagnoli, M. Canepa, E. Coillet, J. Degallaix, V. Dolique, D. Forest, M. Granata, V. Martinez, C. Michel, L. Pinard, B. Sassolas, and J. Teillon, J. Physics: Conf. Ser. 957 , 012006 (2018).
- [33]33. R. Robie, 'Characterisation of the mechanical properties of thin-film mirror coating materials for use in future interferometric gravitational wave detectors,' Ph.D. thesis, University of Glasgow (2018).
Cited by
Sorted by citations
Frequency stability of cryogenic silicon cavities with semiconductor crystalline coatings
Kedar, D., Yu, J., Oelker, E. G., Staron, A. L., Milner, W. R., Robinson, J. M., Legero, T., Riehle, F., Sterr, U., & Ye, J. (2023) · Optica · doi:10.1364/optica.479462 · Cited by 63 · see citing works
Self-citationExcess Noise and Photoinduced Effects in Highly Reflective Crystalline Mirror Coatings
Yu, J., Häfner, S., Legero, T., Herbers, S., Nicolodi, D., Ma, C. Y., Riehle, F., Sterr, U., Kedar, D., Robinson, J. M., et al. (2023) · Physical Review X · doi:10.1103/physrevx.13.041002 · Cited by 41 · see citing works
Self-citationFrequency Stability of 2.5 × 10 − 17 from a Si Cavity with AlGaAs Crystalline Mirrors
Lee, D., Hu, Z. Z., Lewis, B., Aeppli, A., Kim, K., Yao, Z., Legero, T., Nicolodi, D., Riehle, F., Sterr, U., et al. (2025) · Physical Review Letters · doi:10.1103/zgrm-cjbb · Cited by 20 · see citing works
Self-citationAn ultrastable 1397-nm laser stabilized by a crystalline-coated room-temperature cavity
Zhu, X.-Q., Cui, X.-Y., Kong, D.-Q., Yu, H.-W., Zhai, X., Zheng, M.-Y., Xie, X.-P., Zhang, Q., Jiang, X. Q., Zhang, X., et al. (2024) · Review of Scientific Instruments · doi:10.1063/5.0200553 · Cited by 12 · see citing works
Chen, Z.-A., Zeng, H.-R., Wang, W., Zhang, H., Lei, R.-Q., Li, J., Pang, C.-Y., Huang, S.-S., & Zhang, X. (2025) · 中国科学通报:英文版 · doi:10.1016/j.scib.2025.08.050 · Cited by 11 · see citing works
Thermal Noise in Cubic Optical Cavities
Xu, G., Jiao, D., Chen, L., Zhang, L., Dong, R., Liu, T., & Wang, J. (2021) · Photonics · doi:10.3390/photonics8070261 · Cited by 10 · see citing works
Transportable single-crystal silicon ultra-stable cavity toward space applications
Zhu, X.-Q., Zhai, X., Xie, Y. J., Yuan, M., Yu, H.-W., Kong, D.-Q., Song, W.-L., Zhang, Y., Hu, Y. B., Cui, X.-Y., et al. (2025) · Optica · doi:10.1364/optica.568436 · Cited by 6 · see citing works
Jiao, D., Gao, J., Zhang, L., Deng, X., Zang, Q., Xu, G., Dong, R., Liu, T., & Zhang, S. (2023) · Optics Communications · doi:10.1016/j.optcom.2023.129459 · Cited by 4 · see citing works
Detecting ultrathin ice on materials for optical coatings at cryogenic temperatures
Magnozzi, M., Bisio, F., Gemme, G., Granata, M., Michel, C., Pinard, L., & Canepa, M. (2023) · Journal of Physics D Applied Physics · doi:10.1088/1361-6463/acef35 · Cited by 4 · see citing works
Metal Oxide Thin Films for Advanced Photonic Applications
Stîngescu, M.-L., Șopronyi, M.-A., Antohe, Ș., & Scărișoreanu, N.-D. (2026) · Crystals · doi:10.3390/cryst16030164 · Cited by 2 · see citing works
Performance manipulation of the squeezed coherent light source based on four-wave mixing
Jin, L. (2021) · Optics Express · doi:10.1364/oe.435735 · Cited by 2 · see citing works
Optimization of thermal noise propagation and mechanical properties at composite material interfaces
Liu, X., Liu, M., Xu, J., Ai, Q., & Shuai, Y. (2025) · International Journal of Thermal Sciences · doi:10.1016/j.ijthermalsci.2025.110106 · Cited by 2 · see citing works
Mechanical loss and stability analysis of NEXCERA in ultra-stable optical cavities
Wagner, N., Narożnik, M., Bober, M., Sauer, S., Zawada, M., & Kroker, S. (2025) · Journal of the Optical Society of America B · doi:10.1364/josab.578004 · Cited by 2 · see citing works
Molecular dynamics study of the effect of substrate temperature on the properties of SiO2 thin films
Grigoriev, F. V., Sulimov, V. B., & Tikhonravov, A. V. (2025) · Physica B Condensed Matter · doi:10.1016/j.physb.2025.418035 · Cited by 1 · see citing works
Optical-Comb-Based Frequency Stability Transfer Across the Spectrum With a Multichannel FPGA
Savio, P., Goti, I., Pizzocaro, M., Levi, F., Calonico, D., & Clivati, C. (2025) · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · doi:10.1109/tuffc.2025.3526761 · Cited by 1 · see citing works
Research on Brownian Thermal Noise Limit of a Cylindrical Ultra-Stable Cavity with Support Pads
Jiao, D., Xu, G., Zhang, L., Gao, J., Li, Y., Dong, R., Liu, T., & Zhang, S. (2022) · Crystals · doi:10.3390/cryst12111682 · Cited by 1 · see citing works
Coherent noise suppression at high-efficiency wavelength doubling for high-precision experiments
Gurs, J., Korobko, M., Darsow-Fromm, C., Steinlechner, S., & Schnabel, R. (2024) · Optics & Laser Technology · doi:10.1016/j.optlastec.2024.112179 · Cited by 1 · see citing works
Zjawin, B., Bober, M., Ciuryło, R., Lisak, D., Zawada, M., & Wcisło, P. (2021) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/ac3da3
Gao, J., Jiao, D., Zhang, L., Xu, G., Deng, X., Zang, Q., Yang, H., Dong, R., Liu, T., & Zhang, S. (2023) · Open Physics · doi:10.1515/phys-2022-0269
Modeling a convex–concave ultra-stable optical cavity
Vartehparvar, O., Narożnik, M., Bober, M., & Zawada, M. (2025) · Journal of the Optical Society of America B · doi:10.1364/josab.575040
Nela, A., Buchovska, I., Cumming, A., Dicorato, M., Dugmore, S. K., Graham, V., Haughian, K., Hammond, G. D., Hough, J., Jones, R., et al. (2026) · Journal of Physics Conference Series · doi:10.1088/1742-6596/3177/1/012109
Cordierite-based optical resonators with extremely low thermal expansion
Wagner, N., Legero, T., & Kroker, S. (2026) · Optical Materials Express · doi:10.1364/ome.599638
Self-citationCole, G., Legero, T., Sterr, U., Lee, D., Ye, J., Gretarsson, A. M., Harry, G. M., Penn, S., Pinard, L., Menoni, C. S., et al. (2026) · Optica · doi:10.1364/optica.601572
Self-citation
- Authors
- Robinson, J. M., Oelker, E., Milner, W. R., Kedar, D., Zhang, W., Legero, T., Matei, D. G., Häfner, S., Riehle, F., Sterr, U., & Ye, J.
- Affiliations
- Joint Institute for Laboratory Astrophysics (US)
- Physikalisch-Technische Bundesanstalt (DE)
- ORCID
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2021-01-25
- Volume
- 46
- Issue
- 3
- Pages
- 592
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W3101593409
- Cited by
- 23
- References
- 31
- Citations by year
- 2026: 3 · 2025: 9 · 2024: 2 · 2023: 5 · 2022: 1 · 2021: 3
- FWCI
- 0.92
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- National Science Foundation (QLCI 2016244)
- Defense Advanced Research Projects Agency
- National Institute of Standards and Technology
- PTB
- Deutsche Forschungsgemeinschaft (EXC-2123 Quantum Frontiers)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Mechanical and Optical Resonators
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Pulsars and Gravitational Waves Research
- Physical Sciences › Materials Science › Surfaces, Coatings and Films › Optical Coatings and Gratings
- Keywords
- thermal noise, mechanical losses, dielectric mirror coatings, cryogenic temperatures, quality factor, ringdown, reference cavity, gravitational wave detectors, optical local oscillator, atomic clocks
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review