Fundamental limits and optimal estimation of the resonance frequency of a linear harmonic oscillator
All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we...
Saved in:
| Published in | Communications physics Vol. 4; no. 1; pp. 1 - 11 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Nature Publishing Group UK
15.09.2021
Nature Publishing Group Nature Portfolio |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈10
−5
for τ = 30 μs) and measurements using thermal fluctuations alone (<10
−6
). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.
Thermodynamic and quantum fluctuations limit the accuracy with which conventional methods can measure observables, often depending on the method chosen. Here, information theory is employed to determine the minimum uncertainty in the resonant frequency of a harmonic oscillator in a method-independent way. |
|---|---|
| AbstractList | All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically-driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically-limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈ 10-5 for τ=30μs) and measurements using thermal fluctuations alone (<10-6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically-driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically-limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈ 10-5 for τ=30μs) and measurements using thermal fluctuations alone (<10-6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains. All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈10 −5 for τ = 30 μs) and measurements using thermal fluctuations alone (<10 −6 ). Beyond nanomechanics, these results advance frequency-based metrology across physical domains. All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈10 −5 for τ = 30 μs) and measurements using thermal fluctuations alone (<10 −6 ). Beyond nanomechanics, these results advance frequency-based metrology across physical domains. Thermodynamic and quantum fluctuations limit the accuracy with which conventional methods can measure observables, often depending on the method chosen. Here, information theory is employed to determine the minimum uncertainty in the resonant frequency of a harmonic oscillator in a method-independent way. Thermodynamic and quantum fluctuations limit the accuracy with which conventional methods can measure observables, often depending on the method chosen. Here, information theory is employed to determine the minimum uncertainty in the resonant frequency of a harmonic oscillator in a method-independent way. All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈10−5 for τ = 30 μs) and measurements using thermal fluctuations alone (<10−6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.Thermodynamic and quantum fluctuations limit the accuracy with which conventional methods can measure observables, often depending on the method chosen. Here, information theory is employed to determine the minimum uncertainty in the resonant frequency of a harmonic oscillator in a method-independent way. All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically-driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically-limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈ 10 for ) and measurements using thermal fluctuations alone (<10 ). Beyond nanomechanics, these results advance frequency-based metrology across physical domains. |
| ArticleNumber | 207 |
| Author | Liu, Yuxiang Aksyuk, Vladimir A. Zhang, Rui Wang, Mingkang Ilic, Robert |
| Author_xml | – sequence: 1 givenname: Mingkang orcidid: 0000-0003-0418-4284 surname: Wang fullname: Wang, Mingkang organization: Microsystems and Nanotechnology Division, National Institute of Standards and Technology, Institute for Research in Electronics and Applied Physics, University of Maryland – sequence: 2 givenname: Rui surname: Zhang fullname: Zhang, Rui organization: Department of Mechanical Engineering, Worcester Polytechnic Institute – sequence: 3 givenname: Robert orcidid: 0000-0003-2504-4045 surname: Ilic fullname: Ilic, Robert organization: Microsystems and Nanotechnology Division, National Institute of Standards and Technology – sequence: 4 givenname: Yuxiang surname: Liu fullname: Liu, Yuxiang organization: Department of Mechanical Engineering, Worcester Polytechnic Institute – sequence: 5 givenname: Vladimir A. orcidid: 0000-0002-9653-4722 surname: Aksyuk fullname: Aksyuk, Vladimir A. email: vladimir.aksyuk@nist.gov organization: Microsystems and Nanotechnology Division, National Institute of Standards and Technology |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/38680632$$D View this record in MEDLINE/PubMed |
| BookMark | eNp9UcFu1TAQtFARLaU_wAFF4sIlsInt2DmiqoVKlbjA2fKz162fEvthO4f-Pc5LC6iHHqxd7c6MZj1vyUmIAQl538HnDqj8klkPwFvouxZAALTDK3LW03Fs6cDh5L_-lFzkvAeoUAaCDm_IKZWDhIH2Z8ReL8HqGUPRUzP52Zfc6GCbeCh-riPMay0-hia6ptxjkzDHoIPBxiX8vWAwD-tKV3ZAnZp7neYYvGliNn6adInpHXnt9JTx4rGek1_XVz8vv7e3P77dXH69bQ2TvLSD1TDiKKpN7SR3IzWWAddS7CSItZeasmpcSz06LgU3dEDGeuNA9HV3Tm42XRv1Xh1SdZ4eVNReHQcx3SmdijcTKkRAaZ3mOxRMUrtjzFgKYNjQMTd2VevTpnVIsV6Zi5p9NlgPChiXrCgwycb6hgr9-Ay6j0sK9VLVc9EL2g98RX14RC27Ge1fe09ZVIDcACbFnBM6ZXw5fn1J2k-qA7Umr7bkVY1THZNXq3b_jPqk_iKJbqRcweEO0z_bL7D-AHGovvM |
| CitedBy_id | crossref_primary_10_3390_math12243981 crossref_primary_10_1103_PhysRevA_105_053517 crossref_primary_10_1103_PhysRevX_13_011018 crossref_primary_10_1126_sciadv_adf7595 crossref_primary_10_1103_PhysRevApplied_19_054074 |
| Cites_doi | 10.1364/OE.20.018268 10.1021/acs.nanolett.9b04995 10.1063/1.1642738 10.1038/32373 10.1109/18.481776 10.1103/PhysRevB.61.9968 10.1038/nnano.2016.19 10.1063/1.1499745 10.1038/s41586-018-0861-0 10.1109/T-UFFC.1987.26997 10.1038/nmeth.2071 10.1103/PhysRevLett.118.221101 10.1038/nature16066 10.1038/srep30306 10.1126/science.aad2449 10.1063/1.1853631 10.1063/1.5093310 10.1038/ncomms3860 10.1186/1297-9686-31-3-269 10.1038/nnano.2009.152 10.1063/1.347347 10.1103/RevModPhys.82.1155 10.1109/29.45547 10.1038/nphoton.2015.139 10.1038/nmeth.1449 10.1038/nature02658 10.1017/CBO9781139179027 10.1016/j.mee.2007.01.232 10.1063/1.4975347 10.1126/science.aar5220 10.1007/BF02888835 10.1038/nnano.2012.42 |
| ContentType | Journal Article |
| Copyright | This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021 This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021 – notice: This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION NPM 3V. 7XB 88I 8FE 8FG 8FK ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ L6V M2P M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U 7X8 DOA |
| DOI | 10.1038/s42005-021-00700-6 |
| DatabaseName | Springer Nature OA Free Journals CrossRef PubMed ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection ProQuest Engineering Collection Science Database (ProQuest) Engineering Database ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection (ProQuest) ProQuest Central Basic MEDLINE - Academic DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef PubMed Publicly Available Content Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) MEDLINE - Academic |
| DatabaseTitleList | MEDLINE - Academic CrossRef Publicly Available Content Database PubMed |
| Database_xml | – sequence: 1 dbid: C6C name: Springer Nature OA Free Journals url: http://www.springeropen.com/ sourceTypes: Publisher – sequence: 2 dbid: DOA name: DOAJ (Directory of Open Access Journals) url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 3 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 4 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2399-3650 |
| EndPage | 11 |
| ExternalDocumentID | oai_doaj_org_article_ee0e8dfa5be7483db44cd300c4614f91 38680632 10_1038_s42005_021_00700_6 |
| Genre | Journal Article |
| GrantInformation_xml | – fundername: Intramural NIST DOC grantid: 9999-NIST |
| GroupedDBID | 0R~ 88I AAFWJ AAJSJ ABDBF ABJCF ABUWG ACGFS ACSMW ACUHS ADBBV ADMLS AFKRA AJTQC ALMA_UNASSIGNED_HOLDINGS AZQEC BCNDV BENPR BGLVJ C6C CCPQU DWQXO EBLON EBS GNUQQ GROUPED_DOAJ HCIFZ M2P M7S M~E NAO O9- OK1 PIMPY PTHSS RNT SNYQT AASML AAYXX AFPKN CITATION PHGZM PHGZT EJD H13 NPM PMFND 3V. 7XB 8FE 8FG 8FK AARCD L6V PKEHL PQEST PQGLB PQQKQ PQUKI PRINS Q9U 7X8 PUEGO |
| ID | FETCH-LOGICAL-c485t-6da09e97140af85f93cd405a87b807cd408a34806a8a9f5875c36e442cf0728a3 |
| IEDL.DBID | C6C |
| ISSN | 2399-3650 |
| IngestDate | Wed Aug 27 01:29:51 EDT 2025 Fri Jul 11 04:28:19 EDT 2025 Wed Aug 13 08:40:25 EDT 2025 Sat May 31 02:13:23 EDT 2025 Tue Jul 01 04:29:29 EDT 2025 Thu Apr 24 22:55:19 EDT 2025 Fri Feb 21 02:37:35 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c485t-6da09e97140af85f93cd405a87b807cd408a34806a8a9f5875c36e442cf0728a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| ORCID | 0000-0002-9653-4722 0000-0003-0418-4284 0000-0003-2504-4045 |
| OpenAccessLink | https://www.nature.com/articles/s42005-021-00700-6 |
| PMID | 38680632 |
| PQID | 2572732656 |
| PQPubID | 4669724 |
| PageCount | 11 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_ee0e8dfa5be7483db44cd300c4614f91 proquest_miscellaneous_3048494846 proquest_journals_2572732656 pubmed_primary_38680632 crossref_citationtrail_10_1038_s42005_021_00700_6 crossref_primary_10_1038_s42005_021_00700_6 springer_journals_10_1038_s42005_021_00700_6 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2021-09-15 |
| PublicationDateYYYYMMDD | 2021-09-15 |
| PublicationDate_xml | – month: 09 year: 2021 text: 2021-09-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationPlace | London |
| PublicationPlace_xml | – name: London – name: England |
| PublicationTitle | Communications physics |
| PublicationTitleAbbrev | Commun Phys |
| PublicationTitleAlternate | Commun Phys |
| PublicationYear | 2021 |
| Publisher | Nature Publishing Group UK Nature Publishing Group Nature Portfolio |
| Publisher_xml | – name: Nature Publishing Group UK – name: Nature Publishing Group – name: Nature Portfolio |
| References | Rugar, Budakian, Mamin, Chui (CR7) 2004; 430 Clerk, Devoret, Girvin, Marquardt, Schoelkopf (CR31) 2010; 82 Cleland, Roukes (CR12) 2002; 92 Sansa (CR15) 2016; 11 CR19 Lee, Lee, Lee, Nha (CR26) 2016; 6 Gavartin, Verlot, Kippenberg (CR14) 2013; 4 Campos (CR17) 1979; 30 Errico (CR21) 2015; 527 CR34 Tanaka (CR9) 2007; 84 Gelman, Carlin, Stern, Rubin (CR32) 2014 Hänggi, Ingold (CR33) 2005; 15 Liu, Miao, Aksyuk, Srinivasan (CR29) 2012; 20 Losby (CR3) 2015; 350 Smith, Joseph, Rieger, Lidke (CR24) 2010; 7 Malécot (CR18) 1999; 31 Naik, Hanay, Hiebert, Feng, Roukes (CR8) 2009; 4 Giessibl, Bielefeldt (CR10) 2000; 61 Sauer, Diao, Westwood-Bachman, Freeman, Hiebert (CR5) 2017; 7 Jacobs (CR30) 2014 Roy, Sauer, Westwood-Bachman, Venkatasubramanian, Hiebert (CR16) 2018; 360 Chaste (CR2) 2012; 7 Allan (CR28) 1987; 34 Cleland, Roukes (CR4) 1998; 392 Wang, Zhang, Ilic, Aksyuk, Liu (CR35) 2020; 20 Berni (CR25) 2015; 9 (CR1) 2017; 118 Albrecht, Grütter, Horne, Rugar (CR11) 1991; 69 Zhou, Handley, Carles, Harvey (CR22) 2019; 4 Rissanen (CR20) 1996; 42 Ekinci, Yang, Roukes (CR13) 2004; 95 Parthasarathy (CR23) 2012; 9 Kay (CR27) 1989; 37 Barnard, Zhang, Wiederhecker, Lipson, McEuen (CR6) 2019; 566 JJ Rissanen (700_CR20) 1996; 42 LIGO Scientific and Virgo Collaboration. (700_CR1) 2017; 118 M Sansa (700_CR15) 2016; 11 CS Smith (700_CR24) 2010; 7 J Chaste (700_CR2) 2012; 7 KL Ekinci (700_CR13) 2004; 95 AN Cleland (700_CR4) 1998; 392 FJ Giessibl (700_CR10) 2000; 61 AW Barnard (700_CR6) 2019; 566 G Malécot (700_CR18) 1999; 31 SK Roy (700_CR16) 2018; 360 700_CR19 A Gelman (700_CR32) 2014 TR Albrecht (700_CR11) 1991; 69 K Jacobs (700_CR30) 2014 700_CR34 P Hänggi (700_CR33) 2005; 15 AK Naik (700_CR8) 2009; 4 M Wang (700_CR35) 2020; 20 R Parthasarathy (700_CR23) 2012; 9 DW Allan (700_CR28) 1987; 34 AN Cleland (700_CR12) 2002; 92 S Kay (700_CR27) 1989; 37 AD Campos (700_CR17) 1979; 30 C Errico (700_CR21) 2015; 527 AA Berni (700_CR25) 2015; 9 Y Liu (700_CR29) 2012; 20 D Rugar (700_CR7) 2004; 430 Y Zhou (700_CR22) 2019; 4 S-Y Lee (700_CR26) 2016; 6 M Tanaka (700_CR9) 2007; 84 VTK Sauer (700_CR5) 2017; 7 JE Losby (700_CR3) 2015; 350 E Gavartin (700_CR14) 2013; 4 AA Clerk (700_CR31) 2010; 82 |
| References_xml | – volume: 20 start-page: 18268 year: 2012 end-page: 18280 ident: CR29 article-title: Wide cantilever stiffness range cavity optomechanical sensors for atomic force microscopy publication-title: Opt. Express, OE doi: 10.1364/OE.20.018268 – volume: 20 start-page: 3050 year: 2020 end-page: 3057 ident: CR35 article-title: Frequency Stabilization of Nanomechanical Resonators Using Thermally Invariant Strain Engineering publication-title: Nano Lett. doi: 10.1021/acs.nanolett.9b04995 – volume: 95 start-page: 2682 year: 2004 end-page: 2689 ident: CR13 article-title: Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems publication-title: J. Appl. Phys. doi: 10.1063/1.1642738 – volume: 392 start-page: 160 year: 1998 end-page: 162 ident: CR4 article-title: A nanometre-scale mechanical electrometer publication-title: Nature doi: 10.1038/32373 – volume: 42 start-page: 40 year: 1996 end-page: 47 ident: CR20 article-title: Fisher information and stochastic complexity publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.481776 – volume: 61 start-page: 9968 year: 2000 end-page: 9971 ident: CR10 article-title: Physical interpretation of frequency-modulation atomic force microscopy publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.61.9968 – volume: 11 start-page: 552 year: 2016 end-page: 558 ident: CR15 article-title: Frequency fluctuations in silicon nanoresonators publication-title: Nat. Nanotech doi: 10.1038/nnano.2016.19 – volume: 92 start-page: 2758 year: 2002 end-page: 2769 ident: CR12 article-title: Noise processes in nanomechanical resonators publication-title: J. Appl. Phys. doi: 10.1063/1.1499745 – volume: 566 start-page: 89 year: 2019 end-page: 93 ident: CR6 article-title: Real-time vibrations of a carbon nanotube publication-title: Nature doi: 10.1038/s41586-018-0861-0 – volume: 34 start-page: 647 year: 1987 end-page: 654 ident: CR28 article-title: Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators publication-title: IEEE Trans. Ultrason., Ferroelect., Freq. Contr. doi: 10.1109/T-UFFC.1987.26997 – volume: 9 start-page: 724 year: 2012 end-page: 726 ident: CR23 article-title: Rapid, accurate particle tracking by calculation of radial symmetry centers publication-title: Nat. Methods doi: 10.1038/nmeth.2071 – year: 2014 ident: CR32 – volume: 118 start-page: 221101 year: 2017 ident: CR1 article-title: GW170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.118.221101 – volume: 527 start-page: 499 year: 2015 end-page: 502 ident: CR21 article-title: Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging publication-title: Nature doi: 10.1038/nature16066 – volume: 6 start-page: 30306 year: 2016 ident: CR26 article-title: Quantum phase estimation using path-symmetric entangled states publication-title: Sci. Rep. doi: 10.1038/srep30306 – volume: 350 start-page: 798 year: 2015 end-page: 801 ident: CR3 article-title: Torque-mixing magnetic resonance spectroscopy publication-title: Science doi: 10.1126/science.aad2449 – volume: 15 start-page: 026105 year: 2005 ident: CR33 article-title: Fundamental aspects of quantum Brownian motion publication-title: Chaos doi: 10.1063/1.1853631 – ident: CR19 – volume: 4 start-page: 060901 year: 2019 ident: CR22 article-title: Advances in 3D single particle localization microscopy publication-title: APL Photonics doi: 10.1063/1.5093310 – volume: 4 year: 2013 ident: CR14 article-title: Stabilization of a linear nanomechanical oscillator to its thermodynamic limit publication-title: Nat. Commun. doi: 10.1038/ncomms3860 – volume: 31 year: 1999 ident: CR18 article-title: Statistical methods and the subjective basis of scientific knowledge publication-title: Genet. Selection Evolution doi: 10.1186/1297-9686-31-3-269 – volume: 4 start-page: 445 year: 2009 end-page: 450 ident: CR8 article-title: Towards single-molecule nanomechanical mass spectrometry publication-title: Nat. Nanotech doi: 10.1038/nnano.2009.152 – volume: 69 start-page: 668 year: 1991 end-page: 673 ident: CR11 article-title: Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity publication-title: J. Appl. Phys. doi: 10.1063/1.347347 – volume: 82 start-page: 1155 year: 2010 end-page: 1208 ident: CR31 article-title: Introduction to quantum noise, measurement, and amplification publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.82.1155 – volume: 37 start-page: 1987 year: 1989 end-page: 1990 ident: CR27 article-title: A fast and accurate single frequency estimator publication-title: IEEE Trans. Acoust., Speech, Signal Process. doi: 10.1109/29.45547 – volume: 9 start-page: 577 year: 2015 end-page: 581 ident: CR25 article-title: Ab initio quantum-enhanced optical phase estimation using real-time feedback control publication-title: Nat. Photonics doi: 10.1038/nphoton.2015.139 – volume: 7 start-page: 373 year: 2010 end-page: 375 ident: CR24 article-title: Fast, single-molecule localization that achieves theoretically minimum uncertainty publication-title: Nat. Methods doi: 10.1038/nmeth.1449 – volume: 430 start-page: 329 year: 2004 end-page: 332 ident: CR7 article-title: Single spin detection by magnetic resonance force microscopy publication-title: Nature doi: 10.1038/nature02658 – year: 2014 ident: CR30 doi: 10.1017/CBO9781139179027 – volume: 84 start-page: 1341 year: 2007 end-page: 1344 ident: CR9 article-title: An industrial and applied review of new MEMS devices features publication-title: Microelectron. Eng. doi: 10.1016/j.mee.2007.01.232 – volume: 7 start-page: 015115 year: 2017 ident: CR5 article-title: Single laser modulated drive and detection of a nano-optomechanical cantilever publication-title: AIP Adv. doi: 10.1063/1.4975347 – volume: 360 start-page: eaar5220 year: 2018 ident: CR16 article-title: Improving mechanical sensor performance through larger damping publication-title: Science doi: 10.1126/science.aar5220 – ident: CR34 – volume: 30 start-page: 65 year: 1979 end-page: 70 ident: CR17 article-title: An extension of the Cramér-Rao inequality for the sequential case publication-title: Trabajos de. Estad. y. de. Investigacion Operativa doi: 10.1007/BF02888835 – volume: 7 start-page: 301 year: 2012 end-page: 304 ident: CR2 article-title: A nanomechanical mass sensor with yoctogram resolution publication-title: Nat. Nanotech doi: 10.1038/nnano.2012.42 – volume: 118 start-page: 221101 year: 2017 ident: 700_CR1 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.118.221101 – volume: 7 start-page: 015115 year: 2017 ident: 700_CR5 publication-title: AIP Adv. doi: 10.1063/1.4975347 – volume: 392 start-page: 160 year: 1998 ident: 700_CR4 publication-title: Nature doi: 10.1038/32373 – volume: 37 start-page: 1987 year: 1989 ident: 700_CR27 publication-title: IEEE Trans. Acoust., Speech, Signal Process. doi: 10.1109/29.45547 – volume-title: Bayesian data analysis year: 2014 ident: 700_CR32 – volume-title: Quantum Measurement Theory and its Applications year: 2014 ident: 700_CR30 doi: 10.1017/CBO9781139179027 – volume: 7 start-page: 301 year: 2012 ident: 700_CR2 publication-title: Nat. Nanotech doi: 10.1038/nnano.2012.42 – volume: 9 start-page: 577 year: 2015 ident: 700_CR25 publication-title: Nat. Photonics doi: 10.1038/nphoton.2015.139 – volume: 6 start-page: 30306 year: 2016 ident: 700_CR26 publication-title: Sci. Rep. doi: 10.1038/srep30306 – volume: 15 start-page: 026105 year: 2005 ident: 700_CR33 publication-title: Chaos doi: 10.1063/1.1853631 – volume: 360 start-page: eaar5220 year: 2018 ident: 700_CR16 publication-title: Science doi: 10.1126/science.aar5220 – volume: 527 start-page: 499 year: 2015 ident: 700_CR21 publication-title: Nature doi: 10.1038/nature16066 – volume: 430 start-page: 329 year: 2004 ident: 700_CR7 publication-title: Nature doi: 10.1038/nature02658 – volume: 95 start-page: 2682 year: 2004 ident: 700_CR13 publication-title: J. Appl. Phys. doi: 10.1063/1.1642738 – volume: 4 start-page: 060901 year: 2019 ident: 700_CR22 publication-title: APL Photonics doi: 10.1063/1.5093310 – volume: 82 start-page: 1155 year: 2010 ident: 700_CR31 publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.82.1155 – volume: 7 start-page: 373 year: 2010 ident: 700_CR24 publication-title: Nat. Methods doi: 10.1038/nmeth.1449 – volume: 11 start-page: 552 year: 2016 ident: 700_CR15 publication-title: Nat. Nanotech doi: 10.1038/nnano.2016.19 – volume: 92 start-page: 2758 year: 2002 ident: 700_CR12 publication-title: J. Appl. Phys. doi: 10.1063/1.1499745 – volume: 69 start-page: 668 year: 1991 ident: 700_CR11 publication-title: J. Appl. Phys. doi: 10.1063/1.347347 – volume: 9 start-page: 724 year: 2012 ident: 700_CR23 publication-title: Nat. Methods doi: 10.1038/nmeth.2071 – volume: 4 year: 2013 ident: 700_CR14 publication-title: Nat. Commun. doi: 10.1038/ncomms3860 – volume: 20 start-page: 18268 year: 2012 ident: 700_CR29 publication-title: Opt. Express, OE doi: 10.1364/OE.20.018268 – volume: 30 start-page: 65 year: 1979 ident: 700_CR17 publication-title: Trabajos de. Estad. y. de. Investigacion Operativa doi: 10.1007/BF02888835 – volume: 31 year: 1999 ident: 700_CR18 publication-title: Genet. Selection Evolution doi: 10.1186/1297-9686-31-3-269 – volume: 350 start-page: 798 year: 2015 ident: 700_CR3 publication-title: Science doi: 10.1126/science.aad2449 – volume: 61 start-page: 9968 year: 2000 ident: 700_CR10 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.61.9968 – volume: 34 start-page: 647 year: 1987 ident: 700_CR28 publication-title: IEEE Trans. Ultrason., Ferroelect., Freq. Contr. doi: 10.1109/T-UFFC.1987.26997 – ident: 700_CR34 – volume: 84 start-page: 1341 year: 2007 ident: 700_CR9 publication-title: Microelectron. Eng. doi: 10.1016/j.mee.2007.01.232 – ident: 700_CR19 – volume: 4 start-page: 445 year: 2009 ident: 700_CR8 publication-title: Nat. Nanotech doi: 10.1038/nnano.2009.152 – volume: 42 start-page: 40 year: 1996 ident: 700_CR20 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.481776 – volume: 566 start-page: 89 year: 2019 ident: 700_CR6 publication-title: Nature doi: 10.1038/s41586-018-0861-0 – volume: 20 start-page: 3050 year: 2020 ident: 700_CR35 publication-title: Nano Lett. doi: 10.1021/acs.nanolett.9b04995 |
| SSID | ssj0002140736 |
| Score | 2.2316558 |
| Snippet | All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses... Thermodynamic and quantum fluctuations limit the accuracy with which conventional methods can measure observables, often depending on the method chosen. Here,... |
| SourceID | doaj proquest pubmed crossref springer |
| SourceType | Open Website Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1 |
| SubjectTerms | 639/766/530/2804 639/925/927 Bandwidths Fisher information Frequency analysis Frequency measurement Harmonic oscillators Information theory Lower bounds Maximum likelihood estimators Noise Oscillators Perturbation Physics Physics and Astronomy Resonance Resonant frequencies Silicon nitride Uncertainty |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9wgEEZVTrlUrfryNo2IlFtrLQaM8bGpuooipadE2hsaYzht7Wq9e8i_74zxOlv1dcnNAoxgGJhvNMwHY5dSxgjCtnlZaZNrNBh5A3VDXITeKyiMCRTRvf1mru_1zbpcHz31RXfCEj1wEtwyBBFsG6FsQqWtahutfauE8NivTnnrEm3ekTNFZ7BEv6GiuOQi5ZXb5aBH0k26kUAUN-gz_WKJRsL-P6HM3yKko-FZvWDPJ8TIP6eRvmTPQveKtSvK4EjE_HxDSUoDh67lPZ4A37GIuDNSUiLvI0eQx9Gt7olcI_C4TdenH6gKOOFM2HKisCaaXE7slqgb6Iu_Zverr3dfrvPpwYTca1vuctOCqENNHHwQbRlr5VsEZGCrxoqKvi0obYUBC3Us0VXxygStpY-iklj3hp10fRfeMV5I2UBhfQAJWiiobah91IVH8y6bQmasOAjP-YlNnB612Lgxqq2sSwJ3KHA3CtyZjH2c__mRuDT-2fqK1mRuSTzYYwFqh5u0w_1POzJ2dlhRN23OweEphaBNIpLN2MVcjduKYiXQhX4_OIUnGzHnaGzzNmnCPBJlDcpQoQw-HVTjsfO_T2jxFBN6z07lqMN1XpRn7GS33YcPCIt2zfm4A34CvEUGiQ priority: 102 providerName: Directory of Open Access Journals – databaseName: ProQuest Central dbid: BENPR link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3NaxUxEA-1RfAiWr9eW0sEb7o0m2SzyUms9FEKFhELvYVsPry0u_Xt68H_vjPZvC2i9rYk2SU7mcxHZuYXQt5znpJjOlRNK1UlQWFUnTMdYhF6L1ytVMSI7tdzdXohzy6by3LgNpa0yo1MzII6DB7PyI-AtUDTcjA_Pt38qvDWKIyulis0HpEdEMEanK-d45Pzb9_nUxYO_kOL8cm9qb5cH40yg29iZgJC3YDv9IdGysD9_7I2_4qUZgW0fEaeFsuRfp6W-jnZiv0ueZwzOP34goQl1nRMUP30CsuWRur6QAeQCdfQhGgaU5kiHRIFs4-Coz0g3EakaTUlVP_GLkfR8nQriqDWCJxLEe8SuAW885fkYnny48tpVa5QqLzUzbpSwTETDaLyuaSbZIQPYKI53XaatfisnZCaKaedSQ04L16oKCX3ibUc-l6R7X7o4xtCa847V2sfHXeSCWd0ND7J2oPC513NF6TekNH6gi-O11xc2RznFtpOpLdAeptJb9WCfJjfuZnQNR4cfYyrM49EZOzcMKx-2rLRbIws6pBc08VWahE6KX0QjHngQ5lMvSAHm7W1ZbuO9p65FuTd3A0bDaMnro_D7WgFyDrE0pEw5vXEE_NMhFZAQwE0-LhhkvuP__-H9h6eyz55wjOfmqpuDsj2enUb34IJtO4OC5_fAdOxAaE priority: 102 providerName: ProQuest |
| Title | Fundamental limits and optimal estimation of the resonance frequency of a linear harmonic oscillator |
| URI | https://link.springer.com/article/10.1038/s42005-021-00700-6 https://www.ncbi.nlm.nih.gov/pubmed/38680632 https://www.proquest.com/docview/2572732656 https://www.proquest.com/docview/3048494846 https://doaj.org/article/ee0e8dfa5be7483db44cd300c4614f91 |
| Volume | 4 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlZ1La9wwEICHPCj0UpI-N0kXFXprTW1JluXjZsk2LDSUtoHchCxLvSR2WW8O_feZkR-hNC3kZGPJxh6PpBnPzGeA95yHYFNdJ3khVSJxwUgqW1bEInRO2EwpTxHdLxfq_FKur_KrHeBjLUxM2o9IyzhNj9lhnzoZmZmUUECEGnR5dmGf0O2k1Uu1nL6rcPQYCopIHvUV5fqBU_9YgyKq_yH78q_YaFxyVgfwbLAV2aK_u0PY8c1zeBJzNl33AuoVVXH0cH52TYVKHbNNzVqcBW7wEPEz-sJE1gaGhh5D17olwIZnYdOnUP-mJsvI1rQbRhhrQuUyIlyifqA__hIuV2c_lufJ8NOExEmdbxNV27T0JXH4bNB5KIWr0Sizuqh0WtC-tkLqVFlty5Cju-KE8lJyF9KCY9sr2Gvaxr8BlnFe2Uw7b7mVqbCl9qULMnO4xPMq4zPIRjEaNxDF6ccW1yZGtoU2vegNit5E0Rs1gw_TOb96nsZ_e5_S25l6Egs7Hmg3P82gG8b71Os62LzyhdSirqR0tUhTh5onQ5nN4GR8t2YYoJ3BmQoNN47W7AzeTc04tCheYhvf3nZG4OxG9ByJfV73OjHdidAKZShQBh9HJbm_-L8f6Ohx3Y_hKY96WyZZfgJ7282tf4tG0Laaw65efZ7D_mKx_r7G7enZxddv8zgW5vHDwh2gdALQ |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwEB6VIgQXxLNsKWAkOEHUxHYS-4AQr2VLH6dW6s04js2lJCXZCvVP8RuZcTapENBbb5HtWMn483js8XwD8ILzEGyq6iQvZZFIXDCSyuqKuAidEzYrCk8e3f2DYnEkvxznx2vwa4yFoWuVo06MirpuHZ2RbyO0cKXlaH68Pf2RUNYo8q6OKTQGWOz685-4Zevf7HzE8X3J-fzT4YdFssoqkDip8mVS1DbVXhNRnQ0qD1q4Gq0Wq8pKpSU9KyukSgurrA452vNOFF5K7kJacqzDfq_BdSmEphml5p-nMx2OfZbkDd0cotnVdi8j1SfdgyBiHdyp_bH-xTQB_7Jt__LLxuVufgdur-xU9m4A1l1Y8809uBHvi7r-PtRziiAZEgOwEwqS6pltataiBvqORcTdMQRFsjYwNDIZbutbIvfwLHTD9e1zqrKM7FzbMaLQJppeRuyaiM1l2z2AoysR7UNYb9rGPwKWcV7ZTDlvuZWpsFp57YLMHJoXvMr4DLJRjMat2MwpqcaJiV51ocwgeoOiN1H0ppjBq-md04HL49LW72l0ppbEwx0L2u6bWU1r433qVR1sXvlSKlFXUrpapKlD1MugsxlsjWNrVsqhNxdQnsHzqRqnNflqbOPbs94I1KzE3COxzcaAielLhCpQhgJl8HoEyUXn__-hzcu_5RncXBzu75m9nYPdx3CLR8zqJMu3YH3ZnfknaHwtq6cR8Qy-XvUU-w0iqDvz |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Jb9UwELZKEagXxM5rCxiJG4Q6tuPYR_rgqWwVByr1ZjleuJSkenk99N8z4yyoolTiFnmJnPHY_iYz85mQ15yn5JgORVVLVUg4MIrGmQa5CL0XrlQqokf327E6OpGfT6vTLaKmXJgctJ8pLfM2PUWHHfQyc2ZiQAEy1IDJ8-48pFvkNuBthkbXUi3nfyscrIYavZK7Q1a5vqb7lXMo0_VfhzH_8o_mY2d1n9wb8SJ9P4zwAdmK7UNyJ8dt-v4RCSvM5BgI-ukZJiv11LWBdrAT_IIi5NAYkhNplyiAPQrmdYckG5Gm9RBGfYlVjiLedGuKVNZIl0uR5RJ0BGzyx-Rk9fHH8qgYL04ovNTVplDBMRMNcvG5pKtkhA8AzJyuG81qfNZOSM2U086kCkTohYpScp9YzaHuCdluuzY-I7TkvHGl9tFxJ5lwRkfjkyw9HPO8KfmClJMYrR9ZxfFyizObvdtC20H0FkRvs-itWpA3c5_zgVPjxtaHODtzS-TDzgXd-qcd9cPGyKIOyVVNrKUWoZHSB8GYB-2TyZQLsj_NrR0XaW9htwLwxgHRLsiruRqWF_pMXBu7i94K2OGQQUdCm6eDTswjEVqBDAXI4O2kJH9e_u8P2v2_5i_J3e8fVvbrp-Mve2SHZxU2RVntk-3N-iI-B0y0aV7kBfAbYIgBxw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Fundamental+limits+and+optimal+estimation+of+the+resonance+frequency+of+a+linear+harmonic+oscillator&rft.jtitle=Communications+physics&rft.au=Wang%2C+Mingkang&rft.au=Zhang%2C+Rui&rft.au=Ilic%2C+Robert&rft.au=Liu%2C+Yuxiang&rft.date=2021-09-15&rft.pub=Nature+Publishing+Group+UK&rft.eissn=2399-3650&rft.volume=4&rft.issue=1&rft_id=info:doi/10.1038%2Fs42005-021-00700-6&rft.externalDocID=10_1038_s42005_021_00700_6 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2399-3650&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2399-3650&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2399-3650&client=summon |