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09.-13.09.2013 Microkelvin Workshop 2013 1

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09.-13.09.2013 Microkelvin Workshop 2013 2 Mise en pratique for the definition of the kelvin updated version, Comité consultatif de thermométrie (CCT), 2011 http://www.bipm.org/en/publications/mep_kelvin/ Scope: “This document provides the information needed to perform a practical measurement of temperature in accord with the International System of Units (SI).” The mise en pratique serves as a reference for: the text of the ITS-90 and PLTS-2000 a Technical Annex of material deemed essential to realisation of the ITS-90 or PLTS-2000, but not included in the scale definitions themselves descriptions of primary thermometers for direct measurement of thermodynamic temperature assessments of the uncertainty of the ITS-90, PLTS-2000, and measurements made by primary thermometry Traceable thermometry

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09.-13.09.2013 Microkelvin Workshop 2013 3 Mise en pratique for the definition of the kelvin updated version, Comité consultatif de thermométrie (CCT), 2011 http://www.bipm.org/en/publications/mep_kelvin/ fundamental change in the practice of traceable temperature measurement direct measurements by primary thermometers more flexible approach → user no longer will be tied to the ITS removes the short-term need for establishing a new unified international temperature scale from the lowest to the highest temperatures Traceable thermometry

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09.-13.09.2013 Microkelvin Workshop 2013 4 Temperature scales time

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09.-13.09.2013 Microkelvin Workshop 2013 5 Temperature scales 3 He vapour pressure scale PTB-2006 PTB-2006 ≡ ITS-90 2 K ≤ T ≤ 3.2 K PTB-2006 ≡ PLTS-2000 0.65 K ≤ T ≤ 1 K 3 He vapour pressure scale PTB-2006 PTB-2006 ≡ ITS-90 2 K ≤ T ≤ 3.2 K PTB-2006 ≡ PLTS-2000 0.65 K ≤ T ≤ 1 K Schuster G. et al., Temperature, its Measurement and Control in Science and Industry, Vol. 6, (Edited by J.F. Schooley), New York, American Institute of Physics, pp. 97-100 (1992) Fogle W.E. et al., ibid. pp. 85-90 Engert et al., Metrologia, 44, 40 (2007) ITS-90 ↔ PLTS-2000 ? PTB-2006 Engert et al., Metrologia, 44, 40 (2007)

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09.-13.09.2013 Microkelvin Workshop 2013 6 p m / MPa = a i (T 2000 / K) i (i = -3···9) T range:0.9 mK to 1 K p range:2.9 MPa to 4 MPafixed pointsp 3He / MPaT 2000 / mK Minimum 2.93113315.24 A 3.43407 2.444 A-B 3.43609 1.896 Néel 3.43934 0.902 p m / MPa = a i (T 2000 / K) i (i = -3···9) T range:0.9 mK to 1 K p range:2.9 MPa to 4 MPafixed pointsp 3He / MPaT 2000 / mK Minimum 2.93113315.24 A 3.43407 2.444 A-B 3.43609 1.896 Néel 3.43934 0.902 Temperature scales

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09.-13.09.2013 Microkelvin Workshop 2013 7 Uncertainty for the realization of the PLTS-2000 in comparison to an approximation using a pressure calibration of the MPT adjusted to the 3 He melting pressure minimum, calibrated superconductive reference point samples (W, Mo) and an interpolating resistance thermometer for the region around the minimum. Red lines show the uncertainty of the PLTS-2000 in terms of thermodynamic temperature. PLTS-2000 - Realization

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09.-13.09.2013 Microkelvin Workshop 2013 8 PLTS-2000 - Dissemination Resistance thermometers Superconductive reference point samples MFFTs, CSNTs

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09.-13.09.2013 Microkelvin Workshop 2013 9 Practical noise thermometry → Nyquist relation dc-SQUID based detection of thermal magnetic flux noise generated by noise currents in a metallic temperature sensor Measurement of power spectral density (PSD): S(f,T) fTRkU B 2 4 PLTS-2000 - Dissemination Magnetic Field Fluctuation Thermometer (MFFT) “Low-pass-like” spectral shape depends on geometry. If R = const(T): S (f = 0 Hz, T) ~ T spectral shape is independent of T Magnetic Field Fluctuation Thermometer (MFFT) “Low-pass-like” spectral shape depends on geometry. If R = const(T): S (f = 0 Hz, T) ~ T spectral shape is independent of T Current Sensing Noise Thermometer (CSNT) 1 st order low-pass spectrum with fall-off frequency f c = R/(2 π L). If R = const(T): S (f = 0 Hz, T) ~ T Current Sensing Noise Thermometer (CSNT) 1 st order low-pass spectrum with fall-off frequency f c = R/(2 π L). If R = const(T): S (f = 0 Hz, T) ~ T b 2a c 0 1 ),( f f Ts TfS 2 c 2 b 1 4 ),( f f R TMk TfS

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09.-13.09.2013 Microkelvin Workshop 2013 10 MFFT-1 Noise Thermometer Magnicon GmbH MFFT-1 Noise Thermometer Magnicon GmbH PLTS-2000 - Dissemination

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09.-13.09.2013 Microkelvin Workshop 2013 11 PLTS-2000 - Dissemination Uncertainty of T measurement with a calibrated MFFT Goal → temperature measurement with relative expanded uncertainty U rel (T MFFT ) ~ 1% (k = 2, 95%) within ~ 60 s calibration of the MFFT atT cal calibration temperature f s sample rate N s number of samples, M avg number of averages for calibration measurement N avg number of averages for temperature measurement f = f high - f low frequency range used for T determination N f number of frequency bins in f

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09.-13.09.2013 Microkelvin Workshop 2013 12 Parametric model: fit of PSD at T cal → Θ cal ={s 0, a, b, f c } fit of measured PSD with Θ cal → T p, u(T p ) Non-parametric model: T np → may be affected by bias Improved non-parametric model: Bayesian approach: coherent uncertainty estimates using MCMC techniques probability density functions V(t) → FFT → PSD → averaging Wübbeler et al., Meas. Sci. Technol. 23, 125004 (2012), ibid. 2013 PLTS-2000 - Dissemination b 2a c 0 1 ),( f f Ts TfS cal ),( ),( T TfS TfS T f N f f TfS TfS N T T ),( ),( np cal np f N f f TfS TfS N T M T ),( ),( ) 1 1( cal inp cal avg inp ffcal NMNNT Tu T Tu avg 2 2 2 inp 2 11 )( )( dTTpT T y| B TpTTTu T )|()-()( 2 BB 2 y

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09.-13.09.2013 Microkelvin Workshop 2013 13 PLTS-2000 - Dissemination Temperature estimates and uncertainties obtained by the Bayesian treatment T B, by the parametric approach T P and by the two non-parametric approaches T np and T inp. The error bars indicate 95 % credible intervals for the Bayesian treatment and 95 % coverage intervals for T p, T np and T inp Wübbeler et al., Meas. Sci. Technol., to appear 2013 (a) T cal = 850 mK M avg = 2400 N avg = 10 (b) T cal = 850 mK M avg = 10 N avg = 2400

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09.-13.09.2013 Microkelvin Workshop 2013 14 PLTS-2000 - Dissemination U rel (T MFFT ) ≤ 1%

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09.-13.09.2013 Microkelvin Workshop 2013 15 Calibration certificate parameters for SQUID setup parameters for DAQ box PSD at calibration temperature calibration parameters T min for U ≤ 1% PLTS-2000 - Dissemination

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09.-13.09.2013 Microkelvin Workshop 2013 16 Ultra low-temperature 195 Pt-NMR On the way to a ultra low-temperature scale T ≤ 1 mK

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09.-13.09.2013 Microkelvin Workshop 2013 17 z (cm) r (cm) B z (T) Experimental set-up : Cu-Pt nuclear cooling stages Pt-NMR #1Pt-NMR #2Pt-NMR #3 Reference-point device Heat switchCu nuclear cooling stageHeat switch Pt nuclear cooling stage Ultra low-temperature 195 Pt-NMR

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09.-13.09.2013 Microkelvin Workshop 2013 18 Ziele 2012 Pulsed Pt-NMR thermometry is based on measurements of nuclear magnetisation of a high-purity bulk samples. The temperature fields and result from the thermodynamic process of thermometry and are compared to the recorded free induction decay (FID). Ultra low-temperature 195 Pt-NMR

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09.-13.09.2013 Microkelvin Workshop 2013 19 nuclear demagnetization cooling and magnetic thermometry = two aspects of one and the same thermodynamic process, → solution of thermodynamic field equations investigation of properties of Pt → susceptometer Ultra low-temperature 195 Pt-NMR ),( e txT ),( N txT

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09.-13.09.2013 Microkelvin Workshop 2013 20 PLTS-2000 - Background data PTB- and NIST-Scale T : 30 mK < T < 750 mK, T/T < 0.3 % p : p = 110 Pa (at the minimum) PTB- and NIST-Scale T : 30 mK < T < 750 mK, T/T < 0.3 % p : p = 110 Pa (at the minimum) PTB- and UF-Scale T N T UF - T PTB = 54 µK (6 %) T B T UF - T PTB = 78 µK (4 %) T A T UF - T PTB = 95 µK (4 %) PTB- and UF-Scale T N T UF - T PTB = 54 µK (6 %) T B T UF - T PTB = 78 µK (4 %) T A T UF - T PTB = 95 µK (4 %)

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09.-13.09.2013 Microkelvin Workshop 2013 21 InK - Project European Metrology Research Programme (EMRP) “Implementing the new Kelvin” - InK project2012 – 2015 → T-T 90, T-T 2000 14 national metrological institutes, 3 res. Grants, NPL – coordinator http://projects.npl.co.uk/ink/ Work package 4 - “Primary thermometry for low temperatures” development of primary thermometers → T-T 2000 CSNT, CBT, MFFT to resolve the long standing discrepancy between the background data on which PLTS-2000 is based

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09.-13.09.2013 Microkelvin Workshop 2013 22 Conclusions - Outlook International Temperature Scales are essential for maintenance and dissemination of the Kelvin with low uncertainties T ≥ 1mK Dissemination of ITS-90 and PLTS-2000 down to 1 mK sc. reference points, resistance thermometers practical noise thermometers → MFFT, on-chip CSNT new calibration service, U(T MFFT )≤ 1% Discrepancies in the background data of PLTS-2000 below 10 mK EMRP-project→ “InK” T ≤ 1mK ultra-low temperature scale - part of a follow-up project ? choice of scale carrier - investigation of material properties development and evaluation of primary thermometers comparison measurements between different thermometers/laboratories development of transfer standards

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09.-13.09.2013 Microkelvin Workshop 2013 23 Acknowledgments PTBJ. Beyer, D. Drung, M. Schmidt, Th. Schurig D. Heyer, B. Fellmuth, J. Fischer P. Strehlow, E. Bork G. Wübbeler, F. Schmähling, C. Elster Magnicon GmbH H.-J. Barthelmess S. AliValiollahi University of Heidelberg, Kirchhoff Institute of Physics Ch. Enss et al. Royal Holloway University of London J. Saunders et al.

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09.-13.09.2013 Microkelvin Workshop 2013 24

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09.-13.09.2013 Microkelvin Workshop 2013 25 http://www.bipm.org/utils/en/pdf/Estimates_Differences_T-T90_2010.pdf Estimates of the differences between thermodynamic temperature and the ITS-90

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09.-13.09.2013 Microkelvin Workshop 2013 26 Relative deviation of T noise from T 2000/90 for different noise thermometers. Linearity of T noise in terms of T 2000/90 for different noise thermometers..

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09.-13.09.2013 Microkelvin Workshop 2013 27 Both Nuclear Demagnetisation Cooling and Magnetic Thermometry are two aspects of one and the same thermodynamic process. It arises from solution of proper field equations for boundary and initial values that can be controlled in the demagnetisation experiment. Thermodynamic field equations are derived from the Boltzmann equation for the phase density of metal electrons and the Master equation for the probability density to find a nuclei with z-spin. energy density of metal electrons energy density of nuclear spins heat flux magnetisation caloric and thermal equations of state Both the thermodynamic temperature and the spin temperature result from the numerical solution of field equations for a given demagnetisation process. Ultra low-temperature 195 Pt-NMR

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