ITALIAN PHYSICAL SOCIETY

PROCEEDINGS OF THE

INTERNATIONAL SCHOOL OF PHYSICS

"ENRICO FERMI"

COURSE CLXVI edited by T. W. HÄNSCH, S. LESCHIUTTA and A. J. WALLARD

Directors of the Course

and

M. L. RASTELLO

VARENNA ON LAKE COMO

VILLA MONASTERO

18 - 28 July 2006

Metrology and Fundamental Constants

2007

IOS Press

AMSTERDAM, OXFORD, TOKIO, WASHINGTON DC

INDICE

Т . HÄNSCH, S. L E S C H I U T T A and A. J . W A L L A R D - Preface pag. XXI

Gruppo fotografico dei partecipanti al Corso » XXIV

A. J . W A L L A R D - Metrology and society » 1

1. Introduction » 1 2. Metrology and trade » 1

2'1. The general case » 1 2'2. Traceability in trade » 2 2'3. Mutual recognition of NMI standards: the CIPM MRA » 3 2'4. The essential points of the CIPM MRA » 3 2'5. The key comparison database » 5 2'6. Take up of the CIPM MRA » 5 2'7. The importance of Mutual Recognition Arrangements » 6

3. Metrology and innovation » 6 4. Metrology and medicine » 7

4T. Uses » 7 4'2. Why is chemical metrology "difficult"? » 8

5. And there is more! » 9

A . J . W A L L A R D - The evolution of metrology: Past t imes to the present day » 11

1. The roots and evolution of metrology » 11 2. 20th Century metrology —the National Metrology Institutes » 14 3. The international System of Units, the SI » 15 4. Physics, engineering . . . and then chemistry » 16 5. Metrology in the 21st Century » 17

5T. Industrial challenges » 17 5'2. New science—changes to the SI » 19

A. J. W A L L A R D - The organization of metrology » 21

1. Structures » 21 2. Metre Convention » 21

2T. The Metre Convention » 21

VII

VIII INDICE

2 2 . The BIPM » 22 2-3. The MKS system » 22 2'4. The SI Brochure » 23

3. BIPM: the first 75 years » 23 4. National structures: The National Metrology Institutes (NMIs) » 26

4T. National Metrology Institutes » 26 4'2. NMI science » 27

5. Traceability: The birth of accreditation » 27 5 1 . Traceability » 27 5'2. Accreditation bodies » 27 5 3 . ILAC » 28 5'4. A National Measurement System » 28 5'5. Definitions of traceability » 28

6. Regional Metrology Organisations » 28 6T. The birth of RMOs » 28 6'2. RMOs today » 29 6'3. Equivalence of national measurement standards » 29

7. Mutual recognition of NMI standards: the CIPM MRA » 30 П . The significance of the CIPM MRA » 30 7'2. Launch » 30

8. The essential points of the CIPM MRA » 30 8'1. Objectives » 30 8'2. Technical competence » 30 8'3. Comparisons and quality systems » 31 8'4. The NMIs commitment » 31 8'5. Associates of the General Conference » 31 8'6. The Key Comparison Database (KCDB) » 32

9. Take up of the CIPM MRA » 32 9 1 . Regulators and the CIPM MRA » 32 9'2. A market for NMI calibration services » 32 9'3. Consequences for NMI services » 32

10. Other metrology bodies » 33 101. The World Metrology System » 33 10'2. Accreditation and ILAC » 33 103. The importance of MRAs » 33 10'4. Measurement Accreditation and Standardization » 33

11. Closing comments » 33

S. LESCHIUTTA - Measurements and discoveries: The role of instruments . . » 35 1. Introduction » 35 2. Summary and aim of this lecture » 37 3. Some roles of measurements » 38

3T. Galileo was suddenly loosing any interest in the measurement or in the instruments he was using or improving, as soon the general pattern of the law appeared in his mind » 38

IX

3'2. What is the form of the "force" in a moving body with mass? Where is the energy of a body at rest stored? What is the difference between the "dead force" and the force "alive", in other terms what is the quantity of interest: kinetic energy, motion quantity, energy, pulse? » 39

3'3. Very early measurements of the equivalence principle » 39 4. Some roles of instruments, the special case of pendula » 39

4'1. External conditions fostering the birth of a new instrument » 39 4'2. Why also pendula are to be considered » 41 4'3. Metrological application of pendula » 41

4'3.1. Early vertical pendula » 44 4'3.2. Horizontal pendula and torsion balances, 1700-now » 44

5. Conclusions » 44

S. L E S C H I U T T A - History of s tandard definitions: An outline » 45

1. Introduction » 45 2. Metric systems » 47

2"1. Families of standards and units based on the energy needed to reach a given goal » 48

2'2. Families of standards based on anthropomorphism » 48 2'3. Families based on agreed (or imposed) material artifacts » 49 2'4. Families based on some traditional historical definition, usually sup­

ported by artifacts » 50 2'5. Families based on any property of Nature or Physics » 50

3. General and essential characteristic to be provided by any metric system . » 51 3'1. Universality » 51 3'2. Uniformity » 52 3'3. Perennity » 53 3'4. Accuracy, precision, stability, independence from influence quantities » 53

T . QuiNN - Physical quantities » 59

1. Introduction » 59 2. History » 61 3. Quantities and quantity equations » 65

3"1. Definitions of quantities » 65 3'2. Quantities of the same kind » 67 3'3. Quantity equations and numerical value equations » 68

4. The equations of physics, definitional constants » 68 5. The problem of electrical quantities and units » 70 6. The International System of Units, the SI, a coherent system of units . . . . » 72 7. Biological quantities and units » 74

7'1. Photobiological quantities » 74 7'2. Quantities for ionizing radiation » 75 7'3. Biological quantities for medicine » 75

8. The use of the fundamental constants as reference quantities for the defini­tion of units » 76

9. Final remarks » 79

X INDICE

W . B I C H - Recent developments in uncertainty evaluation » 81

1. Introduction » 81 2. The present GUM » 82

2T. Fundamentals » 82 2*2. Merits and limits » 83

2*2.1. The GUM is Bayesian » 83 2*2.2. The GUM is frequentist » 83

2'3. Confidence interval, interval of confidence and expanded uncertainty » 84 2'4. Arbitrary number of measurands » 86 2'5. Comments » 87

3. Supplements to the GUM » 87 3T. Propagation of distributions » 88

3*1.1. PDFs for input quantities » 88 3'1.2. Counterpart to degrees of freedom for type-B evaluations . . . » 91 3'1.3. Multivariate example » 91 3*1.4. Propagation » 92

4. Conclusions » 93

H. BACHMAIR - Electrical metrology » 95

1. Introduction » 95 2. SI and electrical units » 95 3. Definition of a unit . . : » 97 4. Realisation of a unit » 98 5. Reproduction of a unit » 104 6. Maintenance and dissemination of a unit » 108 7. Impedance measurements » 111 8. Bridge and ratio techniques » 114 9. AC/DC transfer » 121 10. Power and energy measurements » 128 11. International comparisons » 131

B. JECKELMANN and B. JEANNERET - The application of the Josephson and quantum Hall effects in electrical metrology » 135

1. Introduction » 135 2. The conventional system of electrical units » 137

2*1. The determination of Дк and Kj » 137 2'2. Conventional values for Дк and Kj » 139

3. The Josephson voltage standard » 139 3*1. Theoretical background of the Josephson effect » 140 3'2. Conventional Josephson voltage standard » 142

3'2.1. Junctions and arrays design » 142 3'2.2. Measurement system » 145 3'2.3. Application in d.c. voltage metrology » 146

3'3. Programmable voltage standards » 147 3'3.1. Binary arrays » 149 3'3.2. Pulse-driven arrays » 152

INDICE XI

4. The quantum Hall resistance standard » 154 4*1. Basic principles » 155 4'2. Edge state model » 157 4'3. The two-dimensional electron gas » 160 4'4. Measurement techniques » 161 4'5. Universality of the quantised Hall resistance » 164

4'5.1. Contact effects » 165 4'6. The use of the QHR as a standard of resistance » 166

4'6.1. Quantum Hall array resistance standards » 167 4'7. A.c. measurements of the QHR » 169

5. Conclusions » 170

F. PIQUEMAL, L. DEVOILLE, N. FELTIN and B. STECK - Single charge transport s tandards and quantum-metrological triangle experiments » 181

1. Introduction » 181 2. Single electron devices » 183

2T. The elementary device based on Coulomb blockade » 183 2'2. The single-electron transistor » 185 2'3. The electron pump » 188

3. Other single charge transport devices » 190 3T. RF-SET-transistor-based electron counter » 190 3 2 . SETSAW pump » 190 3'3. Cooper pair pump » 192 3'4. New devices » 192

4. New electrical standards and quantum metrological triangle experiments . » 193 4T. Electrical standards » 193 4'2. Quantum-Metrological Triangle » 194

42 .1 . QMT by applying Ohm's law U = RI » 195 4'2.2. QMT and electron counting capacitance standard » 196 4'2.3. Observational equations » 197 4'2.4. Determination of the elementary charge » 197

4'3. QMT experimental set-up using a CCC » 198 4'3.1. Cryogenic current comparator (CCC) » 198 4'3.2. CCC used as a current amplifier » 201 4'3.3. CCC used both in the calibration of a cryogenic resistance and

as current detector » 204 4'4. QMT experimental set-up using an electron counting capacitance

standard » 205 5. Conclusion and prospects » 207

K. H E L M E R S O N and W . D. P H I L L I P S - Cooling, t rapping and manipulation

of atoms and Bose-Einstein condensates: Applications to metrology » 211

1. Introduction » 211 2. Radiative forces » 212

2T. The scattering force » 213 22. The dipole force » 213

XII INDICE

2'3. Doppler cooling » 215 3. Deceleration and cooling of an atomic beam » 218

3 1 . Chirp cooling » 219 3'2. Zeeman tuning » 220 3'3. Optical pumping » 222

4. Traps for neutral atoms » 222 4'1. Dipole force traps » 224 4'2. Radiation pressure force traps » 225 4'3. Magneto-static traps » 227

5. Sub-Doppler laser cooling » 229 5'1. Observation of sub-Doppler temperatures » 229 5'2. New cooling mechanisms » 230

6. Metrology with cold atoms » 232 6 1 . Atomic fountain clocks » 233 6'2. Atom interferometers » 234

7. Coherent manipulation of Bose-Einstein condensates with light » 236 7 1 . The triaxial TOP trap for sodium » 237 72 . ВЕС of sodium in a TOP trap » 238 7'3. Diffraction of atoms by a standing wave » 240 7'4. Bragg diffraction of atoms » 242 7'5. Raman output coupling: Demonstration of a CW atom laser » 243

8. Nonlinear atom optics with Bose-Einstein condensates » 245 8T. Four-wave mixing with matter-waves » 246 8'2. Quantum phase engineering » 247 8'3. Solitons in а ВЕС » 248 8'4. Observation of solitons in а ВЕС » 249 8'5. Quantum atom optics » 251

P . L E M O N D E - Metrology with cold atoms » 263

1. Introduction » 263 2. Description of atomic fountains » 266

2T. Atomic preparation » 266 2'2. Clock transition interrogation » 268 2 3 . Detection » 269 2'4. Operation of the fountain clock » 269

3. Performances of fountains » 270 3T. Frequency stability and quantum projection noise » 271 3'2. Frequency accuracy, collisions between cold atoms » 273

4. Beyond fountains » 276 4T. Optical clocks with neutral atoms in free fall » 277 4'2. Optical clocks with trapped ions » 277 4'3. Optical clocks with trapped neutral atoms » 278

5. Applications and prospects » 278 5T. Cold atom clocks in space » 279 5'2. Fundamental physics » 279

INDICE XIII

A. BAUCH - Atomic frequency standards, properties and applications » 287

1. Introduction » 287 2. Atomic frequency standards: principle of operation and characterization of

their performance » 288 3. Caesium clocks, classical and optically pumped » 291

3 1 . Caesium clocks with magnetic selection » 291 3'2. Caesium AFS with optical pumping » 295 3'3. Systematic frequency offsets » 295 3'4. Development of the accuracy with time » 296 3'5. Commercial caesium clocks » 296

4. More accurate, more complex » 298 4'1. Primary clocks » 298 4'2. Atomic fountains » 299 4 3 . Optical clocks » 301

5. A survey on other AFS in practical use » 302 5'1. General remarks » 302 5'2. The hydrogen maser » 303

5*2.1. The active hydrogen maser » 303 5'2.2. The passive hydrogen maser » 305 5'2.3. Properties of hydrogen masers » 305

5'3. Rubidium gas cell frequency standards » 305 5'4. Current trend in gas cell AFS » 308

6. Applications » 308 6T. A short note on the realization of TAI » 308 6'2. Timing aspects of the future European satellite navigation system

Galileo » 309 6'3. Synchronization of the networks for electrical power distribution . . . » 311 6'4. The search for the variability of the fundamental constants » 311

7. Conclusion » 312 8. Disclaimer » 313

T H . UDEM and F. RIEHLE - Frequency combs applications and optical frequency standards » 317

1. Introduction » 317 2. Frequency combs from mode locked lasers » 319

2'1. Derivation from cavity boundary conditions » 319 2'2. Derivation from the pulse train » 322 2'3. Linewidth of a single mode » 326 2'4. Generating an octave spanning comb » 328

3. Self-referencing » 332 4. Scientific applications » 338

4'1. Hydrogen and drifting constants » 338 4'2. Fine structure constant » 342 4'3. Optical frequencies in astronomy » 343 4'4. Reconstructing pulse transients and generating attosecond pulses . . . » 344 4'5. Frequency comb spectroscopy » 346

5. All optical clocks » 350 6. Optical frequency standards » 353

XIV INDICE

6 1 . Optical frequency standards based on single ions » 354 6'1.1. Clock interrogation by use of quantum jumps » 354 6T.2. Yb + and Hg+ single-ion standards » 355 6T.3. 88Sr+ single-ion standard » 356

6*2. Neutral atom optical frequency standards » 357 6'2.1. Atomic beam standards » 357 6'2.2. Neutral atom standards based on ballistic atoms » 357 6'2.3. Optical lattice clocks » 359

7. Conclusions » 361

E. F. ARIAS - Time scales and relativity » 367

1. Introduction » 367 2. Evolution of time scales and their associated interval units » 368

2 1 . Universal Time (UT) » 368 2*2. Ephemeris Time (ET) » 370 2'3. The downing of atomic time » 371 24 . The birth of Coordinated Universal Time UTC » 372

3. Metrologie qualities of a time scale » 374 4. Relativity and time scales » 375

4T. Proper and coordinate quantities » 375 4'2. Coordinate systems » 376 4'3. Practical realizations of the coordinate systems » 377 4'4. Coordinate times » 378

5. Realization of TAI and UTC . » 379 5'1. An essential tool: clock comparisons » 379 5*2. Use of GPS for time transfer » 381 5'3. Two-way satellite time and frequency transfer » 382 5'4. Calibration of time transfer equipment and link uncertainties » 383

6. The algorithm Algos » 384 6'1. The general scheme » 384 6*2. Clocks in TAI » 385 6'3. Free Atomic Time Scale (EAL), clock weighting and frequency pre­

diction » 385 6'4. Primary frequency standards (PFS) » 385

7. Secondary representations of the second » 387 8. Dissemination and access to the time scales » 388 9. List of acronyms used in the text (in English and French when applicable) » 389

R. RUSBY - Temperature metrology: Low and ultra-low temperatures . . . . » 393

1. Introduction » 393 2. Refrigeration and thermometry » 394 3. Secondary thermometers » 395 4. The unit of thermodynamic temperature » 397 5. The measurement of thermodynamic temperature » 399

5*1. Gas thermometry » 399 5*2. Acoustic gas thermometry » 402 5*3. Other thermodynamic techniques » 403

INDICE XV

6. International Temperature Scale of 1990, ITS-90 » 405 6 1 . The ITS-90 below the triple point of neon, 24.5561 К » 409 6'2. Thermodynamic accuracy of the ITS-90 » 410

7. Ultra-low temperatures » 411 7'1. Nuclear cooling » 412

8. ULT Thermometry » 413 8T. Superconductive reference points » 414 8'2. Magnetic thermometry » 415 8'3. Noise thermometry with SQUIDS » 417

9. 3He melting pressure thermometry and the PLTS-2000 » 419 9'1. Realisation of the PLTS-2000 » 421

10. Future prospects » 422

J. FISCHER - High-temperature metrology and prospects for a new definition of the kelvin » 427

1. Introduction: a brief course into history » 427 2. Measurement of thermodynamic temperature » 428 3. Gas thermometry » 429

3T. Constant-volume gas thermometers » 430 3'2. Acoustic gas thermometers » 431 3'3. Dielectric-constant gas thermometers » 432

4. Noise thermometry » 434 5. Total radiation thermometry » 435 6. Spectral radiation thermometry » 438

6'1. Relative mode referenced to known temperature » 438 6'2. Absolute mode » 439

7. Doppler broadening thermometry » 441 8. Practical high-temperature metrology » 443

8'1. The International Temperature Scale of 1990 » 443 8'2. Melting and freezing points of metals » 445 8'3. Eutectic points of metal-carbon compositions » 446

9. New definition of the kelvin » 448

R. M. G A V I O S O - Metrological applications of acoustic and microwave res­onators » 455

1. Introduction » 455 2. Basic description of some physical properties of dilute monoatomic gases . » 456

2T. Thermophysical and transport properties » 456 2'2. Electrical properties » 457

3. Basic theory and operation of acoustic and microwave resonators » 458 3'1. Acoustic and microwave frequencies in a spherical cavity » 458 3'2. Effects of perturbed geometry on achievable precision and accuracy . » 460

4. Speed of sound as a thermodynamic temperature standard » 462 4'1. Relationship between speed of sound and thermodynamic temperature » 463 4'2. Physical meaning of the Boltzmann constant and primary acoustic

thermometry » 463

XVI INDICE

4'3. Review of recent results obtained by primary acoustic thermometry. » 464 4'4. Redetermination of the molar gas constant R and the Boltzmann con­

stant к » 465 5. Speed of light for an atomic pressure standard » 467

5'1. Working equations for an electric primary pressure standard » 468 5'2. Current precision and accuracy achievable with a primary pressure

standard » 470

R. S. DAVIS - Mass metrology: Underlying assumptions, present best prac­tice, new frontiers » 473

1. Introduction » 473 2. What do mass metrologists measure? » 474

2'1. The relation between mass metrology and contemporary physics . . . » 474 2'2. Traditional mass metrology » 475

3. The kilogram and the International System of Units » 478 4. How modern balances work » 481

4 1 . Ultimate performance » 482 4'1.1. Anelasticity » 482 4'1.2. Effect of servocontrol and detector noise » 484

4'2. Commercial analytical balances » 485 4'2.1. Centring » 486 4'2.2. Scale calibration » 486 4'2.3. Nonlinearity » 487 4'2.4. Magnetic interactions » 488 4'2.5. Thermal effects » 488

5. Legal metrology and conventional mass » 489 5T. What scientists should know about conventional mass » 489 5'2. Another way to view conventional mass » 491

6. Nanograms to yoctograms ("there's plenty of room at the bottom") » 491 6T. Mass and nanometrology » 491 6'2. Cantilever systems » 492 6'3. Calibration of AFMs using calibrated mass standards (deadweights) » 493 6'4. Oscillating cantilevers » 495 6'5. Gravitational mass of a neutron » 495

7. Conclusion » 497

P . R I C H A R D - Redefinition of the kilogram based on a fundamental constant » 499

1. Introduction » 499 2. Present status of the kilogram » 501

2T. Role of the kilogram in the SI » 501 2'2. Results of periodic verifications of national prototypes » 502

3. Counting atoms using ion accumulation » 503 4. Electromechanical methods » 505

4T. The watt balance experiment » 505 4'2. Other electrical methods » 508

4'2.1. The superconducting magnetic levitation » 508 4'2.2. The voltage balance » 510

INDICE XVII

5. Possible new definitions of the kilogram and conclusions » 510 5'1. Definitions that fix the value of the Avogadro constant » 511 5'2. Definitions that fix the value of the Planck constant » 511 5'3. Planck and Avogadro constants » 512 5'4. A decision whose time will come » 514

P. BECKER, М. JENTSCHEL, G. MANA and G. Zosi - Towards an atomic realization of the kilogram: The measurements of ЛГд and N^h » 519

1. Introduction » 519 2. Weighing 7-ray photons » 520

2'1. 7-ray spectroscopy » 522 2'2. Mass spectroscopy » 525

3. X-ray crystal density measurement of N\ » 526 3'1. Molar mass » 528 3'2. Lattice parameter » 529 3 3 . Density » 530

4. Conclusions » 530

К. С. CARNEIRO - Metrology to support the development of nanotechnology » 533 1. Introduction » 533 2. Early scanning probe microscopes and metrology developments » 535

Traceability to the meter » 536 Uncertainties » 536 Interlaboratory comparisons » 536 Calibration software for industrial instruments » 537 Setting up nanofacilities for future needs » 538 Surface physics application in vacuum » 538 Alternative methods to SPM » 538

3. What nanotechnology needs » 539 4. Practical examples » 540

Example 1: roughness of a silicon wafer » 540 Example 2: Parameters of an optical grating » 540

5. New developments. Optical diffraction microscopy » 543 6. Summary » 547

M. J . T . M I L T O N - Metrology for chemical measurements in the environment » 549 Introduction » 549 1. Measurement of composition » 549 2. The mole » 551 3. Primary methods of measurement » 552 4. The "grande salle" metaphor » 553 5. Isotope Dilution Mass Spectrometry (IDMS) » 554 6. pH and electrochemistry » 558 7. Primary methods in practice » 559

INDICE

8. Measurement standards for gases » 561 9. Preparative comparisons » 563 10. Complete mixture methods » 564 11. Photochemical pollution » 564 12. Monitoring photochemical pollution » 565 13. Volatile organic compounds (VOCs) » 565 14. Ozone in the atmosphere » 567 15. Measuring ozone with the NIST SRP » 568 16. Measuring ozone by gas phase titration » 568 17. Coherence of ozone measurements » 569 18. Particles » 570 19. Summary. Why traceability to the SI? » 570

P . F o x - Developments in optical radiometry » 573

1. Introduction » 573 2. History » 574 3. Base radiometric units or methods » 575

3'1. Sources » 576 31.1 . Black bodies » 576 3T.2. Synchrotrons » 577

3'2. Techniques and methods » 577 3 3 . Detectors » 578

3'3.1. Laser radiometry » 578 3'3.2. Thermal-detector-based scales » 580 З'З.З. Photon-detector-based scales » 580

4. Cryogenic radiometry » 581 4'1. Background » 581 4'2. Applications of cryogenic radiometers » 583 4'3. Confirmation of accuracy » 585 4'4. Future developments » 589

5. Basis for optical radiation scales » 589 5T. Spectral responsivity scales » 589 5'2. Transfer standard detectors » 591

6. Thermal radiometry » 594 6T. Primary quantities » 594

7. Spectral irradiance and radiance » 596 8. Photometric units » 597 9. Transfer standards for source measurements » 598 10. Climate change » 599

lO'l. Radiometric requirements » 599 10'2. Total Solar Irradiance (TSI) » 600 10'3. Earth viewing instruments » 600 10'4. Traceable Radiometry Underpinning Terrestrial and Helio Studies

(TRUTHS) » 603 11. Spectrophotometry, colour and sensory metrology » 605

l l ' l . Spectrophotometry » 605 11'2. Colour, » 605 1ГЗ. Sensory metrology » 605

INDICE XIX

12. Conclusion » 607

M. L. R A S T E L L O - Classical and quantum techniques for photon metrology » 611

1. Introduction 2. Classical primary methods 3. Quantum techniques for photon metrology

3'1. Quantization 3'2. Entanglement 3'3. Photodetection

4. Quantum primary methods 4'1. The SPDC scheme for calibrating single-photon detectors 4'2. Calibration of analog detectors by SPDC correlations 4'3. Calibration of analog detectors by stimulated SPDC

» » » » » » » » » »

611 613 619 620 623 626 627 628 630 634

Elenco dei partecipanti » 639