Ebook: Metrology and Fundamental Constants

This Course on Metrology and Fundamental Constants was held in Varenna in July 2006 and was organised by the Italian Physical Society, the Istituto Nazionale di Ricerca Metrologica of Italy (INRIM), and the Bureau International des Poids et Mesures. Co-incidentally 2006 marks the first year of the existence of INRIM, the new Metrological Institution of Italy, resulting from the merging of the Istituto di Metrologia “Gustavo Colonnetti” (IMGC) and the Istituto Elettrotecnico Nazionale “Galileo Ferraris” (IEN).

Besides this particular event, the School in Varenna, as well as the Summer School on Metrology organized by the BIPM in Paris, is justified by three facts, the need to provide, from time to time, a co-ordinated set of lectures which present the relevant progress in Metrology, the increasing intertwining between Fundamental Physics and the practice of Metrological Measurements, and, third, the flurry of new and unexpected discoveries in this field, with a correlated series of Nobel Prizes bestowed to individuals working in Fundamental Constants research and novel experimental methods.

This is the fourth of the Enrico Fermi Schools on Metrology and Fundamental Constants organized by the Italian Physical Society. The first was held in 1976, the second and the third respectively in 1989 and 2000, all of which were supported by the direct presence of BIPM via the Director pro tempore and the strong presence of the National Metrological Laboratories. This presence was felt in two ways, first by sending many of their experts as lecturers and, secondly, by supporting the attendance of a large number of their researchers at the School.

One of the most fascinating and exciting characteristics of metrology is its intimate relationship between fundamental physics and the leading edge of technology which is needed to perform advanced and challenging experiments and measurements, as well as the determination of the values and interrelations between the Fundamental Constants.

In some cases, such as the caesium fountains clocks or the optical frequency standards, the definition of the value of a quantity is, in the laboratory, in the region of 10⁻¹⁶ and experiments are under way to reach 10⁻¹⁸.

Many of these results and the avenues leading to further advances were discussed during the School, along a major step in metrology, expected in the near future, which could change the “old” definition of the kilogram, still based on a mechanical artefact, toward a new definition resting on a fixed value of a fundamental constant. The current possibilities include a fixed value of the Planck Constants or the Avogadro Number. Several National Metrological Institutes (NMIs) and other organizations are collaborating, worldwide, in the International Avogadro Consortium, and a number of NMIs are involved in the so-called “Watt balance” in the mechanical watt ( measurement of a force and of a speed ) is directly compared with the electrical watt in the same device (measured via Josephson and von Klitzing effects) and which would led to a measurement of the Planck Constant.

The success of this fourth Course was made possible by the close co-operation and the dedication of many Institutions and individuals.

The Directors wish to thank the Italian Physical Society and the INRIM for having provided the financial support for the organization of the School and for the attendance of several student. Of the some seventy or so students attending the School, two thirds were supported by their parent Institution, and the others directly by the School.

The Directors also wish to express their warm thanks to all the lecturers and seminar speakers who offered their expertise to the students, not only during the scheduled lectures, but also by being available for discussions and seminars; their enthusiasm and competence were crucial elements for ths success of the school and were duly appreciated by the students.

A particular debt of gratitude must be expressed to Maria Luisa Rastello who acted as Scientific Secretary of the School, mainly in the three-year period needed to prepare and to organize the school. During the same period the Directors met on a number of times to optimise the program and to identify the Speakers to be invited.

Finally the extremely valuable help and the friendly co-operation of Mrs. Barbara Alzani and Carmen Vasini acting on behalf of SIF must be acknowledged.

The Directors hope that the friendship created, as well as the information shared, will be valuable elements in building the students' future careers. For many metrologists, attendance at a the Varenna school is a seminal point in their training and development. The Directors look forward to seeing many of the 2006 students appear in the future as leaders and specialists in their fields. If the school has played even a small part in this, we shall have achieved our aim.

T. Hänsch, S. Leschiutta and A. J. Wallard

1. Introduction; 2. Metrology and trade; 2.1. The general case; 2.2. Traceability in trade; 2.3. Mutual recognition of NMI standards: the CIPM MRA; 2.4. The essential points of the CIPM MRA; 2.5. The key comparison database; 2.6. Take up of the CIPM MRA; 2.7. The importance of Mutual Recognition Arrangements; 3. Metrology and innovation; 4. Metrology and medicine; 4.1. Uses; 4.2. Why is chemical metrology “difficult”? 5. And there is more!

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

1. Structures; 2. Metre Convention; 2.1. The Metre Convention; 2.2. The BIPM; 2.3. The MKS system; 2.4. The SI Brochure; 3. BIPM: the first 75 years; 4. National structures: The National Metrology Institutes (NMIs); 4.1 National Metrology Institutes; 4.2. NMI science; 5. Traceability: The birth of accreditation; 5.1. Traceability; 5.2. Accreditation bodies; 5.3. ILAC; 5.4. A National Measurement System; 5.5. Definitions of traceability; 6. Regional Metrology Organisations; 6.1. The birth of RMOs; 6.2. RMOs today; 6.3. Equivalence of national measurement standards; 7. Mutual recognition of NMI standards: the CIPM MRA; 7.1. The significance of the CIPM MRA; 7.2. Launch; 8. The essential points of the CIPM MRA; 8.1. Objectives; 8.2. Technical competence; 8.3. Comparisons and quality systems; 8.4. The NMIs commitment; 8.5. Associates of the General Conference; 8.6. The Key Comparison Database (KCDB); 9. Take up of the CIPM MRA; 9.1. Regulators and the CIPM MRA; 9.2. A market for NMI calibration services; 9.3. Consequences for NMI services; 10. Other metrology bodies; 10.1. The World Metrology System; 10.2. Accreditation and ILAC; 10.3. The importance of MRAs; 10.4. Measurement Accreditation and Standardization; 11. Closing comments

1. Introduction; 2. Summary and aim of this lecture; 3. Some roles of measurements; 3.1. 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; 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? 3.3. Very early measurements of the equivalence principle; 4. Some roles of instruments, the special case of pendula; 4.1. External conditions fostering the birth of a new instrument; 4.2. Why also pendula are to be considered; 4.3. Metrological application of pendula; 5. Conclusions

1. Introduction; 2. Metric systems; 2.1. Families of standards and units based on the energy needed to reach a given goal; 2.2. Families of standards based on anthropomorphism; 2.3. Families based on agreed (or imposed) material artifacts; 2.4. Families based on some traditional historical definition, usually supported by artifacts; 2.5. Families based on any property of Nature or Physics; 3. General and essential characteristic to be provided by any metric system; 3.1. Universality; 3.2. Uniformity; 3.3. Perennity; 3.4. Accuracy, precision, stability, independence from influence quantities

1. Introduction; 2. History; 3. Quantities and quantity equations; 3.1. Definitions of quantities; 3.2. Quantities of the same kind; 3.3. Quantity equations and numerical value equations; 4. The equations of physics, definitional constants; 5. The problem of electrical quantities and units; 6. The International System of Units, the SI, a coherent system of units; 7. Biological quantities and units; 7.1. Photobiological quantities; 7.2. Quantities for ionizing radiation; 7.3. Biological quantities for medicine; 8. The use of the fundamental constants as reference quantities for the definition of units; 9. Final remarks

The publication in 1993/1995 of the Guide to the Expression of Uncertainty in Measurement, GUM, stimulated a great development of research concerning measurand estimation and uncertainty evaluation. The application of the GUM method has brought into light its merits and limits. This paper reviews them and discusses the recent evolution of concepts and methods in the specific field of uncertainty evaluation.

1. Introduction; 2. SI and electrical units; 3. Definition of a unit; 4. Realisation of a unit; 5. Reproduction of a unit; 6. Maintenance and dissemination of a unit; 7. Impedance measurements; 8. Bridge and ratio techniques; 9. AC/DC transfer; 10. Power and energy measurements; 11. International comparisons

1. Introduction; 2. The conventional system of electrical units; 2.1. The determination of R_K and K_J ; 2.2. Conventional values for R_K and K_J ; 3. The Josephson voltage standard; 3.1. Theoretical background of the Josephson effect; 3.2. Conventional Josephson voltage standard; 3.3. Programmable voltage standards; 4. The quantum Hall resistance standard; 4.1. Basic principles; 4.2. Edge state model; 4.3. The two-dimensional electron gas; 4.4. Measurement techniques; 4.5. Universality of the quantised Hall resistance; 4.6. The use of the QHR as a standard of resistance; 4.7. A.c. measurements of the QHR; 5. Conclusions

1. Introduction; 2. Single electron devices; 2.1. The elementary device based on Coulomb blockade; 2.2. The single-electron transistor; 2.3. The electron pump; 3. Other single charge transport devices; 3.1. RF-SET-transistor–based electron counter; 3.2. SETSAW pump; 3.3. Cooper pair pump; 3.4. New devices; 4. New electrical standards and quantum metrological triangle experiments; 4.1. Electrical standards; 4.2. Quantum-Metrological Triangle; 4.3. QMT experimental set-up using a CCC; 4.4. QMT experimental set-up using an electron counting capacitance standard; 5. Conclusion and prospects

1. Introduction; 2. Radiative forces; 2.1. The scattering force; 2.2. The dipole force; 2.3. Doppler cooling; 3. Deceleration and cooling of an atomic beam; 3.1. Chirp cooling; 3.2. Zeeman tuning; 3.3. Optical pumping; 4. Traps for neutral atoms; 4.1. Dipole force traps; 4.2. Radiation pressure force traps; 4.3. Magneto-static traps; 5. Sub-Doppler laser cooling; 5.1. Observation of sub-Doppler temperatures; 5.2. New cooling mechanisms; 6. Metrology with cold atoms; 6.1. Atomic fountain clocks; 6.2. Atom interferometers; 7. Coherent manipulation of Bose-Einstein condensates with light; 7.1. The triaxial TOP trap for sodium; 7.2. BEC of sodium in a TOP trap; 7.3. Diffraction of atoms by a standing wave; 7.4. Bragg diffraction of atoms; 7.5. Raman output coupling: Demonstration of a CW atom laser; 8. Nonlinear atom optics with Bose-Einstein condensates; 8.1. Four-wave mixing with matter-waves; 8.2. Quantum phase engineering; 8.3. Solitons in a BEC; 8.4. Observation of solitons in a BEC; 8.5. Quantum atom optics

1. Introduction; 2. Description of atomic fountains; 2.1. Atomic preparation; 2.2. Clock transition interrogation; 2.3. Detection; 2.4. Operation of the fountain clock; 3. Performances of fountains; 3.1. Frequency stability and quantum projection noise; 3.2. Frequency accuracy, collisions between cold atoms; 4. Beyond fountains; 4.1. Optical clocks with neutral atoms in free fall; 4.2. Optical clocks with trapped ions; 4.3. Optical clocks with trapped neutral atoms; 5. Applications and prospects; 5.1. Cold atom clocks in space; 5.2. Fundamental physics

1. Introduction; 2. Atomic frequency standards: principle of operation and characterization of their performance; 3. Caesium clocks, classical and optically pumped; 3.1. Caesium clocks with magnetic selection; 3.2. Caesium AFS with optical pumping; 3.3. Systematic frequency offsets; 3.4. Development of the accuracy with time; 3.5. Commercial caesium clocks; 4. More accurate, more complex; 4.1. Primary clocks; 4.2. Atomic fountains; 4.3. Optical clocks; 5. A survey on other AFS in practical use; 5.1. General remarks; 5.2. The hydrogen maser; 5.3. Rubidium gas cell frequency standards; 5.4. Current trend in gas cell AFS; 6. Applications; 6.1. A short note on the realization of TAI; 6.2. Timing aspects of the future European satellite navigation system Galileo; 6.3. Synchronization of the networks for electrical power distribution; 6.4. The search for the variability of the fundamental constants; 7. Conclusion; 8. Disclaimer

A laser frequency comb allows the conversion of the very rapid oscillations of visible light of some 100's of THz down to frequencies that can be handled with conventional electronics, say below 100 GHz. This capability has enabled the most precise laser spectroscopy experiments yet that allowed to test quantum electrodynamics, to determine fundamental constants and to search for possible slow changes of these constants. Using an optical frequency reference in combination with a laser frequency comb has made it possible to construct all optical atomic clocks, that are about to outperform the current cesium atomic clocks.

1. Introduction; 2. Evolution of time scales and their associated interval units; 2.1. Universal Time (UT); 2.2. Ephemeris Time (ET); 2.3. The downing of atomic time; 2.4. The birth of Coordinated Universal Time UTC; 3. Metrologic qualities of a time scale; 4. Relativity and time scales; 4.1. Proper and coordinate quantities; 4.2. Coordinate systems; 4.3. Practical realizations of the coordinate systems; 4.4. Coordinate times; 5. Realization of TAI and UTC; 5.1. An essential tool: clock comparisons; 5.2. Use of GPS for time transfer; 5.3. Two-way satellite time and frequency transfer; 5.4. Calibration of time transfer equipment and link uncertainties; 6. The algorithm Algos; 6.1. The general scheme; 6.2. Clocks in TAI; 6.3. Free Atomic Time Scale (EAL), clock weighting and frequency prediction; 6.4. Primary frequency standards (PFS); 7. Secondary representations of the second; 8. Dissemination and access to the time scales; 9. List of acronyms used in the text (in English and French when applicable)

1. Introduction; 2. Refrigeration and thermometry; 3. Secondary thermometers; 4. The unit of thermodynamic temperature; 5. The measurement of thermodynamic temperature; 5.1. Gas thermometry; 5.2. Acoustic gas thermometry; 5.3. Other thermodynamic techniques; 6. International Temperature Scale of 1990, ITS-90; 6.1. The ITS-90 below the triple point of neon, 24.5561 K; 6.2. Thermodynamic accuracy of the ITS-90; 7. Ultra-low temperatures; 7.1. Nuclear cooling; 8. ULT Thermometry; 8.1. Superconductive reference points; 8.2. Magnetic thermometry; 8.3. Noise thermometry with SQUIDS; 9. ³He melting pressure thermometry and the PLTS-2000; 9.1. Realisation of the PLTS-2000; 10. Future prospects

1. Introduction: a brief course into history; 2. Measurement of thermodynamic temperature; 3. Gas thermometry; 3.1. Constant-volume gas thermometers; 3.2. Acoustic gas thermometers; 3.3. Dielectric-constant gas thermometers; 4. Noise thermometry; 5. Total radiation thermometry; 6. Spectral radiation thermometry; 6.1. Relative mode referenced to known temperature; 6.2. Absolute mode; 7. Doppler broadening thermometry; 8. Practical high-temperature metrology; 8.1. The International Temperature Scale of 1990; 8.2. Melting and freezing points of metals; 8.3. Eutectic points of metal-carbon compositions; 9. New definition of the kelvin

1. Introduction; 2. Basic description of some physical properties of dilute monoatomic gases; 2.1. Thermophysical and transport properties; 2.2. Electrical properties; 3. Basic theory and operation of acoustic and microwave resonators; 3.1. Acoustic and microwave frequencies in a spherical cavity; 3.2. Effects of perturbed geometry on achievable precision and accuracy; 4. Speed of sound as a thermodynamic temperature standard; 4.1. Relationship between speed of sound and thermodynamic temperature; 4.2. Physical meaning of the Boltzmann constant and primary acoustic thermometry; 4.3. Review of recent results obtained by primary acoustic thermometry; 4.4. Redetermination of the molar gas constant R and the Boltzmann constant k; 5. Speed of light for an atomic pressure standard; 5.1. Working equations for an electric primary pressure standard; 5.2. Current precision and accuracy achievable with a primary pressure standard

1. Introduction; 2. What do mass metrologists measure? 2.1. The relation between mass metrology and contemporary physics; 2.2. Traditional mass metrology; 3. The kilogram and the International System of Units; 4. How modern balances work; 4.1. Ultimate performance; 4.2. Commercial analytical balances; 5. Legal metrology and conventional mass; 5.1. What scientists should know about conventional mass; 5.2. Another way to view conventional mass; 6. Nanograms to yoctograms (“there's plenty of room at the bottom”); 6.1. Mass and nanometrology; 6.2. Cantilever systems; 6.3. Calibration of AFMs using calibrated mass standards (deadweights); 6.4. Oscillating cantilevers; 6.5. Gravitational mass of a neutron; 7. Conclusion

1. Introduction; 2. Present status of the kilogram; 2.1. Role of the kilogram in the SI; 2.2. Results of periodic verifications of national prototypes; 3. Counting atoms using ion accumulation; 4. Electromechanical methods; 4.1. The watt balance experiment; 4.2. Other electrical methods; 5. Possible new definitions of the kilogram and conclusions; 5.1. Definitions that fix the value of the Avogadro constant; 5.2. Definitions that fix the value of the Planck constant; 5.3. Planck and Avogadro constants; 5.4. A decision whose time will come

1. Introduction; 2. Weighing γ-ray photons; 2.1. γ-ray spectroscopy; 2.2. Mass spectroscopy; 3. X-ray crystal density measurement of N_A ; 3.1. Molar mass; 3.2. Lattice parameter; 3.3. Density; 4. Conclusions

1. Introduction; 2. Early scanning probe microscopes and metrology developments; 3. What nanotechnology needs; 4. Practical examples; 5. New developments. Optical diffraction microscopy; 6. Summary

Introduction; 1. Measurement of composition; 2. The mole; 3. Primary methods of measurement; 4. The “grande salle” metaphor; 5. Isotope Dilution Mass Spectrometry (IDMS); 6. pH and electrochemistry; 7. Primary methods in practice; 8. Measurement standards for gases; 9. Preparative comparisons; 10. Complete mixture methods; 11. Photochemical pollution; 12. Monitoring photochemical pollution; 13. Volatile organic compounds (VOCs); 14. Ozone in the atmosphere; 15. Measuring ozone with the NIST SRP; 16. Measuring ozone by gas phase titration; 17. Coherence of ozone measurements; 18. Particles; 19. Summary. Why traceability to the SI?

1. Introduction; 2. History; 3. Base radiometric units or methods; 3.1. Sources; 3.2. Techniques and methods; 3.3. Detectors; 4. Cryogenic radiometry; 4.1. Background; 4.2. Applications of cryogenic radiometers; 4.3. Confirmation of accuracy; 4.4. Future developments; 5. Basis for optical radiation scales; 5.1. Spectral responsivity scales; 5.2. Transfer standard detectors; 6. Thermal radiometry; 6.1. Primary quantities; 7. Spectral irradiance and radiance; 8. Photometric units; 9. Transfer standards for source measurements; 10. Climate change; 10.1. Radiometric requirements; 10.2. Total Solar Irradiance (TSI); 10.3. Earth viewing instruments; 10.4. Traceable Radiometry Underpinning Terrestrial and Helio Studies (TRUTHS); 11. Spectrophotometry, colour and sensory metrology; 11.1. Spectrophotometry; 11.2. Colour; 11.3. Sensory metrology; 12. Conclusion