Fundamental Constants and Units -...

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  • Lecture I

    Fundamental Constants and Units

    Ekkehard Peik

    Physikalisch-Technische BundesanstaltTime and Frequency Department

    Braunschweig, Germany

    Schladming Winter School 2010: Masses and Constants

  • Physikalisch-Technische Bundesanstalt:

    the National Metrology Institute of GermanyMetrology: The science of measurement

    with applications for science, technology, economy, society



  • Lecture I

    The International System of units SI Units based on fundamental constants Routes towards a new definition of the kilogram A new generation of atomic clocks

    Lecture II

    Variations of fundamental constants: Motivation Search in geo- and astrophysics Search for new physics in precision experiments with

    atomic clocks

  • The International System of Units SI: Seven base units

    Brochure on the SI, for download at: (English, French) (German)

  • The base unit of mass

  • The base unit of time

  • The base unit of length

  • Relative uncertainties in the realization of the SI Base Units

    Second 6*10-16Meter 10-10 (definition linked to the second, c fixed)Kilogramm 0 (for prototype, 10-9 for comparisons)Ampere 4*10-8Kelvin 3*10-7Candela 10-4Mol 8*10-8

  • James Clerk Maxwell, 1870: If, then, we wish to obtain standards of length, time, and mass which shall beabsolutely permanent, we must seek them not in the dimensions, or the motion,or the mass of our planet, but in the wave-length, the period of vibration, and theabsolute mass of these imperishable and unalterable and perfectly similarmolecules.

    An early proposal of quantum metrology

    Postulate: Atomic energies and masses are natural constants and do not dependon space or time (apart from relativistic effects).(Einsteins Equivalence Principle)

    Status: Maxwells idea is now realized for time and length, but not for mass and theelectrical units.

  • Important (quantum) relations of Units and Constants

    Second E=h atomic clock (Cs HFS or other transition)Meter c= optical interferometryVolt U=n h/e Josephson effectAmpere I=e single electron transistorOhm Rk=h/e2 quantum Hall effect (von Klitzing)Kelvin E=kBT Boltzmann constant as conversion factor

    involves h,c,e (not G, no masses) frequency appears in 4 relations importance of atomic clocks

  • Possible reform: Modify the SI by exactly fixing the valuesof a set of fundamental constants


  • The International System of units SI Units based on fundamental constants Routes towards a new definition of the kilogram A new generation of atomic clocks

  • A problem of the kilogram definition: unexplained drift


    50 g

    Mass changes of copies relative to the prototype

    The intra-group drift is of order50 g/kg over 100 years50 10-9 over 100 years90% Pt, 10% Ir

    46.4 cm3

  • The Watt Balance (B. Kibble, NPL, 1975)Comparison of mechanical and electrical work

    static mode:mg=kcBI

    dynamic mode:U=kcBv

    keep kcB constant,equate: mgv=UI

    measure g,v with laser interferometers, U,I via electrical quantum standards

    This relates the macroscopic mass m with Plancks constant h:KJ=2e/h RK=h/e2 h=4/RK KJ2

  • The NIST Watt Balance

  • Watt-Balance definition of the kilogram

    The kilogram is defined such that the Planck constant is equal to exactly 6.626 068 96 1034 Js.


    The kilogram is the mass of a body at rest whose equivalent energyequals the energy of a photon of frequency 1.35639274 x 1050 Hz.

    (Values might change according to the most recent CODATA evaluation)

  • The Avogadro Projectlinks atomic number and macroscopic mass measure atomic mass ratio of Si-28 and C-12 (cyclotron freq. in ion traps) grow isotopically pure perfect single crystal of Si-28 measure lattice constant of Si-28 via X-ray interferometry produce perfectly round sphere, measure volume and mass

  • Anticipated uncertainty budget (enriched Si-28)

  • Avogadro definition of the kilogram

    Present situation for the kilogram redefinition:Both approaches (Watt Balance and Avogadro) strive to reduce their uncertainties and to obtain consistency.

  • Possible new SI based on fundamental constants

  • The International System of units SI Units based on fundamental constants Routes towards a new definition of the kilogram A new generation of atomic clocks

  • Schematic of an atomic clock



    Atome, Molekle oder Ionen






    Absorptions- signal


    Atoms, molecules, or ions


    Error signal

    Absorption signal


    Electronic servo

  • Caesium Beam Clock with Magnetic State Selection

    flop-in detection of atomsthat have made thehyperfine transition

    Magnetic dipole forstate selection(Stern-Gerlach configuration)

    Ramsey interactionregion withhomogeneousC-field.

    Detection viasurface ionsationof caesium

    Oven at T=100oC

  • Commercial Caesium Beam Clock

    Cs clock HP 5071A, observed accuracy ~2*10-13

  • Cesium clock with laser cooled atoms: Cesium Fountain

  • Ramsey resonance signal in a cesium fountain:Interaction time 1 s results in linewidth 1 Hz @ 9.19 GHzRelative uncertainty: < 1x10-15

    S. Weyers, R. Wynands, PTB

  • Optical Frequency Standard


    forbidden transition of atomsin a laser-cooled sample

    Laserlocked to atomic resonance,short-term stabilized to passiveFabry-Perot cavity


    optical clockwork, provides radiofrequencyOutput and means for comparison with otheroptical frequencies

  • Optical Clock with a Single Laser-Cooled Ion in a Paul Trap

    ~ QuadrupoleElectrodes

    The spectroscopists ideal: an isolated atom at restin free space

    Lamb-Dicke confinement withsmall trap shifts

    laser cooling to < mK unlimited interaction time well controlled interactions(collisions, fields)

    Very low uncertainty is possible (to 10-18)proposed by Hans Dehmelt 1975

    Experiments with Hg+ , Al+ (NIST), Yb+ (PTB, NPL), In+ (U Wash., NICT),Sr+ (NRC, NPL), Ba+, Ca+ (Innsbruck, Marseille), ....

  • Projection Noise Limited State Detection via Electron Shelving

    Coolingtransition(dipoleallowed) "forbidden" transition

    Time (s)




    nt R


    Single ion data (In+):Observation of a Quantum Jump

    Fluorescence Detection and Observation of Quantum Jumps

    Fluorescence from8 Mg+ ions in a linear trap

    (data from MPQ)

  • absolute measurement

    comparison of an optical frequency and a Cs frequency standard

    frequency division

    generation of a microwave frequency from an optical reference,optical clockwork

    How to measure optical frequencies?

  • Femtosecond laser as optical frequency comb generator




    t = 1/frep




    (m) = ceo + m frep

    T. Hnsch, MPQ, J. Hall, JILA NIST PTB ILP...

    Temporal profile of a sequence offemtosecond pulses

    Measurement of ceo and frep (both in the radiofrequency range) fixes the frequencies of all modes.

    Corresponding opticalspectrum(105 106 lines)

  • Setup for absolute optical frequency measurements

    Clock laserH MaserFemtosecondfrequency combgenerator

    Cs fountain Yb trap+

    5 MHz

    100 MHz 344 THz (871 nm)200 fib li k

    688 THz(435.5 nm)

    in units of SI Hertz



    Laser frequency servo,time constant: 10...30 s

  • prepared by P. Gill, NPL

    Accuracy of primary cesium clocks and of optical frequency standards

  • Summary of Lecture I

    Work is under way to establish a more precise and consistent system of units based on fixed values of fundamental constants: c, h, e, kB, NA

    The present focus is on redefinitions of kg, K and theelectrical units.

    Time and frequency can be linked to a suitably chosenatomic transition and can be measured with the highestprecision.

    Trapping and cooling of ions allows to build opticalclocks with precision approaching 10-18.