Fundamental Constants and Units

Transcription

1 Schladming Winter School 2010: Masses and Constants Lecture I Fundamental Constants and Units Ekkehard Peik Physikalisch-Technische Bundesanstalt Time and Frequency Department Braunschweig, Germany

2 Physikalisch-Technische Bundesanstalt: the National Metrology Institute of Germany Metrology: The science of measurement with applications for science, technology, economy, society Metrology Meteorology

3 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

4 The International System of Units SI: Seven base units Brochure on the SI, for download at: (English, French) (German)

5 Thebaseunitof mass

6 The base unit of time

7 The base unit of length

8 Relative uncertainties in the realization of the SI Base Units Second 6*10-16 Meter (definition linked to the second, c fixed) Kilogramm 0 (for prototype, 10-9 for comparisons) Ampere 4*10-8 Kelvin 3*10-7 Candela 10-4 Mol 8*10-8

9 An early proposal of quantum metrology James Clerk Maxwell, 1870: If, then, we wish to obtain standards of length, time, and mass which shall be absolutely 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 the absolute mass of these imperishable and unalterable and perfectly similar molecules. Postulate: Atomic energies and masses are natural constants and do not depend on space or time (apart from relativistic effects). (Einstein s Equivalence Principle) Status: Maxwell s idea is now realized for time and length, but not for mass and the electrical units.

10 Important (quantum) relations of Units and Constants Second ΔE=hν atomic clock (Cs HFS or other transition) Meter c=νλ optical interferometry Volt U=n hν/e Josephson effect Ampere I=eν single electron transistor Ohm R k =h/e 2 quantum Hall effect (von Klitzing) Kelvin E=k B T Boltzmann constant as conversion factor involves h,c,e (not G, no masses) frequency ν appears in 4 relations importance of atomic clocks

11 Possible reform: Modify the SI by exactly fixing the values of a set of fundamental constants?

12 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

13 A problem of the kilogram definition: unexplained drift 50 μg Mass changes of copies relative to the prototype BIPM 90% Pt, 10% Ir 46.4 cm 3 The intra-group drift is of order 50 µg/kg over 100 years over 100 years

14 The Watt Balance (B. Kibble, NPL, 1975) Comparison of mechanical and electrical work static mode: mg=k c BI dynamic mode: U=k c Bv keep k c B constant, equate: mgv=ui measure g,v with laser interferometers, U,I via electrical quantum standards This relates the macroscopic mass m with Planck s constant h: K J =2e/h R K =h/e 2 h=4/r K K J 2

15 The NIST Watt Balance

16 Watt-Balance definition of the kilogram The kilogram is defined such that the Planck constant is equal to exactly Js. Or: The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a photon of frequency x Hz. (Values might change according to the most recent CODATA evaluation)

17 The Avogadro Project links 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

18 Anticipated uncertainty budget (enriched Si-28)

19 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.

20 Possible new SI based on fundamental constants

21 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

22 Schematic of an atomic clock Atome, Moleküle oder Ionen Atoms, molecules, or ions Oszillator Oscillator Detektor Detector ν 0 Regelungselektronik Electronic servo S ν 0 ν Absorptions- signal signal Fehlersignal Error signal ds dν ν 0 ν

23 Caesium Beam Clock with Magnetic State Selection Oven at T=100 o C Magnetic dipole for state selection (Stern-Gerlach configuration) Ramsey interaction region with homogeneous C-field. flop-in detection of atoms that have made the hyperfine transition Detection via surface ionsation of caesium

24 Commercial Caesium Beam Clock Cs clock HP 5071A, observed accuracy ~2*10-13

25 Cesium clock with laser cooled atoms: Cesium Fountain

26 Ramsey resonance signal in a cesium fountain: Interaction time 1 s results in linewidth GHz Relative uncertainty: < 1x10-15 S. Weyers, R. Wynands, PTB

27 Optical Frequency Standard Atomic Reference forbidden transition of atoms in a laser-cooled sample Laser locked to atomic resonance, short-term stabilized to passive Fabry-Perot cavity fs-comb Generator optical clockwork, provides radiofrequency Output and means for comparison with other optical frequencies

28 Optical Clock with a Single Laser-Cooled Ion in a Paul Trap The spectroscopist s ideal: an isolated atom at rest in free space Lamb-Dicke confinement with small trap shifts laser cooling to < mk unlimited interaction time well controlled interactions (collisions, fields) ~ Quadrupole Electrodes Very low uncertainty is possible (to ) proposed by Hans Dehmelt 1975 Experiments with Hg +, Al + (NIST), Yb + (PTB, NPL), In + (U Wash., NICT), Sr + (NRC, NPL), Ba +, Ca + (Innsbruck, Marseille),...

29 Fluorescence Detection and Observation of Quantum Jumps Fluorescence from 8 Mg+ ions in a linear trap Cooling transition (dipole allowed) "forbidden" transition Photon Count Rate (data from MPQ) Single ion data (In+): Observation of a Quantum Jump Time (s) Projection Noise Limited State Detection via Electron Shelving

30 How to measure optical frequencies? 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

31 Femtosecond laser as optical frequency comb generator T. Hänsch, MPQ, J. Hall, JILA NIST PTB ILP... ΔΦ gpo time Temporal profile of a sequence of femtosecond pulses Δt = 1/f rep f rep ν(m) Corresponding optical spectrum ( lines) ν=0 frequency ν ceo ν(m) = ν ceo + m f rep Measurement of ν ceo and f rep (both in the radiofrequency range) fixes the frequencies of all modes.

32 Setup for absolute optical frequency measurements Cs fountain Yb+ trap 5 MHz ν Yb+ in units of SI Hertz 688 THz (435.5 nm) Laser frequency servo, time constant: s H Maser Femtosecond frequency comb generator Clock laser Σ Reference cavity 100 MHz 344 THz (871 nm) fib li k

33 Accuracy of primary cesium clocks and of optical frequency standards prepared by P. Gill, NPL

34 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, k B, N A The present focus is on redefinitions of kg, K and the electrical units. Time and frequency can be linked to a suitably chosen atomic transition and can be measured with the highest precision. Trapping and cooling of ions allows to build optical clocks with precision approaching