# 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

Meteorology

Metrology

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:http://www.bipm.org/fr/si/si_brochure/general.html (English, French)http://www.ptb.de/de/publikationen/download/index.html (German)

http://www.bipm.org/fr/si/si_brochure/general.htmlhttp://www.ptb.de/de/publikationen/download/index.html

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

BIPM

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.

Or:

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

Oszillator

0

Atome, Molekle oder Ionen

Detektor

Regelungs-elektronik

0

0

S

Absorptions- signal

FehlersignaldSd

Atoms, molecules, or ions

Oscillator

Error signal

Absorption signal

Detector

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

AtomicReference

forbidden transition of atomsin a laser-cooled sample

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

fs-CombGenerator

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)

Pho

ton

Cou

nt R

ate

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

time

frequency

gpo

t = 1/frep

=0ceo

frep

(m)

(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

Yb+

Referencecavity

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.