Post on 14-Sep-2018
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.