A History of Atomic Clocks


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Lecture slides from a class on atomic clocks, giving an overview of the basic idea and some of the history leading up to modern laser-cooled cesium fountain clocks. Given as part of a class for non-majors titled "A Brief History of Timekeeping."

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A History of Atomic Clocks

  1. 1. Quantum MechanicsThe other great theory of modern physics Deals with very small objects  Electrons, atoms, moleculesGrew out of problems that seemed simple  Black-body radiation  Photoelectric Effect  Atomic SpectraProduces some very strange results…
  2. 2. Quantum HypothesisPlanck’s trick: Each mode has a minimum energy depending on frequency Can only contain an integer multiple of fundamental energyModes with very short wavelength would need more than their share of thermal energy  Amount of radiation drops off very sharply at short wavelength
  3. 3. Photoelectric Effect: EinsteinObservations: 1) Number of electrons depends on intensity Higher intensity More quanta 2) Energy of electrons DOES NOT depend on intensity Only one photon to eject 3) Cut-off frequency: minimum frequency to get any emission Einstein in 1921 Nobel Prize portrait 4) Above cut-off, energy increases linearly Cited for PE Effect with frequency
  4. 4. Bohr Model1913: Neils Bohr comes up with “solar system” model 1) Electrons orbit nucleus in certain “allowed states” 2) Electrons radiate only when moving between allowed states 3) Frequency of emitted/absorbed light determined by Planck rule  Works great for hydrogen, but no reason for ad hoc assumptions
  5. 5. Matter WavesLouis de Broglie: Particles are Waves Electrons occupy standing wave orbits Orbit allowed only if integral number of electron wavelengths h Wavelength determined by momentum  p  Same rule as for light…
  6. 6. Big Molecules430 ATOMS
  7. 7. Light as a ClockLight: Electromagnetic wave Extremely regular oscillation No moving partsUse atoms as a reference: Performance: Lose 1s in 100,000,000 years
  8. 8. Defining TimeHow do you define a second? Initial formal definition: “the fraction 1/86,400 of the mean solar day” Update (1960): “the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.”  More specific, recognizes changing length of year  Precision limited by astronomical observations  Difficult to measure locally
  9. 9. Quality FactorWant a good standard reference fortimekeeping How to characterize clocks? How to quantify performance?Common method: “Q factor” Regular oscillation at some frequency Some small range about average resonance frequencyQ = ratio of central frequency to spread in frequency
  10. 10. Quality Factor frequency Q spreadTwo ways to get high Q: 1) Decrease frequency spread improve measurement improve stability 2) Increase average frequency“Best” oscillator has high frequency, narrow range in frequency (Practical limit: Must be able to convert frequency to useful signal)
  11. 11. Light as a ClockLight: Electromagnetic wave Extremely regular oscillation No moving partsUse atoms as a reference: Performance: Lose 1s in 100,000,000 years
  12. 12. AmmoniaFirst standard based on quantum mechanics: N NH3 molecule: tetrahedral shape H H Two possible arrangements Leads to pairs of states with slight H energy separation H E  hf  h(23,870MHz) H HFirst used as time reference at US National Bureauof Standards in 1949 N
  13. 13. Ammonia E  hf  h(23,870MHz) NOperation: H H 1) Reference oscillator generates signal H 2) See if NH3 absorbs 3) Adjust frequency as needed Oscillator NH3 4) Reference oscillator drives clock (divide frequency electronically)
  14. 14. Ammonia Clock E  hf  h(23,870MHz) NAdvantages: H H 1) Cheap, readily available molecule H 2) Convenient frequency for electronicsDisadvantages Oscillator NH3 1) Doppler effect limits measurement 2) Relatively low frequencyQ ~ 100,000-1,000,000
  15. 15. CesiumDefinition of second since 1967: the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.(Updated to specify at sea level, temperature of absolute zero)“Hyperfine Level”  Lowest energy state split - in two by intrinsic magnetic moments of + nucleus and electron - +
  16. 16. Cesium ClockEarly Cs clocks use atomic beam, magnets: N N Cs oven Microwave Cavity S S OscillatorBasic Scheme: I. I. RabiQ ~ 107-108
  17. 17. Cesium ClockEarly Cs clocks use atomic beam, magnets: N N Cs oven Microwave Cavity S SAdvantages: 1) Atoms move perpendicular to light  reduces Doppler shift 2) Lower frequency than NH3, but better intrinsic uncertaintyLimitations 1) Size of cavity limits measurement time, resolution 2) Still not that high a frequency
  18. 18. Separated FieldsImproved method by Norman Ramsey: Break cavity in two oven Free flight in between RF  Allows longer measurement NIST-7: lose 1s in 3,000,000 years
  19. 19. Limitations of Beam ClocksWhat determined best performance of NIST-7? 1) Doppler shifts oven Atoms moving at >100m/s RF 2) Cavity shifts Hard to make identical 3) Time of flight Only ~100 ms between
  20. 20. Fountain ClockZacharias (1953) proposed solution to cavity and time-of-flight problems  Launch atoms vertically Only one cavity, interact twice Long time-of flight above cavity RF Problem: Hot atoms  High velocities spray all over the place Very few make it back through cavity
  21. 21. Laser-Cooled Fountain ClockUse lasers to slow motion of atoms Reduce velocity to ~cm/s temperature to 10-6 K (Lots of cool physics, different class)  Use single microwave cavity  Around 1s interaction time Primary standards in France, US, UK,… Performance: Lose 1s in ~100,000,000 years