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."

1. Quantum Mechanics
The other great theory of modern physics
Deals with very small objects
 Electrons, atoms, molecules
Grew out of problems that seemed simple
 Black-body radiation
 Photoelectric Effect
 Atomic Spectra
Produces some very strange results…

2. Quantum Hypothesis
Planck’s trick:
Each mode has a minimum energy depending on frequency
Can only contain an integer multiple of fundamental energy
Modes with very short wavelength would need more than their
share of thermal energy
 Amount of radiation drops off very sharply at short wavelength

3. Photoelectric Effect: Einstein
Observations:
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. Bohr Model
1913: 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. Matter Waves
Louis 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. Big Molecules
430 ATOMS

7. Light as a Clock
Light: Electromagnetic wave
Extremely regular oscillation
No moving parts
Use atoms as a reference:
Performance: Lose 1s in 100,000,000 years

8. Defining Time
How 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. Quality Factor
Want a good standard reference for
timekeeping
How to characterize clocks?
How to quantify performance?
Common method: “Q factor”
Regular oscillation at some
frequency
Some small range about average
resonance frequency
Q = ratio of central frequency to spread in frequency

10. Quality Factor
frequency
Q
spread
Two 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. Light as a Clock
Light: Electromagnetic wave
Extremely regular oscillation
No moving parts
Use atoms as a reference:
Performance: Lose 1s in 100,000,000 years

12. Ammonia
First 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 H
First used as time reference at US National Bureau
of Standards in 1949 N

13. Ammonia
E  hf  h(23,870MHz) N
Operation:
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. Ammonia Clock
E  hf  h(23,870MHz) N
Advantages:
H H
1) Cheap, readily available molecule
H
2) Convenient frequency for electronics
Disadvantages Oscillator NH3
1) Doppler effect limits measurement
2) Relatively low frequency
Q ~ 100,000-1,000,000

15. Cesium
Definition 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. Cesium Clock
Early Cs clocks use atomic beam, magnets:
N N
Cs
oven Microwave Cavity
S S
Oscillator
Basic Scheme: I. I. Rabi
Q ~ 107-108

17. Cesium Clock
Early Cs clocks use atomic beam, magnets:
N N
Cs
oven Microwave Cavity
S S
Advantages:
1) Atoms move perpendicular to light  reduces Doppler shift
2) Lower frequency than NH3, but better intrinsic uncertainty
Limitations
1) Size of cavity limits measurement time, resolution
2) Still not that high a frequency

18. Separated Fields
Improved 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. Limitations of Beam Clocks
What 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. Fountain Clock
Zacharias (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. Laser-Cooled Fountain Clock
Use 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