Date post: | 25-May-2015 |
Category: |
Technology |
Upload: | chad-orzel |
View: | 5,147 times |
Download: | 4 times |
Quantum MechanicsThe 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…
Quantum Hypothesis
𝜆𝑛=2𝑛𝐿𝐸𝑛=h𝑓=h
𝑐𝜆𝑛
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 theirshare of thermal energy
Amount of radiation drops off very sharply at short wavelength
Photoelectric Effect: EinsteinObservations:
1) Number of electrons depends on intensity
2) Energy of electrons DOES NOT depend on intensity
3) Cut-off frequency: minimum frequency to get any emission
4) Above cut-off, energy increases linearly with frequency
Higher intensity More quanta
Only one photon to eject
𝐾𝐸=h𝑓 −𝜙 Einstein in 1921Nobel Prize portraitCited for PE Effect
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
Matter WavesLouis de Broglie: Particles are Waves
Electrons occupy standing wave orbits
Orbit allowed only if integral number of electron wavelengths
Wavelength determined by momentumh
p
Same rule as for light…
Big Molecules
430 ATOMS
Light as a ClockLight: Electromagnetic wave
Extremely regular oscillation
No moving parts
Use atoms as a reference:
Performance: Lose 1s in 100,000,000 years
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
Quality FactorWant a good standard reference fortimekeeping
How to characterize clocks?
Common method: “Q factor”
Regular oscillation at some frequencySome small range about average resonance frequency
Q = ratio of central frequency to spread in frequency
How to quantify performance?
Quality Factorfrequency
Qspread
Two ways to get high Q:
1) Decrease frequency spread
improve measurementimprove 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)
Light as a ClockLight: Electromagnetic wave
Extremely regular oscillation
No moving parts
Use atoms as a reference:
Performance: Lose 1s in 100,000,000 years
AmmoniaN
HH
H
First standard based on quantum mechanics:
N
HH
H
NH3 molecule: tetrahedral shapeTwo possible arrangements
Leads to pairs of states with slightenergy separation
(23,870 )E hf h MHz
First used as time reference at US National Bureau of Standards in 1949
AmmoniaN
HH
H
(23,870 )E hf h MHz
NH3Oscillator
Operation:
1) Reference oscillator generates signal
2) See if NH3 absorbs
3) Adjust frequency as needed
4) Reference oscillator drives clock (divide frequency electronically)
Ammonia ClockN
HH
H
(23,870 )E hf h MHz
NH3Oscillator
Advantages:
1) Cheap, readily available molecule
2) Convenient frequency for electronics
Disadvantages
1) Doppler effect limits measurement
2) Relatively low frequency
Q ~ 100,000-1,000,000
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 splitin two by intrinsic magnetic moments ofnucleus and electron
Cesium ClockEarly Cs clocks use atomic beam, magnets:
Csoven
N
S
Microwave Cavity
N
S
Oscillator
Q ~ 107-108
Basic Scheme: I. I. Rabi
Cesium ClockEarly Cs clocks use atomic beam, magnets:
Csoven
N
S
Microwave Cavity
N
S
Advantages:
1) Atoms move perpendicular to light reduces Doppler shift
2) Lower frequency than NH3, but better intrinsic uncertainty
Limitations1) Size of cavity limits measurement time, resolution
2) Still not that high a frequency
Separated Fields
oven
RF
NIST-7: lose 1s in 3,000,000 years
Improved method by Norman Ramsey:
Break cavity in two
Free flight in between
Allows longer measurement
Limitations of Beam Clocks
oven
RF
What determined best performance of NIST-7?
1) Doppler shifts
2) Cavity shifts
3) Time of flight
Atoms moving at >100m/s
Hard to make identical
Only ~100 ms between
Fountain Clock
RF
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
Problem: Hot atoms High velocitiesspray all over the place
Very few make it back through cavity
Laser-Cooled Fountain Clock
Performance: Lose 1s in ~100,000,000 years
Use lasers to slow motion of atoms
Reduce velocity to ~cm/stemperature to 10-6 K
(Lots of cool physics, different class)
Use single microwave cavity
Around 1s interaction time
Primary standards in France, US, UK,…