photon statistics notes
TRANSCRIPT
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PHY 411 / 412 / 436
Part II: Photon statisticsLectures 5 - 8
Quantum Optics
Prof. Mark Fox
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Overview
Topics covered
Photon statistics
sub-Poissonian light
Hanbury Brown-Twiss
experiments
Photon anti-bunchingReading
Quantum Optics
Chapters 5 - 6
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What is quantum optics ?
PhotonsQuantizedQuantum optics
Electromagneticwaves
QuantizedSemi-classicaloptics
Electromagneticwaves
Hertzian dipolesclassical optics
LIGHTATOMSATOM-LIGHTinteraction
Almost all of undergraduate physics is well described
by classical or semi-classical optics !
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Photon counting
low intensity
beam
power P countert
output
PMT / APD integration time setting, T
P
R
N RT
=
= =
Photon flux (photons/s)
Count rate (counts/s)Number of counts in time T
= detector quantum efficiency = counts out / photons in
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Photon streams
1 nW
30 cm
= 633 nm
= 3.1 109 photons / s
average of 3 photons in 30 cm of beam timing random on very short time scales
Poissonian statistics
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Poissonian statistics
( ) exp( )!
nn
P n nn
n n
=
=
mean
standard deviation
n
n
=
=
Random events with discreteoutcomes. [cf normal
(Gaussian) distribution for continuousvariables.]
Average well-defined, but individual events random
Examples: number of rain drops falling in time T
number of radioactive decays in time T
number of photons from starlight detected in time T
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Poisson distributions
( ) exp( )!
nnP n n
n=
0 5 10 15 200.0
0.5
1.0
P(n)
n
0 5 10 15 200.0
0.2
0.4
P(n)
n
0 5 10 15 200.0
0.1
0.2
P(n)
n
0 5 10 15 200.00
0.05
0.10
0.15
n
P(n)
10n =1n =
5n =0.1n =
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Classification by statistics
50 100 1500.00
0.04
0.08
n
P(n)
Poisson
sub-Poissonian
super-Poissonian
n = 100
n n
n n
n n
>
=