photon statistics notes

8/2/2019 Photon Statistics Notes

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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

>

=

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