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Hanbury Brown and Twiss Effect
Anton Kapliy
March 10, 2009
Robert Hanbury Brown (1916 - 2002)
British astronomer / physicist
MS in Electrical Engineering
Radio engineer at Air Ministry
Worked on:
• Radar
• Radio Astronomy
• Intensity Interferometry
• Quantum Optics
Historical background: star diameter
Michelson interferometry:
sum of field amplitudes
Intensity interferometry:
correlations in scalar intensities
Angular resolution:
Practical limit on d was 6 meters.
Thus, for 500 nm light, resolution is
limited to ~ 10-7 radians
This is only good for very large stars
Achieved resolution: ~10-9 rad
Electromagnetic picture: setup
a
1
Incoherent light from a and b
with random phases and
amplitudes (but fixed k)
A  e
b
ikra 1 i a
1
 e
ikrb 1 ib
 I | A | 
2
1
1
|  |   |  |     e
|  |   |  | 
2
2
2
2
*
ik ( ra 1  rb 1 )  i (  a  b )
    e
•Cross terms average out due to phase variations
•Stable average intensity pattern
•Nothing surprising!
*
ik ( ra 1  rb 1 ) i (  a  b )

Electromagnetic picture: two detectors
L
a
θ
1
d
R
Consider intensity correlation
between two detectors:
We get interference fringes!
Simplification: L >> R,d
Now define a correlation function:
b
θ
2
Measuring angular size of Sirius
that’s what we want
Hanbury Brown used discarded military searchlights:
θ = 0.0068'' ± 0.0005'' = 3.1*10-8 radians
This is for an object 2.7 pc away!
Quantum mechanics: a puzzle
Photon 1
I1
Photon 2
I2
Star
Two photons are emitted from opposite sides of a star.
•Photons are independent, i.e. non-coherent
•They never “talk” to each other
BUT: photons tend to be detected “together”!
How can they be correlated at detection?
Breakdown of quantum mechanics?
Temporal coherence: HBT setup
Coherence time - time during which the wave train is stable.
If we know the phase at position z at time t1, we know it to a
high degree of certainty at t2 if t2-t1 << τc
τc = 1/Δω ≈ 1ns, where Δω is spectral width
Temporal coherence: classical model
Write intensities as a deviation from the
mean:
Write intensities as variations from the mean:
(averaging on long time scale)
 I    I (t )I (t   ) 
 I (t )I (t   ) 

 1
I 
I 
2
2
2
chaotic light from atomic
discharge lamp for dopplerbroadened spectrum with
gaussian lineshape:
Quanta of light & photon bunching
Conditional probability of detecting second photon at t=τ,
given that we detected one at t=0.
If photons are coming in sparse intervals: τ=0 is a surprise!
We can modify our classical picture of photons:
we can think of photons as coming in bunches
Extension to particles in general
Bosons (such as a photon) tend to bunch
Fermions tend to anti-bunch, i.e. "spread-out" evenly
Random Poisson arrival
Boson bunching
Fermion antibunching
Quantum mechanics: simple picture
Consider simultaneous detection:
1. Both come from b
2. Both come from a
3. b->B and a->A (red)
4. b->A and a->B (green)
If all amplitudes are M, then:
• Classical: P = 4M2
• Bosons: P=M2+M2+(M+M)2=6M2
• Fermions: P=M2+M2+(M-M)2=2M2
High energy physics: pp collisions
1. Generate a cumulative signal histogram by
taking the momentum difference Q between all
combinations of pion pairs in one pp
event; repeat this for all pp events
2. Generate a random background histogram
by taking the momentum difference Q between
pions pairs in different events
3. Generate a correlation function by taking the
ratio of signal/random
High energy physics: pion correlations
Astro: angular separation of the source
HEP: space-time distribution of production points
Ultra-cold Helium atoms: setup
3He(fermion)
1.
2.
3.
4.
5.
and 4He(boson)
Collect ultra-cold (0.5 μK) metastable Helium in a magnetic trap
Switch off the trap
Cloud expands and falls under gravity
Microchannel plate detects individual atoms (time and position)
Histogram correlations between pairs of detected atoms
micro-channel plate
Ultra-cold Helium atoms: results
Top figure: bosonic Helium
Botton figure: fermionic Helium
Partial list of sources
•http://faculty.virginia.edu/austen/HanburyBrownTwiss.pdf
•http://th-www.if.uj.edu.pl/acta/vol29/pdf/v29p1839.pdf
•http://atomoptic.iota.u-psud.fr/research/helium/helium.html
•http://www.sciencemag.org/cgi/reprint/310/5748/648.pdf
•http://www.fom.nl/live/english/news/archives/2007/artikel.pag?objectnumber=55503
•http://www.nature.com/nature/journal/v445/n7126/full/nature05513.html
•http://faculty.washington.edu/jcramer/PowerPoint/Colima%20RHIC_0311.ppt
•http://mysite.du.edu/~jcalvert/astro/starsiz.htm
•http://arxiv.org/PS_cache/nucl-th/pdf/9804/9804026v2.pdf
•Quantum Optics, textbook by A. M. Fox
•http://cmt.harvard.edu/demler/2008_novosibirsk.ppt
•http://physics.gmu.edu/~isatija/GeorgiaS.07.ppt