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Hanbury Brown and Twiss Effect
Anton KapliyMarch 10, 2009
Robert Hanbury Brown (1916 - 2002)
British astronomer / physicistMS in Electrical EngineeringRadio engineer at Air Ministry
Worked on:• Radar• Radio Astronomy• Intensity Interferometry• Quantum Optics
Historical background: star diameterMichelson 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 radiansThis is only good for very large stars
Achieved resolution: ~10-9 rad
Electromagnetic picture: setup
•Cross terms average out due to phase variations•Stable average intensity pattern•Nothing surprising!
bbaa iikriikr eeA 11
1
a
b
1
22
)()(*)()(*22
2
11
||||
||||
||1111
babababa irrikirrik ee
AI
Incoherent light from a and b with random phases and amplitudes (but fixed k)
Electromagnetic picture: two detectors
We get interference fringes!
Simplification: L >> R,dNow define a correlation function:
a
b
1
2Consider intensity correlation between two detectors:
L
R dθ
θ
Measuring angular size of Sirius
Hanbury Brown used discarded military searchlights:θ = 0.0068'' ± 0.0005'' = 3.1*10-8 radiansThis is for an object 2.7 pc away!
that’s what we want
Quantum mechanics: a puzzle
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?
Star
Photon 1
Photon 2
I1
I2
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:
chaotic light from atomic discharge lamp for doppler-broadened spectrum with gaussian lineshape:
(averaging on long time scale)
22
2 )()(1
)()(
ItItI
ItItII
Write intensities as variations from the mean:
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 bunchFermions 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 b2.Both come from a3.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 events2. Generate a random background histogram by taking the momentum difference Q between pions pairs in different events3. Generate a correlation function by taking the ratio of signal/random
High energy physics: pion correlations
Astro: angular separation of the sourceHEP: space-time distribution of production points
Ultra-cold Helium atoms: setup3He(fermion) and 4He(boson)1. Collect ultra-cold (0.5 μK) metastable Helium in a magnetic trap2. Switch off the trap3. Cloud expands and falls under gravity4. Microchannel plate detects individual atoms (time and position)5. 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