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