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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 ia 1 e ikrb 1 ib 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