1 / 17

Hanbury Brown and Twiss Effect

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.

greg
Download Presentation

Hanbury Brown and Twiss Effect

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hanbury Brown and Twiss Effect Anton Kapliy March 10, 2009

  2. 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

  3. Historical background: star diameter Intensity interferometry: correlations in scalar intensities Michelson interferometry: sum of field amplitudes 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

  4. Electromagnetic picture: setup Incoherent light from a and b with random phases and amplitudes (but fixed k) a 1 • Cross terms average out due to phase variations • Stable average intensity pattern • Nothing surprising! b

  5. Electromagnetic picture: two detectors L a 1 θ d R We get interference fringes! Simplification: L >> R,d Now define a correlation function: Consider intensity correlation between two detectors: θ b 2

  6. 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!

  7. Quantum mechanics: a puzzle I1 Photon 1 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? I2 Photon 2

  8. 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

  9. Temporal coherence: classical model Write intensities as a deviation from the mean: Write intensities as variations from the mean: chaotic light from atomic discharge lamp for doppler-broadened spectrum with gaussian lineshape: (averaging on long time scale)

  10. 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

  11. 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

  12. Quantum mechanics: simple picture Consider simultaneous detection: • Both come from b • Both come from a • b->B and a->A (red) • 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

  13. 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

  14. High energy physics: pion correlations Astro: angular separation of the source HEP: space-time distribution of production points

  15. Ultra-cold Helium atoms: setup 3He(fermion) 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

  16. Ultra-cold Helium atoms: results Top figure: bosonic Helium Botton figure: fermionic Helium

  17. 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

More Related