Hanbury Brown and Twiss Effect Anton Kapliy March 10, 2009

Robert Hanbury Brown ( ) 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 ~ radians This 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! a b 1 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,d Now define a correlation function: a b 1 2 Consider intensity correlation between two detectors: L R d θ θ

Measuring angular size of Sirius Hanbury Brown used discarded military searchlights: θ = '' ± '' = 3.1*10 -8 radians This 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 I1I1 I2I2

Temporal coherence: HBT setup Coherence time - time during which the wave train is stable. If we know the phase at position z at time t 1, we know it to a high degree of certainty at t 2 if t 2 -t 1 << τ c τ c = 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) 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 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 = 4M 2 Bosons: P=M 2 +M 2 +(M+M) 2 =6M 2 Fermions: P=M 2 +M 2 +(M-M) 2 =2M 2

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 3 He(fermion) and 4 He(boson) 1.Collect ultra-cold (0.5 μK) metastable Helium in a magnetic trap 2.Switch off the trap 3.Cloud expands and falls under gravity 4.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 Quantum Optics, textbook by A. M. Fox