1. Classification by statistics
A coherent beam of constant intensity is described by Poisson statistics
If/when an intensity fluctuation is present  Super-Poissonian statistics
Non-classic light  Sub- Poissonian distribution
Not classic light
Perfectly coherent light
Partially coherent, uncoherent, thermal emission
L’osservazione di statistica Poissoniana e super-Poissoniana può essere spiegata dalla teoria classica ondulatoria
Statistica sub-Poissoniana è la firma inequivocabile della natura quantistica della luce Fotone
Vediamo ora un modo diverso di analizzare le caratteristiche della luce in base alla correlazione al secondo ordine
F. De Matteis
Quantum Optics

2. Coherence measurements in astronomy
Michelson stellar interferometer
Varing d and measuring fringe
visibility at screen centrum:
Max from star center
minimum from D/2 if D/L≈l/d
}Cancel
1920 Mount Wilson Red giant Betelgeuse in Orion constellation l/d=500nm/6m~10-7 rad D/L~2,2x10-7 rad
Increase d to improve resolution
Mirror vibrations cancel the interference figure
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Quantum Optics

3. Coherence measurements in astronomy
Hambury-Brown Twiss
Correlate light intensity from two different points of wavefront
The average of the products (Second order corr.) varies in the two cases
2 detectors collect light from two different angles  different area of the wavefront are incoherent
Sirio Star l/d=400nm/188m~2x10-9 rad D/L~3,3x10-8 rad
2 detectors collect light from two close angles  same area of the wavefront (still coherent)
F. De Matteis
Quantum Optics

4. Intensity interferometry experiment
Originate from astronomy studies. The interpretation of the results raised several conceptual difficulties.
The principles of the experiment were tested in laboratory
Each detector measures the fluctuation of the beam intensity (AC coupling)
For chaotic beam, the measured signal is 1 for t<<tc and drop to 0 for t>>tc For choerent light, one gets 0 at any value of delay
F. De Matteis
Quantum Optics

5. Degree of second-order coherence for chaotic light
For classic light (chaotic or coherent)
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Quantum Optics
L6/5

6. Hanbury-Brown Twiss experiments: quantum picture
Single photon-counting configuration
Event=«time elapsed between D1 count and D2 count is t »
Photon flux with long intervals between photons.
Each photon either hits D1 or D2
Bunched stream of photons
Considerando la natura quantistica della luce, fotoni che viaggiano, si giunge a risultati molto diversi che nel caso classico di fluttuazione di intensità
F. De Matteis
Quantum Optics

7. Classification by coherence
Coherent light
Photon statistic Poissonian with intervals between photons completly random  Probability for stop pulse independent by t
Bunched light
Photon statistic SuperPoissoniana with intervals between photon very tight Probability for stop pulse high for small t
Anti-bunched light Intervals between photons very regular Close to start pulse low probability of stop Then increase Sub-Poissoniana   anti-bunching Not exactly the same (Zou&Mandel, PhysRevA 1990)
F. De Matteis
Quantum Optics

8. Experimental demonstrations of antibunching
Signal from single emitter  antibunched beam
Kimble,Dagenais,Mandel, PhysRevLett 1977
A single atom must be in the visual field of measuring device (slit)
Excitation of InAs on GaAs quantum dots
Sub-ideality due to finite response time
of the photon counting system
Michler et al, Science 2000
F. De Matteis
Quantum Optics

9. Single photon sources Quantum criptography, eg.
Emission of a single photon following a trigger pulse
Subsequent emission needs a subsequent trigger
Low quantum eff , T=5K Yuan Science 2002
GaAs-LED P-i-N
InAs quantum dots are inserted in the GaAs intrinsic layer. The QD size distribution produces the l spread
F. De Matteis
Quantum Optics