Cdric Foellmi Laboratoire dAstrophysique de Grenoble, France Salt - - PowerPoint PPT Presentation

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Cdric Foellmi Laboratoire dAstrophysique de Grenoble, France Salt Lake City, January 29 th , 2009 jeudi 29 janvier 2009 1 Quick summary ? g (1) g (2) jeudi 29 janvier 2009 2 The first-order correlation function g (1) g (1) = E

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Cédric Foellmi

Laboratoire d’Astrophysique de Grenoble, France Salt Lake City, January 29th, 2009

1 jeudi 29 janvier 2009

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?

Quick summary

g(1) → g(2)

2 jeudi 29 janvier 2009

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The first-order correlation function g(1)

g(1) = E∗(r1, t1)E(r2, t2) E(r, t)2

Complex!

g(1) is a measurement of the spatial and/or temporal coherence of the wavetrain.

3 jeudi 29 janvier 2009

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Particular case 1: t1 = t2 Theorem of van Cittert-Zernike:

g(1) is equal to the Fourier Transform (FT) of the light distribution on sky, along the projected baseline.

4 jeudi 29 janvier 2009

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V ≡ Imax − Imin Imax + Imin =

  • g(1)
  • The visibility is precisely g(1) !

I = I0

  • 1 ± Re
  • g(1)

Edetector(t1 = t2) ∝ 1 √ 2 (E∗(r1) ± E(r2))

5 jeudi 29 janvier 2009

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Particular case 2: r1 = r2

Theorem of Wiener-Khintchine: g(1) is equal to the FT

  • f the spectral density distribution of the source.

FT spectrometer: interferences are recorded Classical spectrometer: the grating perform the FT.

6 jeudi 29 janvier 2009

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(Very) particular case 3: r1=r2, t1=t2 (Bolometer)

I(t) = I + ∆I(t) ∆I(t) = 0 ∆I(t)2 > 0

Introduction to light statistics

7 jeudi 29 janvier 2009

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Transition

τ

σ

coherence

variance

8 jeudi 29 janvier 2009

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For a laser, its poissonian

A section of 30 cm of a laser lightbeam at 6330Å with a power of 1 nW contains 3 photons in average

30 cm 1 nW

The distribution of the photon number of a monochromatic laser, within an interval Δt, is poissonian

σ2(n) = ¯ n

9 jeudi 29 janvier 2009

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Fundamental reason: the uncertainty principle

∆n ∆ϕ ≥

Number of photons Phase of the wave

10 jeudi 29 janvier 2009

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Classification of light according to statistics

poissonian

(Laser)

random

σ2(n) = ¯ n

sub-poissonian

(Fluorescence)

anti-bunching

σ2(n) < ¯ n

super-poissonian (Thermal)

bunching

σ2(n) > ¯ n

11 jeudi 29 janvier 2009

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( Photodetection: losses )

  • Optics efficiency (only a fraction of

the incident light is collected)

  • Losses through absorption,

difusion, reflections on various surfaces.

  • Efficiency of the detection process

itself (quantum efficiency)

Every process of collection/detection tends to make the statistics more poissonian.

Input Output A Output B A B Detector Detector

A lossy medium acts like a beamsplitter

12 jeudi 29 janvier 2009

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( Photodetection: Variance )

σ2(N) = η2σ2(n) + η(1 − η)¯ n

The quantum efficiency η express the fidelity of the measurement of the statistics.

Observed variance Real variance

Input Output A Output B A B Detector Detector

13 jeudi 29 janvier 2009

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The second-order correlation function g(2)

g(2) = I(r1, t1)I(r2, t2) I(r, t)2

g(2) is a measurement of correlation degree, spatialy and/or temporaly, between photons.

Real!

14 jeudi 29 janvier 2009

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Coherent (laser)

Gaussian Lorentzian

The second-order correlation function g(2)

g(2) = I(r1, t1)I(r2, t2) I(r, t)2

15 jeudi 29 janvier 2009

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g(2) in photon counting.

Gaussian Lorentzian

anti-bunched!

g(2) < 1 reveal the quantum nature of light.

0.0 1.0 2.0

Temps Nombre d'evenements

Photons

Start Stop

Counter

Detector Detector

50:50 Beam splitter

16 jeudi 29 janvier 2009

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( The intensity interferometer )

Robert Hanbury Brown (1916-2002) Richard Quintin Twiss (1920-2005)

Photograph courtesy of Prof. John Davis

They have received the Eddington medal of the RAS en 1968.

17 jeudi 29 janvier 2009

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Why it worked at measuring stellar radii?

Et voilà! For chaotic light (black body):

g(2) = 1 + exp

  • −π

τ τc 2

  • g(1)
  • 2

= g(2) − 1

  • g(1)(τ)
  • = exp
  • −π

2 τ τc

  • Valid for chaotic light only (Glauber, 2007, p115)

18 jeudi 29 janvier 2009

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Observations at Narrabri: Only hot(ter) stars.

K(2.5μ)

V(0.55μ)

S N

  • = V 2
  • Texp

τ 1 exp(hν/kT) − 1 Bose-Einstein Poisson σ2(n) = ¯ n + ¯ n2 σ2(n) = ¯ n

“Signal”

19 jeudi 29 janvier 2009

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Have you seen my big telescope?... Let’s talk about detectors….

g(1) → g(2)

20 jeudi 29 janvier 2009

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[ New Avalanche Photodiodes from CEA/LETI ]

(see J. Rothman et al. 2008, J.Elec.Mat., 37,1303)

η ∼ 100%

15µm < λ < 3000˚ A (→?X)

∆t 80 picoseconds

Possibility to build matrices (at least arrays)

Made in Grenoble

(APDs not in silicium, but in HgCdTe)

21 jeudi 29 janvier 2009

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The quantum limit in the optical

∆E ∆t

R = 40 000

∆t ∼ 80 picoseconds

λ ∼ 6000˚ A

22 jeudi 29 janvier 2009

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Signal-to-Noise, in practice.

S N

  • RMS

= A η R n V 2

  • T

2τ

telescope’s mirror area

  • verall

reflectivity visibility exposure time

detector’s quantum efficiency detector’s bandwidth

23 jeudi 29 janvier 2009

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Comparison with LeBohec & Holder (2005):

η = 0.4, τ = 10-9 s ←→ η = 0.95, τ = 8.10-11 s

24 jeudi 29 janvier 2009

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g(2) so what?

?

g(1) → g(2)

25 jeudi 29 janvier 2009

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Paul K. Feyerabend.

Science is an essentially anarchistic enterprise: theoretical anarchism is more humanitarian and more likely to encourage progress than its law-and-

  • rder alternatives.

26 jeudi 29 janvier 2009

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  • g(1)
  • 2

= g(2) − 1

New techniques, new ideas. Yes we can! New application

  • f the correlation
  • f fluctuations?

Where are accessible cosmic sources with non-thermal light?

27 jeudi 29 janvier 2009

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Topology of the Universe through II of the CMB?

28 jeudi 29 janvier 2009

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Topology? Multi-connected universe?

Luminet et al. 2003

29 jeudi 29 janvier 2009

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Topology of the Universe through II of the CMB?

30 jeudi 29 janvier 2009

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Microquasars:

Sources of “extravagant” radiation in our Galaxy

JET inner disk

See Foellmi et al. 2008a,b. Details in Foellmi et al. 2009, MNRAS, in prep.

Synchrotron emission from jet

  • riginate from non-thermal particles

(power-law spectrum) Jet black-hole spin?

31 jeudi 29 janvier 2009

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Microquasars:

Sources of “extravagant” radiation in our Galaxy Energy flux (νFν ) Photon rate

Microquasar with Mbh=10M☉, Ṁ = 10-2 MEdd, d=10kpc, “hot”

32 jeudi 29 janvier 2009

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In the immense zoo of quantum phenomena

Schützhold et al. 2006,

  • Phys. Rev. Let. 97 (12), 1302

Hawking radiation

“black-hole evaporation”

Unruh effect expected to produce entangled photons!

33 jeudi 29 janvier 2009

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Conclusions

g(1) → g(2)

  • g(1)
  • 2

= g(2) − 1

Beyond intensity interferometry: black-hole physics!

34 jeudi 29 janvier 2009

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Please note:

On the intensity interferometry and the second order correlation function g(2) in astrophysics

  • C. Foellmi, A&A submitted

astro-ph/0901.4587

We are organizing a 2-days workshop on quantum/photonic astrophysics with physicists, astronomers, ingeneers Grenoble, May/June 2009

cedric.foellmi@obs.ujf-grenoble.fr

F u n d i n g a p p r

  • v

a l p e n d i n g

35 jeudi 29 janvier 2009

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36 jeudi 29 janvier 2009