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

Cédric Foellmi Laboratoire d’Astrophysique 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 ∗ ( r 1 , t 1 ) E ( r 2 , t 2 ) � � E ( r, t ) � 2 Complex! g (1) is a measurement of the spatial and/or temporal coherence of the wavetrain. jeudi 29 janvier 2009 3

Particular case 1: t 1 = t 2 Theorem of van Cittert-Zernike: g (1) is equal to the Fourier Transform (FT) of the light distribution on sky, along the projected baseline. jeudi 29 janvier 2009 4

The visibility is precisely g (1) ! 1 E detector ( t 1 = t 2 ) ∝ 2 ( E ∗ ( r 1 ) ± E ( r 2 )) √ � � g (1) �� I = I 0 1 ± Re V ≡ I max − I min � g (1) � � = � � I max + I min � jeudi 29 janvier 2009 5

Particular case 2: r 1 = r 2 Theorem of Wiener-Khintchine: g (1) is equal to the FT of the spectral density distribution of the source. Classical spectrometer: FT spectrometer: the grating perform the FT. interferences are recorded jeudi 29 janvier 2009 6

(Very) particular case 3: r 1 =r 2 , t 1 =t 2 ( Bolometer) Introduction to light statistics I ( t ) = � I � + ∆ I ( t ) � ∆ I ( t ) � = 0 � ∆ I ( t ) 2 � > 0 jeudi 29 janvier 2009 7

Transition τ σ coherence variance jeudi 29 janvier 2009 8

For a laser, its poissonian 30 cm 1 nW A section of 30 cm of a laser lightbeam at 6330Å with a power of 1 nW contains 3 photons in average The distribution of the photon number of a monochromatic laser, within an interval Δ t, is poissonian σ 2 ( n ) = ¯ n jeudi 29 janvier 2009 9

Fundamental reason: the uncertainty principle ∆ n ∆ ϕ ≥ � Number of Phase of photons the wave jeudi 29 janvier 2009 10

Classification of light according to statistics poissonian random σ 2 ( n ) = ¯ (Laser) n σ 2 ( n ) > ¯ super-poissonian bunching (Thermal) n σ 2 ( n ) < ¯ sub-poissonian anti-bunching (Fluorescence) n jeudi 29 janvier 2009 11

( Photodetection: losses ) A lossy medium acts like a beamsplitter • Optics efficiency (only a fraction of the incident light is collected) Detector • Losses through absorption, Detector A difusion, reflections on various surfaces. B • Efficiency of the detection process itself (quantum efficiency) Input Output A Output B Every process of collection/detection tends to make the statistics more poissonian. jeudi 29 janvier 2009 12

( Photodetection: Variance ) Observed Real variance variance σ 2 ( N ) = η 2 σ 2 ( n ) + η (1 − η )¯ n Detector The quantum efficiency η Detector A express the fidelity of the B measurement of the statistics. Input Output A Output B jeudi 29 janvier 2009 13

The second-order correlation function g (2) g (2) = � I ( r 1 , t 1 ) I ( r 2 , t 2 ) � � I ( r, t ) � 2 Real! g (2) is a measurement of correlation degree, spatialy and/or temporaly, between photons. jeudi 29 janvier 2009 14

The second-order correlation function g (2) Gaussian g (2) = � I ( r 1 , t 1 ) I ( r 2 , t 2 ) � � I ( r, t ) � 2 Lorentzian Coherent (laser) jeudi 29 janvier 2009 15

Nombre d'evenements g (2) in photon counting. 0.0 1.0 2.0 Temps 50:50 Beam splitter Detector Photons Gaussian Stop Detector Lorentzian Start Counter g (2) < 1 reveal the anti-bunched! quantum nature of light. jeudi 29 janvier 2009 16

( 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. jeudi 29 janvier 2009 17

Why it worked at measuring stellar radii? For chaotic light (black body): � τ � τ � � 2 � � �� � � − π g (2) = 1 + exp � g (1) ( τ ) � = exp � � − π 2 τ c τ c 2 � � g (1) � = g (2) − 1 � � � Et voilà! Valid for chaotic light only (Glauber, 2007, p115) jeudi 29 janvier 2009 18

Observations at Narrabri: Only hot(ter) stars. Poisson σ 2 ( n ) = ¯ n Bose-Einstein σ 2 ( n ) = ¯ n 2 n + ¯ K(2.5 μ ) V(0.55 μ ) “Signal” � S � � T exp 1 = V 2 N exp( h ν /kT ) − 1 τ jeudi 29 janvier 2009 19

Have you seen my big telescope?... g (1) → g (2) Let’s talk about detectors…. jeudi 29 janvier 2009 20

[ New Avalanche Photodiodes from CEA/LETI ] (see J. Rothman et al. 2008, J.Elec.Mat., 37,1303) Made in η ∼ 100% Grenoble ∆ t � 80 picoseconds 15 µm < λ < 3000˚ A ( → ? X ) Possibility to build matrices (at least arrays) (APDs not in silicium, but in HgCdTe) jeudi 29 janvier 2009 21

The quantum limit in the optical ∆ E ∆ t � � R = 40 000 ∆ t ∼ 80 picoseconds λ ∼ 6000˚ A jeudi 29 janvier 2009 22

Signal-to-Noise, in practice. overall exposure telescope’s reflectivity visibility time mirror area � S � � T = A η R n V 2 N 2 τ RMS detector’s detector’s quantum efficiency bandwidth jeudi 29 janvier 2009 23

Comparison with LeBohec & Holder (2005): η = 0.4, τ = 10 -9 s ←→ η = 0.95, τ = 8.10 -11 s jeudi 29 janvier 2009 24

g (2) so what? ? g (1) → g (2) jeudi 29 janvier 2009 25

Paul K. Feyerabend. Science is an essentially anarchistic enterprise: theoretical anarchism is more humanitarian and more likely to encourage progress than its law-and- order alternatives. jeudi 29 janvier 2009 26

New techniques, new ideas. Yes we can! 2 � � g (1) � = g (2) − 1 � � � New application Where are accessible of the correlation cosmic sources of fluctuations? with non-thermal light? jeudi 29 janvier 2009 27

Topology of the Universe through II of the CMB? jeudi 29 janvier 2009 28

Topology? Multi-connected universe? Luminet et al. 2003 jeudi 29 janvier 2009 29

Topology of the Universe through II of the CMB? jeudi 29 janvier 2009 30

Microquasars: Sources of “extravagant” radiation in our Galaxy Jet black-hole spin? JET inner disk Synchrotron emission from jet originate from non-thermal particles (power-law spectrum) See Foellmi et al. 2008a,b. Details in Foellmi et al. 2009, MNRAS, in prep. jeudi 29 janvier 2009 31

Microquasars: Sources of “extravagant” radiation in our Galaxy Energy flux ( ν F ν ) Photon rate Microquasar with M bh =10M ☉ , Ṁ = 10 -2 M Edd , d=10kpc, “hot” jeudi 29 janvier 2009 32

In the immense zoo of quantum phenomena Unruh effect expected to produce entangled photons! Schützhold et al. 2006, Phys. Rev. Let. 97 (12), 1302 Hawking radiation “black-hole evaporation” jeudi 29 janvier 2009 33

Conclusions 2 � � g (1) � = g (2) − 1 � � � g (1) → g (2) Beyond intensity interferometry: black-hole physics! jeudi 29 janvier 2009 34

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 F We are organizing a 2-days workshop on u n d i n a g p quantum/photonic astrophysics p r o v p a e l n with physicists, astronomers, ingeneers d i n g Grenoble, May/June 2009 cedric.foellmi@obs.ujf-grenoble.fr jeudi 29 janvier 2009 35

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