Slides - University of Utah Physics

Cédric Foellmi
Laboratoire d’Astrophysique de Grenoble, France
Salt Lake City, January 29th, 2009
jeudi 29 janvier 2009
1
Quick summary
(1)
g
jeudi 29 janvier 2009
→
(2)
g
?
2
The first-order correlation function
g
(1)
(1)
g
!E (r1 , t1 )E(r2 , t2 )"
=
2
!E(r, t)"
∗
Complex!
g(1) is a measurement of the spatial and/or
temporal coherence of the wavetrain.
jeudi 29 janvier 2009
3
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.
jeudi 29 janvier 2009
4
The visibility is precisely
(1)
g !
1
Edetector (t1 = t2 ) ∝ √ (E ∗ (r1 ) ± E(r2 ))
2
!
"
I = I0 1 ± Re g (1)
Imax − Imin
V ≡
Imax + Imin
jeudi 29 janvier 2009
#$
!
!
! (1) !
= !g !
5
Particular case 2: r1 = r2
Theorem of Wiener-Khintchine: g(1) is equal to the FT
of the spectral density distribution of the source.
Classical spectrometer:
the grating perform the FT.
jeudi 29 janvier 2009
FT spectrometer:
interferences are recorded
6
(Very) particular case 3: r1=r2, t1=t2 (Bolometer)
Introduction to
light statistics
I(t) = !I" + ∆I(t)
!∆I(t)" = 0
!∆I(t) " > 0
2
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7
Transition
jeudi 29 janvier 2009
τ
σ
coherence
variance
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 Δt, is poissonian
σ (n) = n̄
2
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9
Fundamental reason: the uncertainty principle
∆n ∆ϕ ≥ !
Number of
photons
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Phase of
the wave
10
Classification of light according to statistics
poissonian
σ (n) = n̄
random
(Laser)
super-poissonian
σ (n) > n̄
bunching
(Thermal)
sub-poissonian
σ (n) < n̄
jeudi 29 janvier 2009
2
2
2
anti-bunching (Fluorescence)
11
( 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)
A lossy medium acts like a beamsplitter
Detector
A
Detector
B
Input
Output A
Output B
Every process of collection/detection tends to make
the statistics more poissonian.
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12
( Photodetection: Variance )
Observed
variance
Real
variance
σ (N ) = η σ (n) + η(1 − η)n̄
2
2 2
Detector
The quantum efficiency η
express the fidelity of the
measurement of the statistics.
A
Detector
B
Input
Output A
Output B
jeudi 29 janvier 2009
13
The second-order correlation function
g
(2)
(2)
g
!I(r1 , t1 )I(r2 , t2 )"
=
2
!I(r, t)"
Real!
g(2) is a measurement of correlation degree,
spatialy and/or temporaly, between photons.
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14
The second-order correlation function
g
(2)
!I(r1 , t1 )I(r2 , t2 )"
=
!I(r, t)"2
(2)
g
Gaussian
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
anti-bunched!
jeudi 29 janvier 2009
g(2) < 1 reveal the
quantum nature of light.
16
(
The intensity interferometer
)
Robert Hanbury Brown
(1916-2002)
Richard Quintin Twiss
(1920-2005)
They have received the Eddington medal of the RAS en 1968.
jeudi 29 janvier 2009
Photograph courtesy of Prof. John Davis
17
Why it worked at measuring stellar radii?
For chaotic light (black body):
# $%
"
!
!
π τ
! (1) !
!g (τ )! = exp −
2 τc
g
(2)
!
= 1 + exp −π
!
!2
! (1) !
(2)
!g ! = g − 1
"
τ
τc
#2 $
Et voilà!
Valid for chaotic light only (Glauber, 2007, p115)
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18
Observations at Narrabri: Only hot(ter) stars.
Poisson
σ 2 (n) = n̄
Bose-Einstein
σ (n) = n̄ + n̄
2
2
V(0.55μ)
“Signal”
!
S
N
"
jeudi 29 janvier 2009
=V
K(2.5μ)
2
#
Texp
1
τ exp(hν/kT ) − 1
19
Have you seen my big telescope?...
(1)
g
→
(2)
g
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)
η ∼ 100%
∆t ! 80 picoseconds
Made i
n
Grenob
le
15µm < λ < 3000Å (→?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 ∼ 6000Å
jeudi 29 janvier 2009
22
Signal-to-Noise, in practice.
telescope’s
mirror area
!
S
N
"
overall
reflectivity
=AηRnV
RM S
detector’s
quantum efficiency
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visibility
2
#
exposure
time
T
2τ
detector’s
bandwidth
23
Comparison with LeBohec & Holder (2005):
η = 0.4, τ =
jeudi 29 janvier 2009
-9
10 s
←→ η = 0.95, τ =
-11
8.10 s
24
(2)
g
so what?
(1)
g
jeudi 29 janvier 2009
→
(2)
g
?
25
Paul K. Feyerabend.
Science is an essentially
anarchistic enterprise:
theoretical anarchism is
more humanitarian and
more likely to encourage
progress than its law-andorder alternatives.
jeudi 29 janvier 2009
26
New techniques, new ideas. Yes we can!
!
!2
! (1) !
(2)
!g ! = g − 1
New application
of the correlation
of fluctuations?
jeudi 29 janvier 2009
Where are accessible
cosmic sources
with non-thermal light?
27
Topology of the Universe through II of the CMB?
jeudi 29 janvier 2009
28
Topology? Multi-connected universe?
Luminet et al. 2003
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29
Topology of the Universe through II of the CMB?
jeudi 29 janvier 2009
30
Microquasars:
Sources of “extravagant” radiation in our Galaxy
Jet
JET
black-hole spin?
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 (νFν )
Photon rate
Microquasar with Mbh=10M☉, Ṁ = 10-2 MEdd, 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
! (1) !
(2)
!g ! = g − 1
(1)
g
→
(2)
g
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
We are organizing a 2-days workshop on
quantum/photonic astrophysics
with physicists, astronomers, ingeneers
Grenoble, May/June 2009
Fun
app ding
r
pen oval
din
g
[email protected]
jeudi 29 janvier 2009
35
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