triple photon quantum correlations benoît boulanger (1) audrey dot (1), kamel bencheikh (2), ariel...
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Triple photon quantum correlations
Benoît Boulanger(1)
Audrey Dot(1), Kamel Bencheikh(2), Ariel Levenson(2), Patricia Segonds(1), Corinne Félix(1)
(1)Institut Néel CNRS/UJF, Grenoble, France(2)Laboratoire de Photonique et Nanostructures CNRS, Marcoussis,
France
FRISNO - AussoisMarch 28 – April 1st, 2011
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OUT LINE
Introduction & motivation
Generation of triple photons
Coherence study of triple photons
Conclusion & perspectives
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OUT LINE
Introduction & motivation
Generation of triple photons
Coherence study of triple photons
Conclusion & perspectives
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PROBLEMATICS
Generation, study and manipulation of triple photons
Crystal non linear optics
Quantum optics
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1
02
3
0 1 2 3
(3)
1
3
2
0
Four-Wave-MixingStimulated Raman ScatteringKerr effectTwo Photon Absorption
THIRD ORDER NON LINEAR PARAMETRIC INTERACTIONS
12
3
0
1 2 3 0
(3)
0 1
3
2
3
3
3(3)
Third Harmonic Generation
Triple Photons Generation
ħ0 + ħ1 = ħ2 + ħ3
ħ3 = ħ + ħ + ħ
ħ1 + ħ2 + ħ3 = ħ0
Third order Parametric Fluorescence
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INTEREST OF GENERATING TRIPLE PHOTONS
Fundamental interest in quantum optics:New state of light (GHZ Greenberger, Horne, Shimony, Zeilinger,
Am. J. Phys. 1990 ) ; 3 photons created from the splitting of a single photon exhibit specific quantum correlations different than those of twin photons (Breitenbach, Schiller, Mlynek, Nature 1997).
Fundamental interest in non linear optics :Specific properties of triple photons generation.
Potential interest in quantum cryptography and information : possibility to use two keys instead of one (twin photons), protocole of announced pairs.
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WIGNER FUNCTION OF TRIPLE PHOTONS
Banaszek, Knight, Phys. Rev. A (1997)
Bencheikh, Douady, Gravier, Levenson, Boulanger, Compt. Rend. Phys. Acad. Sciences (2007)
1ˆ( , ) 2 2
2ipxW q p e q x q x dx
.
The case of a degenerate three-photon quantum state:
2 1/ 2
,1 , 10 1 0
( ) ,3!
l
nn nir
l l kn l k
t e e u u n k kn
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Simultaneous production of 2 pairs of photons(Pan, Daniell, Gasparoni, Weihs, Zeilinger, PRL, 2001)
New tests of Bell theorem, but : Observation by destructive selection
forbids any manipulation a posteriori Conditional protocol (small amount of events)
ALTERNATIVE FOR TRIPLE PHOTONS GENERATION
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Interest in producing prepared triple photons states :
at first, a challenge in non linear optics !!!
OUT LINE
Introduction and motivation
Generation of triple photons
Coherence study of triple photons
Conclusion & perspectives
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SPECTRAL SPREADING OF THIRD ORDER PARAMETRIC FLUORESCENCE
Energy conservationħ0 - ħ1 - ħ2 - ħ3 = 0
Momentum conservationħk0 - ħk1 - ħk2 - ħk3 = 0
2 equations and 3 quanta {ħ1, ħ2, ħ3}
Continuum of solutions
KTP crystalPump : 532 nmDirection of propagation : X
Fève, Boulanger, Douady, Phys. Rev. A (2002)
NB : 2 equations and two quanta to fixe for twin photons.
WEAK AMPLITUDE OF THE THIRD ORDER PARAMETRIC FLUORESCENCE
Rate of transition
2
12
3
00 1
3
2
2
321 0,0,0ˆ,,2
iHkkkW
0,0,0
321 ,, kkk
2 5 22(3) 1 2 2 2
2 02 2 3 60 0 3 1 2 3
288( )
8
n n d dcP P L F mismatch
n n
Radiated power in the mode k2
Oxide crystals 10-17 W 10-21 m2/V2 100 GW/cm2 1
Chalcogenide glasses 10-22 W 10-18 m2/V2 1 GW/cm2 10-6 Polymers
P2 Triple photons << 10-9 W of Twin photons
THE IDEAL CRYSTAL FOR TRIPLE PHOTONS GENERATION …
… IS NOT YET BORN!
Centrosymmetric structure
High damage threshold > 100 GW/cm2
High (3) nonlinearity > 10-17 m2/V2
Phase-matchable, i.e. birefringence n > 10-2
10-9 W of Third order parametric fluorescence
NECESSITY TO STIMULATE THE PHOTON SPLITTING
1
3
2
12
3
0
1 2 3 0
(3)
0
3
2
3
2
Choice of a double stimulation
One photon detected at λ1
One generated triple {λ1, λ2, λ3}
λ0- = 532 nm
λ1+
= 1449 nm
λ2+
= λ3- =1681 nm
Phase-matching in KTPfor the generation of triple photons
around 1500 nm
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CLASSICAL THEORY OF TRIPLE PHOTONS GENERATION
Fève, Boulanger, Douady, Phys. Rev. A (2002)Interaction length (a.u.)
Inte
nsiti
es (
W/c
m²)
2 3I I
1I
0I
20 31 01 1 1
0
231 01 1 1
1
2 22,3 31 01 2,3 1 1 1 1
2,3
, 0 |1,
|1,
, 0 . |1 |1,
I Z cn a L mI Z L
sn a L mI Z L
I Z sn a L m cn a L mI Z L
sn(u/m), cn(u/m) : Jacobi elliptic functions
Energy transferbetween photons populations
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Nd:YAG
20 ps -10 Hz x3 OPG
420 - 2300 nm
1679 nm
max = 100 µJ/pulse
32
x2532 nm
max = 1 mJ/impulsion
Optical Delay 0
Power Meter
lenses
Glan-Taylor
2
2
Power Meter prism
32
0
1
KTPx-cut
25 mm
filters
HTHR 532 nm
32
High intensities : 100 GW/cm² sub-nanosecond pulses, focalised beams
Perfect phase-matching tunability of the source
PIONEER EXPERIMENT OF TRIPLE PHOTONS GENERATION
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1650 1655 1660 1665 1670 1675 16801450
1460
1470
1480
1490
1500 CalculMesures
Long
ueur
d'o
nde
géné
rée
1 (n
m)
Longueur d'onde d'injection 3=
2 (nm)
Accord de phase (pompe 4=532 nm)
1 20 3
1 1 1 1
Parametric signature
(nm)32
(nm
)
Phase-matching obtained at : 532 nm(o) 1473.5 nm(e) + 1665.2 nm(e) + 1665.2 nm(o)
SPECTRAL PROPERTIES
Gen
erat
ed e
nerg
y at
(a
.u)
(nm)
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1665.21665.2((
-) -)
1665.21665.2((
+)+) 1473.51473.5((
+) +)
Number of pump photons (532 nm) : 2.0x1015
Number of stimulation photons (1665.2 nm) : 8.4x1014
First experiment of triple photons generation
NUMBER OF GENERATED TRIPLES
3.3x1013 triple photons per pulse
Douady & Boulanger, Optics Letters (2004)
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NEW TRIPLE PHOTONS GENERATOR
Nd:YAG1064 nm-20 ps
x3
x2
OPG accordable420 – 2300 nm
KTPX-cut
λ0 = 532 nm
λ0
λ2=λ
3
λ1 λ1
1064 nm-150 ps
Home-made OPO (fixed wavelength)
L
ξ 1
ξ0
ξi=ξ2+ ξ3
1064 nm(2)
λ/2
(2) (2)F
KTP KTP KTP λ2=λ3=1665.2 nm
High intensities
Possibilityof resonant interactions
λ2=λ3=1665.2 nm
15/39
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VALIDATION OF THE CLASSICAL MODEL
ξ0 = 4.5 mJξi = 182 μJ
ξ0 = 4.5 mJL = 13 mm
ξi = 182 μJL = 13 mm
Gravier & Boulanger, JOSA B (2008)
3 223 0 1 11 1
1
|1²( )
2 2
sn a L mwL
The calculation under the UPA gives a surestimation of a factor 500 !
2(3) 21 0 2 3( ) (0) (0) (0)effL L
<<
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OUT LINE
Introduction & motivation
Generation of triple photons
Coherence study of triple photons
Conclusion & perspectives
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PROTOCOL OF CORRELATIONS STUDIES
Recombinations @ 2 photons @ 3 photons
Delay 2
Delay 3
(3)(2)
1 1474e nm
2 1662e nm
3 1662o nm
1 2 3e e o 1 3
e o 2 3e o
Delay 1
G
Spectral analysis
( )GI f 1 2 3 0
2 31, , )(I f Temporal analysis
at
1 2 3 0
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(3)Stimulated generation
Triple photons + stimulating fields
Sum field Sum field
Following Izo Abram et al in the case of twin photons PRL (1986)
• Quantum calculations Quantization of each electromagnetic field
LPNQUANTUM MODELISATION OF THE TRIPLE FIELDS
• Description of the photons evolution in the non linear crystal by their non linear momentum operator :ˆ
NLG
creation and destruction of a photon
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Non linear momentum evolution of the operators and for all the fields in the crystal, since :
ˆ( , )a z
• Access to the 3 quantum field operators in each point of the crystal
ˆ ( , )a z
1 2 3ˆ ˆ ˆ, and
outgoing photons generated in each mode of the triplet
sum fields issued from the 2 and 3 fields recombination
QUANTUM EXPRESSION OF THE TRIPLE FIELDS
Quantified recombined field, given by the integration of its creation and annihilation operators at each frequency :
• 3-photons recombined field :
or
EXPRESSION OF THE RECOMBINED FIELD
Ap
(3)medium
z0 L1
n20
n30
1 1ˆ ( )L
2 1ˆ ( )L
3 1ˆ ( )L3ˆ (0)
2ˆ (0)
(3)medium
z0 L2
2ˆ ( )sum L
(2)medium
z0 L2
2ˆ ( )sum L
• 2-photons recombined field :
Hence the spectrum of the recombined field:
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3-PHOTON RECOMBINATION
Outgoing photons spectra
(3)
nm
nm
nm
nm
nm
(3)
L L
N2=107
N3=107
N0=1015
Triple photons
Classical Background
Dot, Bencheikh, Boulanger, Levenson PRA, to be published
OUT LINE
Introduction & motivation
Generation of triple photons
Coherence study of triple photons
Conclusion & perspectives
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CONCLUSION
Theory & experiments of triple photons generation from a third order parametric generation
Protocols & calculations showing the quantum correlations
Corresponding experiments in progress
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PERSPECTIVES
Spontaneous triple photons generation in optical fiber using modal phase-matching
! Aaaaaaaaaaaaaaaaaaaaaaa
Measurement of the Wigner functions Quantum information based on triplets
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Third order parametric fluorescence ratefrom 1 W input power at 532 nm
in a one-meter optical fiber
!
Twin photons
FROM TWIN TO TRIPLE PHOTONS
A new storyfor the next 30 years?
0
123
pq
2
Strong impact on :
-Classical nonlinear optics – OPO
-Quantum mechanics and cryptography Aspect, Grangier, Roger, PRL (1981)
Triple photons
An exciting storyover the past 30 years!
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CALL FOR PAPER
Nonlinear Optics (NLO)17-22 July 2011
Marriott Kauai Beach ResortKauai, Hawaii, USA
Submission deadline 15 April 2011
Including a Symposium Celebrating the 50th Anniversary of Nonlinear Optics
Bloembergen, Harris, Yariv, Shen, Byer, …
General chairsDaniel Gautier & Takunori Taira
Program chairsBenoît Boulanger & Steven Cundiff
The Optical Society of America
(2)0 0
0 0
. . . ( )( ) effi E
n
22
4
k
0
2 22 2 2
2 2
22 42 2 2 4
2 4
2
| ( ) | sinh ( ) sinh ( )
sinh ( ) cosh ( ) sinh ( ) sinh ( )2
n m
n
n mn m
nn n n n
n n n
E L L
kL L L L
520 525 530 535 540 545 lambda (nm)
|E
|2 (a
.u.)
SAME PROTOCOLE PREVIOUSLY USED FOR TWIN PHOTONS
Dayan, Phys. Rev. A (2007)
Abram et al, PRL (1986)
ω1ω0 (2)
ω2
(2) ω
22
4
k
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2(2) (2)
, ,
2(2),1
(3) (3)1
cos,
,
I IIeff i eff i
quadi ii i i
eff
knI Z L
I Z L
Cas
cad
ing
rate
(%
) ( . .)(3)
a ueff
Douady & Boulanger, J. Opt A, 2005
SUPPRESSION OF THE SECOND ORDER CASCADING IN KTP
.
Partially non degenerate three-photon quantum state : 1 ≠2=3
Photons in the mode at 1 Photons in the mode at 2=3
WIGNER FUNCTION OF TRIPLE PHOTONS
Bencheikh, Douady, Gravier, Levenson, Boulanger, Compt. Rend. Phys. Acad. Sciences (2007)