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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)
• Institut Néel CNRS/UJF, Grenoble, France
• Laboratoire de Photonique et Nanostructures CNRS,
  Marcoussis, France
• FRISNO - Aussois
• March 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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THIRD ORDER NON LINEAR PARAMETRIC INTERACTIONS
Four-Wave-Mixing Stimulated Raman Scattering Kerr
effect Two Photon Absorption
h?0 h?1 h?2 h?3
Third Harmonic Generation
h3? h? h? h?
Third order Parametric Fluorescence
h?1 h?2 h?3 h?0
Triple Photons Generation
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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
.
The case of a degenerate three-photon quantum
state w1w2w3
Banaszek, Knight, Phys. Rev. A (1997) Bencheikh,
Douady, Gravier, Levenson, Boulanger, Compt.
Rend. Phys. Acad. Sciences (2007)
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ALTERNATIVE FOR TRIPLE PHOTONS GENERATION

• 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)

Interest in producing prepared triple photons
states at first, a challenge in non linear
optics !!!
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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 conservation
• h?0 - h?1 - h?2 - h?3 0
• Momentum conservation
• hk0 - hk1 - hk2 - hk3 0
• 2 equations and 3 quanta
• h?1, h?2, h?3

KTP crystal Pump 532 nm Direction of
propagation X
Continuum of solutions
Fève, Boulanger, Douady, Phys. Rev. A (2002)
NB 2 equations and two quanta to fixe for twin
photons.
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WEAK AMPLITUDE OF THE THIRD ORDER PARAMETRIC
FLUORESCENCE

• Rate of transition

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 ltlt 10-9 W of Twin photons
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THE IDEAL CRYSTAL FOR TRIPLE PHOTONS GENERATION
Centrosymmetric structure High damage
threshold gt 100 GW/cm2 High c(3)
nonlinearity gt 10-17 m2/V2 Phase-matchable,
i.e. birefringence Dn gt 10-2 10-9 W of Third
order parametric fluorescence
IS NOT YET BORN!
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NECESSITY TO STIMULATE THE PHOTON SPLITTING
Choice of a double stimulation
One photon detected at ?1
One generated triple ?1, ?2, ?3
Phase-matching in KTP for 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)

sn(u/m), cn(u/m) Jacobi elliptic functions
Energy transfer between photons populations
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PIONEER EXPERIMENT OF TRIPLE PHOTONS GENERATION
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SPECTRAL PROPERTIES
Generated energy at (a.u)
(nm)
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NUMBER OF GENERATED TRIPLES
3.3x1013 triple photons per pulse
1665.2(-)
1665.2()
1473.5()

• Number of pump photons (532 nm) 2.0x1015
• Number of stimulation photons (1665.2 nm)
  8.4x1014
• First experiment of triple photons generation
  

Douady Boulanger, Optics Letters (2004)
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NEW TRIPLE PHOTONS GENERATOR
?2?31665.2 nm
?0
?1
?1
KTP X-cut
?2?3
NdYAG 1064 nm-20 ps
L
?0 532 nm
15/39
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VALIDATION OF THE CLASSICAL MODEL
?0 4.5 mJ L 13 mm
?i 182 µJ L 13 mm
ltlt
?0 4.5 mJ ?i 182 µJ
The calculation under the UPA gives a
surestimation of a factor 500 !
Gravier Boulanger, JOSA B (2008)
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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
Triple photons stimulating fields
Stimulated generation
at
Sum field
Sum field

Following Izo Abram et al in the case of twin
photons PRL (1986)
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QUANTUM MODELISATION OF THE TRIPLE FIELDS

• Quantum calculations Quantization of each
  electromagnetic field

creation and destruction of a photon

• Description of the photons evolution in the non
  linear crystal by their non linear momentum
  operator

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QUANTUM EXPRESSION OF THE TRIPLE FIELDS

• Non linear momentum evolution of the
  operators and for all
  the fields in the crystal, since
  

• Access to the 3 quantum field operators
  in each point of the crystal

outgoing photons generated
in each mode of the triplet
sum fields issued from the 2 and 3
fields recombination
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NUMBER OF GENERATED PHOTONS
n20
w2
n30
w3
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EXPRESSION OF THE RECOMBINED FIELD

• Quantified recombined field, given by the
  integration of its creation and annihilation
  operators at each frequency

• 3-photons recombined field

or

• 2-photons recombined field

• Hence the spectrum of the recombined field

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3-PHOTON RECOMBINATION
Dl210 nm
Dl210 nm
w2
w2
N2107
Dl111.5 nm
w1
N01015
Dl310nm
Dl310 nm
w3
L
L
N3107
Outgoing photons spectra
Dot, Bencheikh, Boulanger, Levenson PRA, to be
published
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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

Third order parametric fluorescence rate from 1 W
input power at 532 nm in a one-meter optical
fiber
!
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FROM TWIN TO TRIPLE PHOTONS

Triple photons
Twin photons
Strong impact on -Classical nonlinear optics
OPO -Quantum mechanics and cryptography
Aspect, Grangier, Roger, PRL (1981)
A new story for the next 30 years?
An exciting story over the past 30 years!
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17-22 July 2011 Marriott Kauai Beach
Resort Kauai, Hawaii, USA
CALL FOR PAPER Nonlinear Optics (NLO)
Submission deadline 15 April 2011
Including a Symposium Celebrating the 50th
Anniversary of Nonlinear Optics Bloembergen,
Harris, Yariv, Shen, Byer,
General chairs Daniel Gautier Takunori Taira
Program chairs Benoît Boulanger Steven Cundiff
The Optical Society of America
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SAME PROTOCOLE PREVIOUSLY USED FOR TWIN PHOTONS
Abram et al, PRL (1986)
Dayan, Phys. Rev. A (2007)
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SUPPRESSION OF THE SECOND ORDER CASCADING IN KTP
Douady Boulanger, J. Opt A, 2005
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WIGNER FUNCTION OF TRIPLE PHOTONS
.
Partially non degenerate three-photon quantum
state w1 ?w2w3
Photons in the mode at w1 Photons in
the mode at w2w3
Bencheikh, Douady, Gravier, Levenson, Boulanger,
Compt. Rend. Phys. Acad. Sciences (2007)

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RUTILE TiO2 A PROMISING CRYSTAL FOR TRIPLE
PHOTONS GENERATION
THG in KTP
THG in TiO2
Gravier Boulanger, Optics Express (2006)