Triple Photon Quantum Correlations Study: Generation & Coherence Analysis

1. LPN • 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

2. OUT LINE LPN • Introduction & motivation • Generation of triple photons • Coherence study of triple photons • Conclusion & perspectives

3. OUT LINE LPN • Introduction & motivation • Generation of triple photons • Coherencestudy of triple photons • Conclusion & perspectives

4. PROBLEMATICS LPN Generation, study and manipulation of triple photons • Crystal non linear optics • Quantum optics

5. THIRD ORDER NON LINEAR PARAMETRIC INTERACTIONS LPN Four-Wave-Mixing Stimulated Raman Scattering Kerr effect Two Photon Absorption ħ0 + ħ1 = ħ2 + ħ3 Third Harmonic Generation ħ3 = ħ + ħ + ħ Third order Parametric Fluorescence ħ1 + ħ2 + ħ3 = ħ0 Triple Photons Generation

6. INTEREST OF GENERATING TRIPLE PHOTONS LPN • 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.

7. WIGNER FUNCTION OF TRIPLE PHOTONS . LPN The case of a degenerate three-photon quantum state: w1=w2=w3 Banaszek, Knight, Phys. Rev. A (1997) Bencheikh, Douady, Gravier, Levenson, Boulanger, Compt. Rend. Phys. Acad. Sciences (2007)

8. LPN 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 !!!

9. OUT LINE LPN • Introduction and motivation • Generation of triple photons • Coherencestudy of triple photons • Conclusion & perspectives

10. SPECTRAL SPREADING OF THIRD ORDER PARAMETRIC FLUORESCENCE • Energy conservation ħ0 - ħ1 - ħ2 - ħ3 = 0 • Momentum conservation ħk0 - ħk1 - ħk2 - ħk3 = 0 2 equations and 3 quanta {ħ1, ħ2, ħ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.

11. WEAK AMPLITUDE OF THE THIRD ORDER PARAMETRIC FLUORESCENCE Rate of transition Radiated power in the mode k2 Oxidecrystals10-17 W10-21 m2/V2 100 GW/cm2 1 Chalcogenide glasses 10-22 W10-18 m2/V2 1 GW/cm2 10-6 Polymers P2 Triple photons << 10-9 W of Twin photons

12. THE IDEAL CRYSTAL FOR TRIPLE PHOTONS GENERATION … Centrosymmetric structure High damage threshold > 100 GW/cm2 High c(3) nonlinearity > 10-17 m2/V2 Phase-matchable, i.e. birefringence Dn > 10-2 10-9 W of Third order parametric fluorescence … IS NOT YET BORN!

13. λ0-= 532 nm λ1+= 1449 nm λ2+= λ3-=1681 nm NECESSITY TO STIMULATE THE PHOTON SPLITTING LPN Choice of a double stimulation One photon detected atλ1 One generated triple {λ1, λ2, λ3} Phase-matching in KTP for the generation of triple photons around 1500 nm

14. Intensities (W/cm²) Interaction length (a.u.) CLASSICAL THEORY OF TRIPLE PHOTONS GENERATION LPN Fève, Boulanger, Douady, Phys. Rev. A (2002) sn(u/m), cn(u/m) : Jacobi elliptic functions Energy transfer between photons populations

15. High intensities : 100 GW/cm² sub-nanosecond pulses, focalised beams • Perfect phase-matching tunability of the source 1679 nm max = 100 µJ/pulse Nd:YAG 20 ps -10 Hz OPG 420 - 2300 nm x3 Power Meter lenses HTHR 532 nm 532 nm max = 1 mJ/impulsion Optical Delay x2 Glan-Taylor KTPx-cut25 mm Power Meter prism filters PIONEER EXPERIMENT OF TRIPLE PHOTONS GENERATION LPN

16. LPN

17. Phase-matching obtained at : 532 nm(o)1473.5 nm(e) + 1665.2 nm(e) + 1665.2 nm(o) Parametric signature (nm) (nm) SPECTRAL PROPERTIES LPN Generated energy at (a.u) (nm)

18. LPN 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)

19. x3 x2 ξi=ξ2+ ξ3 OPG accordable 420 – 2300 nm Home-made OPO (fixed wavelength) 1064 nm-150 ps ξ1 Possibility of resonant interactions High intensities ξ0 λ2=λ3=1665.2 nm KTP KTP KTP 1064 nm F λ/2 NEW TRIPLE PHOTONS GENERATOR LPN λ2=λ3=1665.2 nm λ0 λ1 λ1 KTP X-cut λ2=λ3 Nd:YAG 1064 nm-20 ps L λ0= 532 nm 15/39

20. VALIDATION OF THE CLASSICAL MODEL LPN ξ0 = 4.5 mJ L = 13 mm ξi= 182 μJ L = 13 mm << ξ0= 4.5 mJ ξi= 182 μJ The calculation under the UPA gives a surestimation of a factor 500 ! Gravier & Boulanger, JOSA B (2008)

21. OUT LINE LPN • Introduction & motivation • Generation of triple photons • Coherencestudy of triple photons • Conclusion & perspectives

22. PROTOCOL OF CORRELATIONS STUDIES LPN Triple photons + stimulating fields Delay 2 Delay 1 Delay 3 Stimulated generation Recombinations @ 2 photons @ 3 photons Spectral analysis at Temporal analysis Sum field Sumfield Following Izo Abram et al in the case of twin photons PRL (1986)

23. QUANTUM MODELISATION OF THE TRIPLE FIELDS LPN • Quantum calculationsQuantization 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 :

24. QUANTUM EXPRESSION OF THE TRIPLE FIELDS LPN • Non linearmomentumevolution 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 sumfieldsissuedfrom the 2 and 3 fieldsrecombination

25. NUMBER OF GENERATED PHOTONS n20 LPN w2 n2(L) n20 n30 np n1(L) w3 n3(L) n30 L z 0 w0

26. EXPRESSION OF THE RECOMBINED FIELD LPN n20 w2 Ap n30 z L2 0 w3 • Quantified recombined field, given by the integration of its creation and annihilation operators at each frequency : L2 z 0 L1 0 z w0 • 3-photons recombined field : or • 2-photons recombined field : • Hence the spectrum of the recombined field:

27. 3-PHOTON RECOMBINATION LPN Dl2=10 nm Dl2=10 nm Triple photons w2 w2 N2=107 Classical Background Dl1=11.5 nm w1 N0=1015 w0 Dl3=10nm Dl3=10 nm w3 N3=107 L L Outgoing photons spectra Dot, Bencheikh, Boulanger, Levenson PRA, to be published

28. OUT LINE LPN • Introduction & motivation • Generation of triple photons • Coherencestudy of triple photons • Conclusion & perspectives

29. CONCLUSION LPN • Theory & experiments of triple photons generationfrom a thirdorderparametricgeneration • Protocols & calculationsshowing the quantum correlations • Correspondingexperiments in progress

30. PERSPECTIVES LPN • Spontaneous triple photons generation in opticalfiberusing modal phase-matching • ! • Aaaaaaaaaaaaaaaaaaaaaaa • Measurementof 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 !

31. c(3) c(2) q p FROM TWIN TO TRIPLE PHOTONS Triple photons LPN Twin photons Strong impact on : -Classicalnonlinearoptics – OPO -Quantum mechanics and cryptography Aspect, Grangier, Roger, PRL (1981) An exciting story over the past 30 years! A new story for the next 30 years?

32. 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

33. SAME PROTOCOLE PREVIOUSLY USED FOR TWIN PHOTONS LPN ω1 ω ω0 |E|2 (a.u.) Abram et al, PRL (1986) ω2 Dayan, Phys. Rev. A (2007) 520 525 530 535 540 545 lambda (nm)

34. Cascading rate (%) SUPPRESSION OF THE SECOND ORDER CASCADING IN KTP Douady & Boulanger, J. Opt A, 2005

35. WIGNER FUNCTION OF TRIPLE PHOTONS . Partially non degenerate three-photon quantum state : w1≠w2=w3 Photons in the mode at w1 Photons in the mode at w2=w3 Bencheikh, Douady, Gravier, Levenson, Boulanger, Compt. Rend. Phys. Acad. Sciences (2007)

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