1. Generation of twin photons in Triple Microcavities Jérôme TIGNON C. Diederichs, D. Taj, T. Lecomte, C. Ciuti, Ph. Roussignol, C. Delalande Laboratoire Pierre Aigrain (LPA), École Normale Supérieure, Paris, France A. Lemaître, J. Bloch, O. Mauguin, L. Largeau Laboratoire Photonique et Nanostructures (LPN), CNRS, Marcoussis, France C. Leyder, A. Bramati, E. Giacobino Laboratoire Kastler Brossel (LKB) Ecole Normale Supérieure, Paris, France

2. Motivations Fundamental  Better understanding and control of light-matter interaction in semicond. nanostructures Practical  Generating quantum correlated photons is the basis for quantum optics applications such as quantum cryptography.  Working systems rely on large and complex optical sources  Possibility to develop an integrated micro-generator of twin photons ?

3. Outline  Non-linear optics Parametric conversion Phase matching OPOs  Light-matter interaction in semiconductors Semiconductor microcavities Weak and Strong coupling regime OPO in single microcavities A triply resonant OPO in a VCSEL-like structure  Quantum optics Noise measurements Quantum correlated photon pairs Fundamental concepts / technical results

4. Optical Parametric Oscillation

5. 2(  pump,k pump ) (  signal,k signal ) + (  idler,k idler ) Oscillation Paramétrique Optique (OPO)  Parametric conversion (for photons): 0 pp ii ss  p ss ii  (2)  (3)  pump  signal  idler  In a cavity: oscillation above a threshold (gain = cavity losses) pp ss ii pump NL Crystal (BBO) cavity - Simple cavities, double (DROPO), triple (TROPO) - Applications : - generation of new frequencies - quantum optics (cryptography, etc).

6. OPO : the phase-matching problem ISP ISP kkk      Problem : phase matching !!  Solutions : (1) birefringence - pbm : GaAs isotropic  Solutions : (2) quasi-phase matching - ex : PPLN - reduction of the size of OPO (  10 cm) - complex fabrication / alignement

7. Light-matter interaction in semiconductor microcavities

8. Miroir de Bragg Miroir de Bragg Cavité Cavity Mode Fabry-Pérot cavity  meV Photon confinement : semiconductor microcavity - Planar F.P. cavity, monolithic - Finesse  10 3, 10 4

9. Without confinement (3D) Microcavity Photon confinement : mode dispersion

10.  xx cc axe de croissance Quantum Well: exciton k // =photon k // k z free photon Fabry-Pérot Microcavity: Selection of a photon k z exciton k // =photon k // k z quantified excitoncavité polariton exciton photons 0 0 Strong and Weak Coupling Regime

11. A brief story of microcavities (a) - In the weak coupling regime: Vertical cavity lasers (VCSELs, Soda et al. Tokyo, 1979) - 1979 : low T°, optical pumping - 1988 : CW, room T° - 2005 : Ethernet, Fiber Channel etc. - Isotropic emission - Low threshold - Parallelisation fabrication / test

12. - Strong Coupling, Microcavity-Polaritons : C. Weisbuch et al. PRL 69 (1992). exciton cavity X laser A brief story of microcavities (b)

13. - First studies : cw spectroscopy (Rabi splitting, dispersion, T° etc). population dynamics (ps, time-resolved PL) - Today: Coherent and non-linear dynamics (fs, P/p, FWM) Stimulated emission, parametric scattering A brief story of microcavities (c)

14. OPO with polaritons in a microcavity (a) P.G. Savvidis et al. PRL 84 1547 (2000) signal idler  k // EE EE pump Pump : 17° Idler Signal 0° OPO in a nanostructure ! OPO with mixt light-matter excitations ! 90°

15. Strong resonant  (3) polaritonique nonlinearity Low OPO threshold R. M. Stevenson et al. PRL 85 3680 (2000) OPO with polaritons in a microcavity (b) o C. Ciuti et al., Phys. Rev. B 62, 4825 (2000) (théorie quantique) o D. M. Whittaker et al., Phys. Rev. B 63, 193305 (2001) (théorie semi-classique) Theory :

16. Gisin et al, Quantum cryptography, REV. MOD. PHYS. 74 (2002) Motivations:  -OPO  Source of twin photons ? quantum optics (quantum cryptography) o Strong coupling regime required Low temperature (max 50 K) o Idler emitted at very large angle + weakly coupled to outside Inefficient collection for twin photons applications o Pump injection at large angle No electrical injection with an integrated system DRAWBACKS: s p i

17. What we want! o Phase-matching without the strong coupling exciton / photon Increase the temperature o High idler intensity (at a smaller emission angle) Efficient collection for twin photons applications o Pump injection at 0° Electrical injection possible

18. Micro-OPO in triple microcavities

19. New Design: a Triple Microcavity C. Diederichs and J. Tignon, APL 87 (2005) Coupling DBR 1 DBR GaAs/AlAs -GaAs cavity 1 Substrate -GaAs cavity 2 -GaAs cavity 3 DBR GaAs/AlAs Coupling DBR 2 In 0.07 GaAs QW Z growth axis 8  m In 0.07 GaAs QW

20. Angle (degree) Energy (eV) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Optical modes (transfer matrices simulation)  Cavity degeneracy lifted For dual-cavities : see e.g. Stanley et al., APL 65 (1994) : strong coupling between 2 cavities Pellandini et al., APL 71 (1997) : dual- laser emission Armitage et al., PRB 57 (1998) : polariton dispersion Uncoupled cavities |Coupled cavities Condition for 2 coupled cavities :  Photonics modes delocalized throughout the whole structure

21. Inclusion of QWs / Weak and Strong coupling regime 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Angle (degree) Energy (eV) Strong CouplingWeak Coupling Strong exciton-photon regime Six polariton modes Cavity-mode degeneracy lifted Three coupled photonic modes

22. Experimental setup Sample Growth: LPN

23. Tuning of the photon modes Single cavities X  Spacer wedge along X by interruption of the rotation at 0° X E cav Triple cavity  Cavity 1 : interruption at 0° (X)  Cavity 2 : no interruption  Cavity 3 : interruption at 90° (Y) X Y E cav X

24. C. Diederichs et al, NATURE 440 (2006) OPO (a)  all beams @ 0°  energy conservation T = 6 K

25. OPO (b)  idler: negative dispersion  momentum conservation T = 6 K C. Diederichs et al, NATURE 440 (2006)

26. Properties of the OPO  Below threshold : 2 kW/cm 2  Above threshold : 3.2 kW/cm 2  gain of 4800  narrowing of the signal and idler from 1 meV to below 200  eV  high conversion efficiency under cw excitation = 10 -2

27. Phase-matching dependence  x : “phase-matching” parameter  Strong non-linear emission of the signal and idler states only for x=0, i.e. for  E=0,  k=0 (phase-matching).

28. Power dependence (a)  OPO threshold : 2.4 kW/cm 2

29. Power dependence (b)  Lasing at 6 kW/cm 2  Low OPO threshold Out of phase-matching

30. Comments / saturation of the idler - Idler at higher energy is degenerate with QW absorption continuum - Idler (and not Signal) is subject to multiple parametric scattering - Signal / Idler ratio important ? - yes for quantum-noise measurements applications - no if one counts coincidences (it just lowers the overal coincidence counting rate)

31. “Horizontal” Parametric Scattering si p Fourier Plane f ’ xx yy Réciprocal space imaging

32. “Horizontal” Parametric Scattering si p i p xx yy s

33. Large Negative detuning Detuning close to zero Horizontal Parametric Scattering (c) Rayleigh Scattering OPO

34. What determines the angles ? Stereographic projection of the crystal Easy defect propagation along some directions The experimental configuration, with an excitation along a high symmetry direction allows probing these axis.

35. X ray diffraction (L. Largeau, LPN) z Characterization by X-ray diffraction No dislocation Mosaicity elastic deformation due to AlAs / GaAs mismatch correlation length 400 nm with underlying crystal symmetry => photonic disorder common effect in all microcavities !!

36. Quantum correlated signal and idler beams

37. pump idler signal Parametric conversion : Production of a photon pair, correlation in space and time +/-- Spectrum Analyzer Parametric oscillation: production of twin beams, correlated in intensity  (2) Twin beams from Optical Parametric Oscillators

38. Beam Noise Spectrum Analyzer is the amplitude quadrature Noise spectral density at the frequency Ω Amplitude fluctuations

39. X Y Vacuum Noise, Beam noise, Squeezing - Fluctuations limited by Heisenberg - Vaccum noise (shot-noise, standard quantum limit) - Beam noise for a coherent state - Squeezing : non-classical state, quantum optics applications

40. Quantum correlations measurement: noise measurements Spectrum Analyzer +/-- I1I1I1I1 I2I2I2I2 I 1 ± I 2 μTROPO Noise of the difference / Vacuum noise < 1 Quantum correlations !

41. S I pump E  xx yy Experiment. (a) Dispersion (b) Fourier Plane

42. Quantum correlations measurement: noise measurements Submitted to publication

43. Noise of the difference is below the Shot Noise

44. Detuning dependence

45. Summary / Outlook  Realization of a triply resonant OPO in a VCSEL-like structure :  -VTROPO  cw operation with low threshold  Operation up to at least 150 K (compare with 50 K)  Generation of photon pairs in various configurations  Generation of quantum correlated twin photon pairs  Electrical injection  Operating temperature Prospects