Generation of twin photons in Triple Microcavities

1. 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 Generation of twin photons in Triple Microcavities

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 Fundamental concepts / technical results • 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

4. Optical Parametric Oscillation

5. widler wpump wsignal ws wi wp wi 2wp ws 0 cavity wp wi pump ws NL Crystal (BBO) Oscillation Paramétrique Optique (OPO) • Parametric conversion (for photons): c(2) c(3) 2(wpump,kpump) (wsignal,ksignal) + (widler,kidler) • In a cavity: oscillation above a threshold (gain = cavity losses) • Simple cavities, double (DROPO), triple (TROPO) - Applications : - generation of new frequencies - quantum optics (cryptography, etc).

6. w w w = + P S I r r r = + k k k P S I OPO : the phase-matching problem • 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. Photon confinement : semiconductor microcavity Fabry-Pérot cavity  meV Miroir de Bragg Miroir de Bragg Cavité  Cavity Mode • Planar F.P. cavity, monolithic • Finesse  103 , 104

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

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

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

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

13. A brief story of microcavities (c) • 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

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

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

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

17. What we want! • Phase-matching without the strong coupling exciton / photon Increase the temperature • High idler intensity (at a smaller emission angle) Efficient collection for twin photons applications • 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) Z growth axis DBR GaAs/AlAs In0.07GaAs QW l-GaAs cavity 1 Coupling DBR 1 In0.07GaAs QW l-GaAs cavity 2 8mm Coupling DBR 2 l-GaAs cavity 3 In0.07GaAs QW DBR GaAs/AlAs Substrate

20. 0.9 0.8 Energy (eV) 0.7 0.6 0.5 0.4 Angle (degree) 0.3 0.2 0.1 Optical modes (transfer matrices simulation) Uncoupled cavities | Coupled cavities • Cavity degeneracy lifted Condition for 2 coupled cavities : • Photonics modes delocalized throughout the whole structure For dual-cavities : see e.g. Stanley et al.,APL65 (1994) : strong coupling between 2 cavities Pellandini et al., APL71 (1997) : dual-l laser emission Armitage et al.,PRB57 (1998) : polariton dispersion

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

22. QW1 QW2 QW3 Optical fiber q substrate CW Ti:sa 850 nm 90° Bragg mirrors Triple microcavity 8mm Experimental setup Sample Growth: LPN

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

24. OPO (a) C. Diederichs et al, NATURE440 (2006) • all beams @ 0° • energy conservation T = 6 K

25. OPO (b) C. Diederichs et al, NATURE440 (2006) • idler: negative dispersion • momentum conservation T = 6 K

26. Properties of the OPO • Below threshold : 2 kW/cm2 • Above threshold : 3.2 kW/cm2 • gain of 4800 • narrowing of the signal and idler from 1 meV to below 200 meV • 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 DE=0, Dk=0 (phase-matching).

28. Power dependence (a) • OPOthreshold : 2.4 kW/cm2

29. Power dependence (b) Out of phase-matching • Lasing at 6 kW/cm2 • Low OPO threshold

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. p s i “Horizontal” Parametric Scattering Réciprocal space imaging qy qx f ’ Fourier Plane

32. p s i “Horizontal” Parametric Scattering s p qy i qx

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

36. Quantum correlated signal and idler beams

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

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

39. Vacuum Noise, Beam noise, Squeezing Y X • 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 I1 I1± I2 μTROPO Spectrum Analyzer I2 Quantum correlations ! Noise of the difference / Vacuum noise < 1

41. Experiment. (a) Dispersion (b) Fourier Plane E qy S pump I qx q

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 : m-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 Prospects • Electrical injection • Operating temperature