1. TWO-PHOTON ABSORPTION IN SEMICONDUCTORS Fabien BOITIER, Antoine GODARD, Emmanuel ROSENCHER Claude FABRE ONERA Palaiseau Laboratoire Kastler Brossel Paris

2. Measuring intensity correlations : Hanbury-Brown Twiss experiment Photon Bunching effect

3. - simple explanation in terms of fluctuating waves - more difficult to understand in terms of photons as particles E1E1 E2E2 D1D1 D2D2 E1E1 E2E2 D1D1 D2D2 Fano’s explanation in terms of constructive interference between undistinguishable paths 1 for shot noise, even present when the intensity is constant, 1 due to extreme fluctuations of the mean intensity in chaotic light Understanding Photon bunching

4. Full quantum treatment given by Glauber 1 2 Coherent (single-mode laser) chaotic bunching Non-classical anti-bunching g (2) <1 : no classical explanation possible g (2) >1 : classical explanation possible… … but full quantum explanation still possible and interesting

5. Detectors response time limits observation of narrow features in time or broad in frequency Experiments usually done with « pseudothermal » light sources laser

6. How to study broadband sources with ultra-short correlation times ? I. Abram et al 1986, Silberberg et al Use Hong Ou Mandel interferometer parametric fluorescence Lame semi-réfléchissante Use fast nonlinear effects

7. Another possibility : two-photon absorption in semi-conductors transient state - Broadband - No phase matching CBCB VBVB

8. Two photon characterization of a GaAs phototube Two photon absorption coefficient:  ≈ 10 cm/GW @1.55 µm  Quadratic response between 0.1 and 100 µW Low efficiency: not yet a two-photon counter

9. Photocount histograms and detection operator What is the two-photon counter observable ? 1 « click » acceptable for photon numbers <3 exact quantum theory of two photon counter remains to be done limited efficiency accounted by attenuator in front for perfect quantum efficiency classical approach

10. 10 Two-photon absorption Intensity correlation apparatus Resolution < fs : ASE High pass filter Pulse counter Asph. Lens Time delay

11. Source: cw ASE @ 1.55µm, 4dBm Detector: Hamamatsu PMT GaAs Intensity correlation function obtained by low pass filtering Interferometric recorded signal

12. g (2) (0)  c (fs) λ 0 (nm)  λ (nm) Laser1.01 ±0.03  1560small ASE1.97 ±0.05 53415306 Blackbody1.8 ±0.1 371130155  Summary table of the main properties Bunching of unfiltered blackbody! Boitier et al., Nature phys. 5, 267(2009)

13. with N. Dubreuil, P. Delaye

14. CW source ↔ 14 / 23

15. Evidence of an extrabunching effect near degeneracy far from degeneracy without dispersion compensation with dispersion compensation

16. Photon correlations in parametric fluorescence (1) : full quantum calculation nothing prevents g (2) (0) to be very large in weak sources with large noise ( value of 28 observed on squeezed vacuum (Ping Koy Lam) quantum state produced by parametric fluorescence of gain G quantum calculation of g (2) (0) (in the experiment G>10 6 )

17. Photon correlations in parametric fluorescence (2) : fluctuating field approach - The signal and idler fields are classical fields taken as a sum of wavepackets with random phases  s and  i   the classical equations of parametric mixing imply:  s +  i  pump vacuum fluctuations are needed to trigger the spontaneous parametric fluorescence

18. Photon correlations in parametric fluorescence (3) : corpuscular approach - accidental - pairs due to the twin photon source - linked to the chaotic distribution of pairs

19.  Ideal case without dispersion  Increase of chromatic dispersion

20. CONCLUSION TPA : efficient technique to measure g (2) (  ) down to femtosecond range not yet a two-photon counter : efficiency can be improved classical and/or quantum effects ? -many competing physical pictures - even classical pictures have some quantum flavour - quantum approach often provides more physical insight and simple calculations than semi-classical ones no measurement so far in the full quantum regime g (2) (  ) <1 in ideal tool for high flux isolated photon sources