Report

TWO-PHOTON ABSORPTION IN SEMICONDUCTORS Fabien BOITIER, Antoine GODARD, Emmanuel ROSENCHER Claude FABRE ONERA Palaiseau Laboratoire Kastler Brossel Paris Measuring intensity correlations : Hanbury-Brown Twiss experiment g (t ) = (2) i (t ) i (t +t ) i (t ) 2 g (2) (0) = 2 Photon Bunching effect Understanding Photon bunching - simple explanation in terms of fluctuating waves - more difficult to understand in terms of photons as particles 1 for shot noise, even present when the intensity is constant, 1 due to extreme fluctuations of the mean intensity in chaotic light Fano’s explanation in terms of constructive interference between undistinguishable paths E2 E1 D2 D1 E2 E1 D2 D1 Full quantum treatment given by Glauber bunching 2 1 chaotic tc =1 D Coherent (single-mode laser) anti-bunching Non-classical g(2)<1 : no classical explanation possible g(2)>1 : classical explanation possible… … but full quantum explanation still possible and interesting Detectors response time limits observation of narrow features in time or broad in frequency Experiments usually done with « pseudothermal » light sources laser How to study broadband sources with ultra-short correlation times ? Use fast nonlinear effects I. Abram et al 1986, Silberberg et al Use Hong Ou Mandel interferometer parametric fluorescence Lame semi-réfléchissante Another possibility : two-photon absorption in semi-conductors transient state C B V B - Broadband - No phase matching Two photon characterization of a GaAs phototube P2 N2 GaAs S z 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 Photocount histograms and detection operator N 2 2 N2 What is the two-photon counter observable ? Nˆ = aˆ+ aˆ + aˆaˆ ? 1 2 a 1 N = Njj N = Nj for perfect quantum efficiency classical approach 2 1+ a Nj 2 1 1 Nˆ = aˆ + aˆ + aˆaˆ = Nˆ j Nˆ j -1 2 2 ( ) acceptable for photon numbers <3 1 « click » ˆ 0 0 -1 1 Nˆ = 1- limited efficiency accounted by attenuator in front exact quantum theory of two photon counter remains to be done Two-photon absorption Intensity correlation apparatus High pass filter Pulse counter ASE 12500 S2() 10000 G(2)() 5000 2500 10 10 Resolution < fs : 7500 0 -1500 -1000 -500 Time delay Counts (Arb. Units) Counts (/s) Asph. Lens 0 (fs) 500 1000 1500 -2 -1 0 (fs) 1 2 Interferometric recorded signal S2 ( ) 1 2G(2) ( ) 4Re F1( )e i Re F2 ( )e 2i G(2) F2 F1 G(2) ( ) F2 ( ) F1( ) -1500 -1000 -500 0 (fs) Source: cw ASE @ 1.55µm , 4dBm Detector: Hamamatsu PMT GaAs 500 1000 1500 E (t )E (t )E * (t )E * (t ) I02 (t ) E (t )2 E *2 (t ) I02 (t ) 2 E (t ) E (t ) 2 E(t )E (t ) * 2 I02 (t ) Intensity correlation function obtained by low pass filtering TPA measurement of g(2)() (1): laser, amplified spontaneous emission, blackbody Boitier et al., Nature phys. 5, 267(2009) Summary table of the main properties g(2)(0) c (fs) λ0 (nm) λ (nm) Laser 1.01 ±0.03 1560 small ASE 1.97 ±0.05 534 1530 6 Blackbody 1.8 ±0.1 37 1130 155 Bunching of unfiltered blackbody! TPA measurement of g(2)() (2): high gain parametric fluorescence with N. Dubreuil, P. Delaye CW source ↔ 14 / 23 Second order correlation function g(2)() 2,4 without dispersion compensation signal alone signal + idler 2,2 (2) g () 2,0 1,8 1,6 1,4 1,2 with dispersion compensation 1,0 -0,4 -0,2 0,0 0,2 0,4 (ps) far from degeneracy near degeneracy Evidence of an extrabunching effect g(2) (0) = 3 Photon correlations in parametric fluorescence (1) : full quantum calculation quantum state produced by parametric fluorescence of gain G n/2 æ 1ö 1 Y = ç1- ÷ å nè Gø G ns = n, ni = n quantum calculation of g(2)(0) ˆ (-) Eˆ (-) Eˆ (+) Eˆ (+) Y Y E 1 g(2) (0) = = 3+ 2 G -1 Y Eˆ (-) Eˆ (+) Y (in the experiment G>106) 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) 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 fs and fi. the classical equations of parametric mixing imply: fs+ fifpump g (0) = 2 + (2) E s Ei 2 I s Ii vacuum fluctuations are needed to trigger the spontaneous parametric fluorescence Photon correlations in parametric fluorescence (3) : corpuscular approach three kinds of photon coincidences: - accidental - pairs due to the twin photon source - linked to the chaotic distribution of pairs in a dispersive medium : Ideal case without dispersion Increase of chromatic dispersion dispersion compensation needed ! CONCLUSION TPA : efficient technique to measure g(2)() down to femtosecond range not yet a two-photon counter : efficiency can be improved no measurement so far in the full quantum regime g(2)() <1 in ideal tool for high flux isolated photon sources 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