Generation of quantum states of light by a semiconductor quantum dot

Single photon sources Thermal light : bunched photons (superpoissonian) Coherent light : independent photons (poissonian) Regulated single photon source Applications: quantum cryptography single photon optics (interferences…) linear optics quantum computing

What is a single photon source ? clic Source able to emit single photons pulses on demand N.B. : Non-classical state of light => Impossible to generate using a thermal source or a laser

Applications of single-photon sources Deterministic emission of light pulses containing one and only one photon Metrology flux+energy standard Quantum Key Distribution Polarisation-encoded single photons Quantum computing single photons as Q-bits ?

Quantum cryptography SPS Alice and Bob share a binary key The protocol is intrinsically secure (Heisenberg !!)  whatever the technological abilities of the spy Bennett & Brassard 84 : spying  error > 25% Alice Telecom fiber /2 + /4 waveplates ‘1’ ‘0’ Single Photon Detectors …. PBS Spy?? Bob

Constraints for secure QKD : 1) dark counts Alice photon per pulse Bob d dark counts per pulse transmission t <1 Error correction possible  t > 10 d  limited secure transmission length (~100km at most at telecom wavelength)

Constraints for secure QKD : 2) multi-photon pulses Lossy channel => « Photon-Number Splitting » attack Alice P(n>1) >0 Bob Eve Analyser Source analyses only multi-photon pulses. resends correct photons to Bob. adjusts bit rate to expected value t PNS works  p(n>1) > t

Single photon sources for quantum cryptography  Attenuated laser : - poissonian distribution of n photons per pulse for =0.1 P(0)=90.5%, P(1)=9.05%, P(2)=0.45% Vulnerable to photon number splitting attack for = P(0)=99.5%, P(1)=0.45%, P(2)=10 -3 %  Parametric downconversion: - poissonian process - detection of a photon allows to trigger the gate of the receiver’s detector  Individual emitters

Strategies for single photon generation Injection controlled by Coulomb blockade (Yamamoto et al, Nature 99) 1e- 1h+ h T<0.1K, no microcavity yet Implementation of a discrete emitter atom molecule quantum dot...

Solid-state single photon emittersMolecule Lounis et Moerner, Nature 407, 491 (2000) F center Nanocristal Core (CdSe) Shell (ZnS, CdS) Self-assembled quantum dots at 300 K ! T<200K until now! Kurtsiefer et al, PRL 85, 290, 00 Michler et al, Nature 406, 968, 00

QD assets for single-photon generation QDs are stable (no blinking, no bleaching) efficient (  ~1) fast (  ~1ns) spectrally narrow at low T + adjustable bandgap/non-resonant pumping OK A QD is not a 2-level system! E CB VB XXX

Single photon generation from a quantum dot CB VB Proposal: J.M. Gérard et B. Gayral, J. Lightwave Technol. 17, 2089 (1999)  3  2 Pulsed non resonant excitation + spectral filtering X XX  Conversion of a poissonian excitation into a non-classical regulated stream of single photons

Optical densities Analyser Spectrometer ~ 920 nm He-flow Cryostat (4K) Sample Stop Start Laser Ti:Sa P=1W =790 nm 50/50 beamsplitter X X Photon correlation setup

Photon Antibunching – Proof of a Two-Level Emitter Probability to detect a stop photon at  =   given that a start photon was detected at  =0 11

Antibunching from a Single Quantum Dot 105 W/cm 2 g 2 (0)=0.1  = 750 ps 55 W/cm 2 g 2 (0)=0.0  = 1.4 ns 15 W/cm 2 g 2 (0)=0.0  = 3.6 ns PL spectrum P=55W/cm 2 T=4K

Autocorrelation experiment Start=X1 Stop=X1 g1 X1 Average

XX-X1 cross-correlation Start=X1 Stop=XX XX X1 g1 average Direct evidence of cascaded emission Detecting X1 after XX Detecting XX after X1

attenuated laser light X line correlation histogram First reports: P. Michler et al, Science 290, 2282 (2000) C. Santori et al, PRL 86, 1502 (2000) Number of coincidences Delay  (ns) « X » photons are emitted one by one Protocol works also for electrical pumping (Yuan et al, Science 195, 102, 2002)

Collecting the single photon with the Purcell effect - Spontaneous emission modification - Selective enhancement in a cavity mode PURCELL EFFECT Fast emission  0 /F p directional PL Intensity Time (ps) « Slow » emission  0

Pump laser injection of several e-h pairs 1 QD on resonance with the fundamental mode Collecting the single photon

Pump laser injection of several e-h pairs Recombination of excess pairs Recombination last e-h pair => Demonstration by Gerard (CEA) and Yamamoto (Stanford) Experimental single mode emission: 40% Collecting the single photon

Few QDs in a micropillar cavity mode

Polarization control in single-mode micropillars PL Intensity (lin.) Energy (eV) x-polarized y-polarized Elliptical cross section 1.4 µm 0.7 µm Non degenerate fundamental mode Gayral et al, APL 72, 1421, 1998 ~ 90% linear polarisation degree of single QD emission Moreau et al, APL 79, 2865, 2001

SPS efficiency for GaAs/AlAs micropillars scattering by sidewall roughness Q spoiling  <   photons emitted into the mode Where do they escape???

SPS efficiency for GaAs/AlAs micropillars Efficiencies around 70% can be reached for state of the art pillars J.M. Gérard et al, quant-ph/

PCs for improved QD-SPS ? QD in high Q PC cavity Monomode PC waveguide  > 0.7 ? YES! Moderate F p (>20) =>  >0.95 Q ~ 1000 => X/XX filtering OK Q uncoupled > 10 =>  > 0.9  > 0.85 Q

Current issues for single photon sources Room temperature operation =>QDs with large X-XX splitting (CdSe, GaN...…) Generation of indistinguishable single photons for optical quantum logical gates Improvement of the collection efficiency (optimized pillars, PBG cavities…) Developpement of a « plug and play » source for quantum key distribution (1.3 µm + electrical pumping + microcavity) …and finding a real market for single photon sources !

Two photon interferences += 0 The two photons must be indistinguishable : i) arrive at the same time ii) have the same polarization iii) have the same spectrum Possibility to make two photons emitted by the same quantum dot interfere?

Experimental demonstration (Stanford) C. Santori, D. Fattal, J. Vuckovic, G.S. Solomon, Y. Yamamoto, Nature (Oct 2002)  Understand and master dephasing processes!!

Specifications : QKD vs quantum computing Quantum cryptographyQuantum computing  High emission yield  Low number of n>1 pulses  Emission of polarized photons  Emission at 1.3 or 1.5 µm (fibered link)  Very efficient single photon source (>99%) Otherwise no error correction code possible  Source of indistinguishable photons Otherwise no interference Specifications much tougher for quantum computing!!!!