A Waveguide-Coupled On-Chip Single Photon Source A. Laucht,1,2 S. Pu¨tz,1 T. Gu¨nthner,1,3 N. Hauke,1 R. Saive,1 S. Fr´ed´erick,1,4 M. Bichler,1 M.-C. Amann,1 A. W. Holleitner,1 M. Kaniber,1 and J. J. Finley1 1Walter Schottky Institut and Physikdepartment, Technische Universita¨t Mu¨nchen, Am Coulombwall 4a, 85748 Garching, Germany 2Centre for Quantum Computation & Communication Technology, The University of New South Wales, Sydney NSW 2052, Australia 3Institute fu¨r Experimentalphysik, Universita¨t Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria 4Institute for Microstructural Sciences - National Research Council of Canada, Ottawa, ON, Canada (Dated: September 26, 2011) 2 We investigate single photon generation from individual self-assembled InGaAs quantum dots 1 coupled to the guided optical mode of a GaAs photonic crystal waveguide. By performing confocal 0 microscopymeasurementsonsingledotspositionedwithinthewaveguide,welocatetheirpositions 2 with a precision better than 0.5 µm. Time-resolved photoluminescence and photon autocorrelation n measurements are used to prove the single photon character of the emission into the propagating a waveguidemode. Theresultsobtaineddemonstratethatsuchnanostructurescanbeusedtorealize J an on-chip, highly directed single photon source with single mode spontaneous emision coupling 1 efficiencies in excess of β ∼85 % and the potential to reach maximum emission rates >1 GHz. Γ 3 PACSnumbers: 42.50.Ct,42.70.Qs,78.67.Hc,78.47.-p,42.82.Et ] l l a The ability to control the direction and rate of spon- intensity and spontaneous emission dynamics detected h taneous emission by tailoring the local density of pho- along an axis perpendicular to the sample surface with - s ton modes experienced by an emitter is a key concept similar measurements detected in the plane of the pho- e to enhance the efficiency of nanoscale light sources such tonic crystal waveguide, we obtain strong evidence for m as single photon sources1–6 and nanoscale lasers.7 Over significant enhancements of the radiative coupling to the . t recent years, several groups have demonstrated the abil- propagatingwaveguidemode. Mostnotably,a∼55±8× a ity to control light-matter coupling using photonic crys- more efficient coupling to the PWG mode is measured m tal nanostructures.8–10 Strong enhancements of sponta- compared to radiation into free space modes along the - neous emission rates have been observed for individ- verticaldetectionaxis. Time-resolvedphotoluminescence d n ual quantum emitters in low mode volume, high-Q de- measurements detected on the same QD transition allow o fect cavities.8,11,12 However, for such systems to be use- us to estimate the fraction of all spontaneous emission c ful one has to spectrally bring the emitter and cav- emitted into the waveguide mode (β ). This can be very Γ [ ity mode into mutual resonance calling for sophisticated high for individual QDs in PWG structures,18,19,22 and 2 electro-13 orthermo-optical14 tuningmethods. Recently, our measurements reveal a lifetime of τ =0.87±0.15 ns v Viasnoff-Schwoob et al.15 demonstrated that enhanced from which we estimate that 85 % < β < 96 %. Sec- Γ 3 light-matter coupling can be obtained over wider band- ond order photon autocorrelation g(2)(τ) measurements 5 widths by coupling emitters to the enhanced density of confirm the single photon character of the QD emission 1 photonic modes close zero-group-velocity points of the into the waveguide mode with a multiphoton probabil- 5 dispersion of a 1D photonic crystal waveguide.16 There- ity of g(2)(0) = 0.27±0.07, compared to a Poissonian . 1 fore, such 1D photonic crystal waveguides (PWGs) pro- source with the same average intensity. The wide band- 0 vide strong promise for use as an on-chip single-photon width of the PWG guided modes (> 25 meV) provides 2 sourcesincetheyeffectivelyfunnelspontaneousemission a highly attractive route towards the design of on-chip 1 into the guided optical mode and obviate the need for quantum optics experiments obviating the need to fine- : v precise spectral tuning of the emitter - photonic sys- tune the QD transition into spectral resonance with a Xi tem.15,17–26 A highly efficient single-photon source is the high-Q photonic crystal cavity mode.13,31 key component required in many quantum communica- r Thesampleinvestigatedwasgrownbymolecularbeam a tion protocols27 and the combination of single quantum epitaxy and consists of a 500 nm thick Al Ga As dots (QDs) coupled to propagating modes on a photonic 0.8 0.2 sacrificial layer, and a 180 nm thick GaAs layer con- crystalchipisofstronginterestforchipbasedimplemen- taining a single layer of nominally In Ga As QDs at tations of linear optics quantum computing.28 0.5 0.5 its midpoint. The QD layer has a relatively low den- In this paper, we present experimental investigations sity ρ < 1 µm−2, which allows us to selectively ex- QD oftheemissioncharacteristicsofsingleself-assembledIn- cite and study the emission characteristics of individual GaAs QDs coupled to the guided mode of a linear defect QDs using a confocal microscope in which the laser is (W1) PWG.29,30 We perform spatially resolved photo- focused to a spot with a diameter of ∼ 1.2 µm. A two- luminescence (PL) measurements to locate the position dimensional photonic crystal formed by defining a trian- of the QD inside the PWG. By comparing the emission gular array of air holes (r ∼ 71±3 nm) with a nom- 2 inal lattice constant of a = 270 nm was realized using ( a ) U n d e re tc h e d ( b ) P C a combination of electron-beam lithography and reac- P W G R e g io n tive ion etching. PWGs were formed by introducing line C le a v e d defects consisting of a single missing row of holes (W1 F a c e t waveguide).29,30 For these specific geometrical parame- ters the guided waveguide modes span the energy range of E =1125−1364 meV (a/λ=0.245−0.297) as deter- mined by finite-difference time-domain simulations and 5 µ m C le a v e d 1 µ m U n d e re tc h e d transmission measurements performed on reference sam- F a c e t R e g io n ples [cf. Fig.1 (d) and (e)]. The sample was then cleaved ( c ) perpendicular to the axis of the PWG, to facilitate di- E x c it a t io n a n d rect optical access to the waveguide mode and to allow T o p D e t e c t io n S id e D e t e c t io n for collection of light directly propagating through the waveguide. Cleaving of the sample was done before we fabricatedthefree-standingmembraneinthewet-etching z stepwithhydrofluoricacid. Theremoteendofthe45µm y (∼165 unit cells) long waveguide is terminated with an input coupler that serves to scatter light into the guided x waveguide modes for transmission experiments.32 In Fig.1 (a) and (b) we present scanning electron ( d ) ( e ) l 1 6 0 0 microscope (SEM) images of the investigated sample. a/0 .3 4 S la b b a n d G a A s Fig.1 (a) shows an image recorded normal to the sam- cy 0 .3 2 L ig h t c o n tin u u m 1 5 0 0 En ple surface. It shows the W1 PWG and the cleaved edge n c o n e 1 4 0 0 e alatrwthhriochugiht tehnedso.miTttheed crolewavoefdafiracheotlersunthsaptedrepfienneditchue- reque00 ..23 80 W M 3 1 3 0 0 rgy (m waveguide. This can be quite easily realized when ori- f0 .2 6 1 2 0 0 e ethnetin[1g1t0h]ecrpyhsotatolnaixcesstroufctthuereGaanAdstshuebcslteraavteed. Tedhgeeiamloangge lized0 .2 4 WW MM 21 1 1 0 0 V) a0 .2 2 1 0 0 0 alsoshowstheunderetchedregionofthewaveguidewhich rm 0 .2 0 .3 0 .4 0 .5 T r a n s m is s io n extends ∼0.6 µm from the photonic crystal into the un- o G W a v e v e c t o r K ' ( a r b . u n it s ) patterned region of the sample. In Fig.1 (b) we present N an image of the cleaved facet of the sample, recorded FIG. 1. (a) and (b) SEM images of the W1 waveguide from along an axis 45◦ to the waveguide axis. We can iden- the top and from the side, respectively. (c) Schematic of the tify the smooth surface of the cleaved facet and also the excitation and detection geometry. (d) Photonic bandstruc- free-standing membrane containing the InGaAs QDs. ture calculations for a W1 waveguide with r/a = 0.26 and For optical characterization the sample is mounted in h/a = 0.6667. The solid blue lines correspond to the pho- a liquid He-flow cryostat and cooled to T = 15 K. For tonic waveguide modes and the light gray region to the slab excitation we use a pulsed Ti-Sapphire laser (80 MHz waveguide modes. The dark gray region indicates the light cone. (e) Spectral transmission of the waveguide for illumi- repetition frequency, 5 ps pulse duration) tuned to the nation from the top at the inner end of the waveguide and low energy absorption edge of the bulk GaAs (λ = laser detection from the side at the cleaved end. The red (light 815 nm). While the sample is always excited from the gray) shaded region marks the spectral region of quantum top (i.e. perpendicular to the sample surface) using a dot emission (bulk GaAs). 100× microscope objective (NA=0.50), the PL signal is either detected from the top using the same objective, or from the cleaved facet of the PWG (i.e. perpendicu- lartothecleavededge)usinga50×microscopeobjective calculations using the software package RSoft.33 We (NA=0.42). Aschematicrepresentationoftheexcitation use optical constants that are appropriate for GaAs anddetectionschemeisshowninFig.1(c). TheQDPLis (n = 3.5) and the geometric parameters for the in- GaAs spectrally analyzed using a 0.5 m imaging monochroma- vestigatedW1photoniccrystalwaveguide(h/a=0.6667 tor and detected using a Si-based, liquid nitrogen cooled and r/a = 0.26). The result of this simulation is pre- CCD detector. For time-resolved spectroscopy we use sented in Fig. 1(d) where we plot the normalized fre- a Si-based avalanche photodiode connected to the side- quency of the photonic bands as a function of k-vector exitofourmonochromatorwithatemporalresolutionof along the Γ - K(cid:48) point direction.34,35 The guided pho- ∼ 350 ps (∼ 150 ps after deconvolution), and for auto- tonic waveguide are depicted as blue solid lines, the slab correlationexperimentsapairofidenticaldetectorswith waveguides modes as a light gray-shaded region and the a temporal resolution of ∼750 ps. regionabovethelightconeisshadeddarkgray.36 Wecal- We determine the spectral properties of the guided culate the lowest energy waveguide mode WM1 to span waveguide mode by conducting photonic bandstructure thenormalizedfrequencyrangea/λ=0.245−0.266,cor- 3 FIG.2. ComparisonofthePLintensityfortopandsidedetection. Spatially-resolvedPLscanperformedwith(a),(c)detection from the top, and (b),(d) detection from the cleaved facet of the waveguide. The PL intensity is integrated over the spectral range of the wetting layer and quantum dot emission E = 1200−1477 meV in (a) and (b), and over the limited spectral int range of a single quantum dot E = 1358.0−1362.5 meV in (c) and (d). The dotted white lines mark the position of the int PWG, while the plain white lines indicate the outline the photonic crystal structure and the cleaved edge of the sample. responding to an energy of E = 1125−1221 meV. The sidethetransmissionbandofthephotoniccrystalwaveg- second waveguide mode WM2 is at a/λ = 0.260−0.272 uide. (E = 1194−1249 meV) and the third waveguide mode We performed spatially resolved photoluminescence WM3 at a/λ=0.288−0.297 (E =1322−1364 meV).37 measurements of the PWG region by scanning the exci- tationspotoverthesamplesurfaceandrecordingspectra Inordertoverifythecalculationsandtocheckthatthe on a 40×15 µm2 square grid with a 0.5 µm pitch. In quantumdotemissionisspectrallyinresonancewithone Fig. 2(a) and (b) we present spatially-resolved contour of the guided modes of the photonic crystal waveguide, plotsofthephotoluminescencesignalintegratedoverthe we measure the spectral transmission of the structure. spectral range E = 1200−1477 meV, i.e. including To do this, the laser is focussed on the inner end of the int photoluminescence from the wetting layer and the quan- photonic crystal waveguide within the body of the pho- tum dots. We performed the measurement in Fig. 2(a) tonic crystal. In this geometry laser light is scattered with excitation and detection from the top and the mea- into the waveguide and the transmitted intensity can surement in Fig. 2(b) with excitation from the top and be detected from the cleaved facet as the wavelength is detection via the cleaved facet of the photonic crystal scanned. Whilethistypeofmeasurementallowsustolo- waveguide. Integration over this energy range allows catethetransmissionbandofthePWG,itisnotpossible us to precisely locate the position of the PWG and the to reliably estimate the transmission losses since the in- cleavedfacetontheluminescencemaps(indicatedbythe coupling and out-coupling efficiencies are unknown and solid white lines). While the PL intensity on the un- difficult to reliably determine. In particular, the outcou- processed material is homogeneous for top detection, we pling efficiency depends critically on the position within observe a general trend to higher intensities in side de- the unit cell where the waveguide is cleaved. Fig. 1(e) tection(redcolor)atpositionsclosertothecleavedfacet showsthespectrumofthetransmittedlightrecordedus- of the waveguide, probably due to the proximity of the ing this method. The open circles correspond to the ex- excitation spot to the outcoupling facet. perimentaldatapointswhilethebluesolidlineisamov- ing 7-point average. The transmission band is centered While integration over a wide spectral range enables at 1323 meV, with a width of 55 meV. This is in fairly us to locate the photonic crystal waveguides, integra- goodaccordwiththesimulationsconductedinFig.1(d). tion over a narrow spectral window allows us to lo- The gray shaded region in Fig. 1(e) indicates the spec- cate the position of individual self-assembled QDs. In tralrangeoverwhichweexpectabsorptionfromthebulk Fig. 2(c) and (d) we integrate the same dataset pre- GaAs,whiletheredshadedregionindicatestherangefor sented in Fig. 2(a) and (b) over a limited spectral range which we observe photoluminescence emission from the E =1358.0−1362.5 meV. Fig. 2(c) and (d) show the int quantum dots, clearly showing that they are located in- signal detected from the top and from the side, respec- 4 FIG. 3. (a) PL spectra of the single quantum dot recorded with detection from the top (black line) and from the side (red line). (b) Power-dependent PL intensity of the single exciton line at E = 1360.4 meV with detection from the top (black X circles) and from the side (red squares). (c) Corresponding time-resolved PL intensity measurements with detection from the side(opencircles). Thesolidredlineisafittothedataandsolidgraylineistheinstrumentresponsefunctionoftheexcitation anddetectionsystem. (d)Correspondingphotonautocorrelationmeasurementwithdetectionfromtheside,provingthesingle photon character of the emission. The excitation power density for this measurement was 4 W/cm2. tively. One particular quantum dot with an energy at tion geometries, at P = 3 W/cm2 the absolute detected the high energy side of the transmission band, at a po- intensity for side detection is ∼ 55±8× higher than for sition deQdDge = 7.3±0.5 µm away from the cleaved facet topdetection(Iside =494±40cts/scf. Itop =9±1cts/s). (highlighted by the blue circle), exhibits extremely weak The intensities obtained for the two different detection out-of-plane emission but comparatively much stronger geometries can be directly compared to obtain informa- in-plane emission. This observation provides evidence tionabouttherelativecouplingstrengthoftheQDtothe for good spatial coupling between this particular quan- PWG mode, compared to other radiation modes of the tum dot and the photonic crystal waveguide mode. system. Top detection of the emission provides informa- tionabouttheradiativeemissionintonon-guidedmodes, In Fig. 3(a) we compare photoluminescence spectra whilesidedetectionsuppliesinformationabouttheradia- recordedforthetwodifferentdetectiongeometrieswhere tive emission into the photonic crystal waveguide mode. the spectrum detected from the topis plotted as red line A ∼55±8× higher intensity for side detection is, there- (note the ×10 enhanced scale) and detection from the fore, a clear signature of the efficient coupling of the QD side is plotted as black line. We observe the same tran- to the propagating PWG mode. sition lines in both detection geometries, albeit with a muchlowerintensityfortopdetectionasdiscussedabove. Further support for this conclusion is provided by the For the line marked with the black arrow, we conduct time-resolved measurement presented in Fig. 3(c). The power-dependent measurements and plot the peak in- black circles correspond to the measured decay tran- tensity in Fig. 3(b) for both top (red squares) and side sient, while the red line is a fit to the data taking into (black circles) detection. In both detection geometries account the instrument response function (IRF) of the we observe a slightly sublinear power law dependence detection and excitation systems (gray line). For the I ∝Pm with m =0.73±0.04 and m =0.81±0.09 specific transition under study we measure a lifetime of top side for non-resonant excitation. This provides evidence that τ = 0.87±0.15 ns. From this value we obtain the β - Γ the transition line investigated has single exciton char- factorwhichiscalculatedfromthespontaneousemission acter.38–41 Whilethepower-dependenceandtheonsetof rates into the waveguide mode (Γ ) and non-guided, WG saturation(P ∼8W/cm2)isverysimilarforbothdetec- radiativemodes(Γ ), andthenon-radiativedecayrate rad 5 (Γ ),18,19,22 using the equation andefficientsinglephotonturnstiledevicewithβ >85% nr andaradiativelifetimethatwouldfacilitateamaximum β = ΓWG = ΓWG . (1) repetition rate f >1 GHz. Photons are emitted directly Γ Γ +Γ +Γ Γ +Γ into an on-chip photonic waveguide providing significant WG rad nr WG int flexibilityforon-chipquantumopticsexperiments. When Here,Γ andΓ canbecombinedtoΓ =Γ +Γ rad nr int rad nr compared to geometries where the quantum dot is reso- which is the intrinsic emission rate of an uncoupled QD. nantly coupled to a cavity mode, in this system there is Typical intrinsic lifetimes of reference QDs emitting into no need to spectrally tune the quantum dot into reso- the two-dimensional photonic bandgap were measured nance and, thus, efficient single photon emission can be to be τ = 1/Γ ∼ 5 − 20 ns42 depending on the int int realized over a wide bandwidth. This opens up perspec- position of the quantum dot within the photonic crys- tives for quantum information experiments with wave- tal.11,22,39 This value is much longer than the short life- length division multiplexing capabilities.43 time of τ = 0.87 ± 0.15 ns for the waveguide coupled In conclusion we investigated the spontaneous emis- dot. Thisobservationindicatesthattheβ-factorisinthe sion properties of a single self-assembled InGaAs quan- range 85 %<β <96 %, in good agreement with values Γ tum dot coupled to the mode of a photonic crystal W1 fromtheliterature.18,19,25 Similarfindingswereobserved defect waveguide. We located a well-coupled quantum for a number of different QDs within the waveguide re- dot 7.3 ± 0.5 µm away from the cleaved facet of the gion,indicatingthatthefractionoflightemittedintothe waveguide by performing spatially resolved photolumi- waveguide mode varies from β < 10 % to β > 90 % de- nescence scans. When comparing the signal obtained in pending on the exact position and frequency of the dot. the two different detection geometries we observed the We note that high β-factors (i.e. efficient QD emission samespectralfeaturesfordetectionperpendiculartothe into the waveguide mode) can be obtained for a wide sample surface and for detection at the cleaved end of range of detunings, however high Purcell-factors1 (i.e. the waveguide, albeit with a different intensity depend- emission enhancement compared to QDs in unprocessed ing mainly on the coupling strength between quantum GaAs material) are usually only obtained when the QD dot and waveguide mode. We estimated a β-factor of transition is in resonance with the flat part of the PWG β >85% from lifetime measurements, and demonstrate mode in the dispersion relation (slow-light regime).18,26 Γ efficientsinglephotonemissionwithg(2)(0)=0.27±0.07, Our approach allows the design of efficient broad-band making these structures prospective candidates for on- single-photonsources,whilethedesignofhighlycoherent chip quantum communication and quantum optical in- single photon sources would still require a tuning mech- vestigations. anism to obtain large Purcell-factors. We continue to present a photon autocorrelation We gratefully acknowledge financial support of the (g(2)(τ)) measurement recorded with side detection in DFG via the SFB 631, the German Excellence Initiative Fig. 3(d) using pulsed excitation with a time-averaged via NIM, the EU-FP7 via SOLID, and the BMBF via power density of 4 W/cm2. The peak at τ = 0 is, QuaHLRep project 01BQ1036. AL acknowledges sup- clearly, much weaker than the adjacent peaks and from portoftheTUM-GS,andSFoftheAlexandervonHum- comparing the areas of the peaks we estimate g(2)(0) = boldt Foundation. 0.27±0.07. This value is significantly below the value of Note added: After submission of this work, another 0.50, proving that almost all of the detected light origi- demonstration of on-chip single-photon emission of a nates from the investigated single exciton transition and quantum dot coupled to a photonic crystal waveguide that we observe clean single photon emission. Thus, the was reported.44 Our work and this work were performed results presented in Fig. 3 demonstrate a highly directed independently. 1 E. M. Purcell. “Spontaneous emission probabilities at 5 M. Fujiwara, K. Toubaru, T. Noda, H.-Q. Zhao, and radio frequencies,” Phys. Rev. 69, 681 (1946). S. Takeuchi. “Highly Efficient Coupling of Photons from 2 M.Pelton,C.Santori,J.Vuckovic,B.Zhang,G.Solomon, NanoemittersintoSingle-ModeOpticalFibers,”NanoLet- J. Plant, and Y. Yamamoto. “Efficient source of single ters 11, 4362 (2011). photons: A single quantum dot in a micropost microcav- 6 M. Davanco, M. T. Rakher, W. Wegscheider, D. Schuh, ity,” Phys. Rev. Lett. 89, 233602 (2002). A. Badolato, and K. Srinivasan. “Efficient quantum 3 C.Santori,D.Fattal,J.Vuckovic,G.Solomon, andY.Ya- dot single photon extraction into an optical fiber using a mamoto. “Indistinguishablephotonsfromasingle-photon nanophotonic directional coupler,” Appl. Phys. Lett. 99, device,” Nature 419, 594 (2002). 121101 (2011). 4 J.Claudon,J.Bleuse,N.S.Malik,M.Bazin,P.Jaffrennou, 7 H. Altug, D. Englund, and J. Vuckovic. “Ultrafast N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gerard. photonic crystal nanocavity laser,” Nature Physics 2, 484 “A highly efficient single-photon source based on a quan- (2006). tumdotinaphotonicnanowire,”NaturePhotonics4,174 8 D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, (2010). T.Nakaoka,Y.Arakawa,Y.Yamamoto, andJ.Vuˆckovi´c. 6 “Controllingthespontaneousemissionrateofsinglequan- quantumdotemissioninaunidirectionalphotoniccrystal tum dots in a two-dimensional photonic crystal,” Phys. waveguide,” Appl. Phys. Lett. 96, 031109 (2010). Rev. Lett. 95, 013904 (2005). 25 H.Thyrrestrup,L.Sapienza, andP.Lodahl. “Extraction 9 A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, of the beta-factor for single quantum dots coupled to a P. M. Petroff, and A. Imamo˘glu. “Deterministic cou- photoniccrystalwaveguide,”Appl.Phys.Lett.96,231106 plingofsinglequantumdotstosinglenanocavitymodes,” (2010). Science 308, 1158 (2005). 26 P. Yao, V. S. C. Manga Rao, and S. Hughes. “On-chip 10 A.Kress,F.Hofbauer,N.Reinelt,M.Kaniber,H.J.Kren- single photon sources using planar photonic crystals and ner,R.Meyer,G.Bohm, andJ.J.Finley. “Manipulation single quantum dots,” Laser & Photonics Reviews 4, 499 of the spontaneous emission dynamics of quantum dots (2010). in two-dimensional photonic crystals,” Phys. Rev. B 71, 27 C. H. Bennett and G. Brassard. “Proceedings of the ieee 241304 (2005). internationalconferenceoncomputers,systemsandsignal 11 M. Kaniber, A. Kress, A. Laucht, M. Bichler, R. Meyer, processing,” , 175 (1984). M. C. Amann, and J. J. Finley. “Efficient spatial re- 28 J. L. O’Brien, A. Furusawa, and J. Vuckovic. “Photonic distribution of quantum dot spontaneous emission from quantum technologies,” Nature Photonics 3, 687 (2009). two-dimensional photonic crystals,” Appl. Phys. Lett. 91, 29 M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, 061106 (2007). A. Scherer, and T. Pearsall. “Waveguiding in planar 12 D.Englund,B.Shields,K.Rivoire,F.Hatami,J.Vuˆckovi´c, photonic crystals,” Appl. Phys. Lett. 77, 1937 (2000). H. Park, and M. D. Lukin. “Deterministic coupling 30 S. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. of a single nitrogen vacancy center to a photonic crystal Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, and cavity,” Nano Letters 10, 3922 (2010). R.Houdr´e. “Mini-stopbandsofaone-dimensionalsystem: 13 A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, Thechannelwaveguideinatwo-dimensionalphotoniccrys- M.Kaniber,G.Bohm,P.Lodahl,M.-C.Amann, andJ.J. tal,” Phys. Rev. B 63, 113311 (2001). Finley. “Electrical control of spontaneous emission and 31 S. Mosor, J. Hendrickson, B. C. Richards, J. Sweet, strong coupling for a single quantum dot,” New J. Phys. G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. 11, 023034 (2009). Shchekin, and D. G. Deppe. “Scanning a photonic crys- 14 D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, talslabnanocavitybycondensationofxenon,”Appl.Phys. and J. Vuˆckovi´c. “Controlling cavity reflectivity with a Lett. 87, 141105 (2005). single quantum dot,” Nature 450, 857 (2007). 32 The low reflectivities of the waveguide terminations com- 15 E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, bined with the expected significant propagation losses for S. Varoutsis, I. Robert-Philip, R. Houdr´e, and C. J. M. thethirdwaveguidemode(WM3)arenotexpectedtosig- Smith. “Spontaneous emission enhancement of quan- nificantlymodifythewaveguidemodedispersioncompared tumdotsinaphotoniccrystalwire,”Phys.Rev.Lett.95, to the infinite waveguide approximation.20,21. 183901 (2005). 33 RSoft, “Rsoft design group products,” http://www. 16 Y.Vlasov,M.O’Boyle,H.Hamann, andS.McNab. “Ac- rsoftdesign.com/. tive control of slow light on a chip with photonic crystal 34 S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. waveguides,” Nature 438, 65 (2005). Joannopoulos. “Linear waveguides in photonic-crystal 17 S.Hughes. “Enhancedsingle-photonemissionfromquan- slabs,” Phys. Rev. B 62, 8212 (2000). tumdotsinphotoniccrystalwaveguidesandnanocavities,” 35 D. F. Dorfner, T. Hu¨rlimann, T. Zabel, L. H. Frandsen, Opt. Lett. 29, 2659 (2004). G.Abstreiter, andJ.J.Finley. “Siliconphotoniccrystal 18 G. Lecamp, P. Lalanne, and J. P. Hugonin. “Very nanostructures for refractive index sensing,” Appl. Phys. largespontaneous-emissionbetafactorsinphotonic-crystal Lett. 93, 181103 (2008). waveguides,” Phys. Rev. Lett. 99, 023902 (2007). 36 Theregionabovethelightconecorrespondstotheenergy- 19 V. S. C. Manga Rao and S. Hughes. “Single quantum- wavevector combinations for which photons are not con- dot Purcell factor and beta factor in a photonic crystal fined to the slab by total internal reflection, i.e. they can waveguide,” Phys. Rev. B 75, 205437 (2007). leave the waveguide in vertical directions. 20 V. S. C. Manga Rao and S. Hughes. “Single quantum 37 Duetothelargeunitcellusedforthesimulations,thethird dot spontaneous emission in a finite-size photonic crystal waveguidemodewashiddenwithinfoldedbandsforr/a= waveguide: Proposal for an efficient “on chip” single pho- 0.26.We,therefore,linearlyextrapolateditspositionfrom ton gun,” Phys. Rev. Lett. 99, 193901 (2007). six calculations performed for r/a=0.29−0.34. 21 V.S.C.MangaRaoandS.Hughes. “Numericalstudyof 38 J. J. Finley, A. D. Ashmore, A. Lemaitre, D. J. Mowbray, exact purcell factors in finite-size planar photonic crystal M.S.Skolnick,I.E.Itskevich,P.A.Maksym,M.Hopkin- waveguides,” Optics Letters 33, 1587 (2008). son, and T. F. Krauss. “Charged and neutral exciton 22 T.Lund-Hansen,S.Stobbe,B.Julsgaard,H.Thyrrestrup, complexes in individual self-assembled in(ga)as quantum T. Suenner, M. Kamp, A. Forchel, and P. Lodahl. “Ex- dots,” Phys. Rev. B 63, 161305(R) (2001). perimental realization of highly efficient broadband cou- 39 M. Kaniber, A. Laucht, T. Hu¨rlimann, M. Bichler, pling of single quantum dots to a photonic crystal waveg- R. Meyer, M.-C. Amann, and J. J. Finley. “Highly uide,” Phys. Rev. Lett. 101, 113903 (2008). efficient single-photon emission from single quantum dots 23 M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams. within a two-dimensional photonic band-gap,” Phys. Rev. “Broadband purcell factor enhancements in photonic- B 77, 073312 (2008). crystalridgewaveguides,”Phys.Rev.B80,125307(2009). 40 M. Abbarchi, C. Mastrandrea, T. Kuroda, T. Mano, 24 S.J.Dewhurst,D.Granados,D.J.P.Ellis,A.J.Bennett, A. Vinattieri, K. Sakoda, and M. Gurioli. “Poissonian R.B.Patel,I.Farrer,D.Anderson,G.A.C.Jones,D.A. statisticsofexcitoniccomplexesinquantumdots,”J.Appl. Ritchie, and A. J. Shields. “Slow-light-enhanced single Phys. 106, 053504 (2009). 7 41 A. Laucht, M. Kaniber, A. Mohtashami, N. Hauke, enser, E. Querasser, T. Matyus, H. Huebel, and M. Bichler, and J. J. Finley. “Temporal Monitoring of A. Zeilinger. “A fully automated entanglement-based NonresonantFeedingofSemiconductorNanocavityModes quantumcryptographysystemfortelecomfibernetworks,” byQuantumDotMultiexcitonTransitions,”Phys.Rev.B New Journal of Physics 11, 045013 (2009). 81, 241302(R) (2010). 44 A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, 42 Forcomparison,thetypicallifetimeoftheInGaAsQDsin G.A.C.Jones,D.A.Ritchie, andA.J.Shields. “On-chip the unprocessed GaAs is 0.5 - 0.8 ns. single photon emission from an integrated semiconductor 43 A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Loru- quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).