Semiconductor quantum light sources

Transcription

1 Semiondutor quntum light soures Lsers nd LEDs hve sttistil distriution in the numer of photons emitted within given time intervl. Applitions exploiting the quntum properties of light require soures for whih either individul photons, or pirs, re generted in regulted strem. Here we review reent reserh on single-photon soures sed on the emission of single semiondutor quntum dot. In just few yers remrkle progress hs een mde in generting indistinguishle single photons nd entngled-photon pirs using suh strutures. This suggests tht it my e possile to relize ompt, roust, LED-like semiondutor devies for quntum light genertion. ANDRE J. SHIELDS Toshi Reserh Europe Limited, 260 Cmridge Siene Prk, Cmridge CB4 0E, UK e-mil: ndrew.shields@rl.toshi.o.uk Applying quntum light sttes to photoni pplitions llows funtionlities tht re not possile using ordinry lssil light. For exmple, rrying informtion with single photons provides mens to test the serey of optil ommunitions, whih ould soon e pplied to the prolem of shring digitl ryptogrphi keys 1,2. Although seure quntum-key-distriution systems sed on wek lser pulses hve lredy een relized for simple pointto-point links, true single-photon soures would improve their performne 3. Furthermore, quntum light soures re importnt for future quntum-ommunition protools, suh s quntum teleporttion 4. Here quntum networks shring entnglement ould e used to distriute keys over longer distnes or through more omplex topologies 5. A nturl progression would e to use photons for quntuminformtion proessing, s well s ommunition. In this regrd it is reltively strightforwrd to enode nd mnipulte quntum informtion on photon. On the other hnd, single photons do not intert strongly with eh nother, whih is prerequisite for simple photon logi gte. In liner-optis quntum omputing 6,7 (LOQC) this prolem is solved using projetive mesurements to indue n effetive intertion etween the photons. Here, triggered soures of single photons nd entngled pirs re required oth s the quit rriers, nd s uxiliry soures to test the suessful opertion of the gtes. Although the omponent requirements for LOQC re hllenging, they hve reently een relxed signifintly y new theoretil shemes 7. Quntum light sttes will lso proly eome inresingly importnt for vrious types of preision optil mesurement 8. For these pplitions, light soures, whih generte pure single-photon sttes on demnd in response to n externl trigger signl, re preferred. Key performne mesures for suh soure re the effiieny, defined s the frtion of photons olleted in the experiment or pplition per trigger, nd the seond-order orreltion funtion t zero dely (see text ox). The seond-order orreltion funtion t zero dely is essentilly mesure of the two-photon rte ompred with lssil soure, with rndom emission times, of the sme verge intensity. In order to onstrut pplitions involving more thn one photon, it is lso importnt tht photons emitted from the soure (t different times), s well s those from different soures, re otherwise indistinguishle. In the sene of onvenient triggered single-photon soure, most experiments in quntum optis rely on nonliner optil proesses for generting quntum light sttes. Optilly pumping rystl with χ (2) nonlinerity hs finite proility of generting pir of lowerenergy photons through prmetri down onversion. This my e used to prepre photon pirs with time-in entnglement 9, entngled polriztions 10,11, or lterntively single-photon sttes herlded y the other photon in the pir 12. A χ (3) nonlinerity in semiondutor hs lso een used to generte entngled pirs 13. As these nonliner proesses our rndomly, there is lwys finite proility of generting two pirs tht inreses with pump power. As doule pirs degrde the fidelity of quntum optil gtes, the pump lser power must e restrited to redue the rte of doule pirs to n eptle level, whih hs detrimentl effet on the effiieny of the soure 14. This mens tht lthough down-onversion soures ontinue to e highly suessful in demonstrting few-photon quntum optil gtes, sling to lrge numers my e prolemti. Solutions hve een proposed sed on swithing multiple soures 15, or storing photons in swithed fire loop 16. Preferly the quntum light soure should generte extly one single photon, or entngled pir, per exittion trigger pulse. This my e hieved using the emission of single quntum system. After relxtion, quntum system is, y definition, no longer exited nd therefore unle to re-emit. Photon ntiunhing the tendeny of quntum soure to emit photons seprted in time ws first demonstrted in the resonne fluoresene of low-density vpour of sodium toms 17, nd susequently for single ion 18. Quntum dots re often referred to s rtifiil toms, s their eletron motion is quntized in ll three sptil diretions, resulting in disrete energy-level spetrum, like tht of n tom. They provide quntum system, whih n e grown within roust, monolithi semiondutor devies nd n e engineered to hve wide rnge of desired properties. In the following, reent progress towrds the reliztion of semiondutor tehnology for quntum photonis is reviewed. An exellent ount of the erly work n e found in ref. 19. Spe restritions limit disussion of work on other quntized systems. For this we refer the reder to the omprehensive review in ref. 20. nture photonis VOL 1 APRIL

2 500 nm 500 nm 10 nm Figure 1 Self-ssemled quntum dots., Imge of lyer of InAs/GAs self-ssemled quntum dots reorded with n tomi-fore mirosope. Eh lo orresponds to dot with typil lterl dimeters of nm nd height of 4 8 nm., Atomi-fore-mirosope imge of lyer of InAs quntum dots whose lotions hve een seeded y mtrix of nnometre-sized pits ptterned onto the wfer surfe. Under optiml onditions, up to 60% of the eth pits ontin single dot. Reprodued with permission from ref. 23. Copyright (2006) JSAP., Cross-setionl snning-tunnelling-mirosope imge of n InAs dot inside GAs devie. Imge ourtesy of P. Koenrd, Eindhoven. s X Detetion polriztion: s X X 2 H s V X + Photoluminesene intensity Vertil Horizontl X 1, , , ,380.5 X 2 H V Ground stte 1,375 1,380 1,385 Photon energy (mev) Figure 2 Optil spetrum of quntum dot., Shemti of the iexiton sde of quntum dot., Typil photoluminesene spetrum of single quntum dot showing shrp line emission due to the iexiton, X 2, nd exiton, X, photon emitted y the sde. The inset shows the polriztion splitting of the trnsitions originting from the spin splitting of the exiton levels. OPTICAL PROPERTIES OF SINGLE QUANTUM DOTS Nnosle quntum dots with good optil properties n e frited using nturl-growth mode of strined-lyer semiondutors 21. hen InAs is deposited on GAs, it initilly grows s strined two-dimensionl sheet, ut eyond some ritil thikness, tiny islnds like those shown in Fig. 1 form in order to minimize the surfe strin. Overgrowth of the islnds leds to the oherent inorportion of In x G 1 x As dots into the rystl struture of the devie, s n e seen in the rosssetionl imge of Fig. 1. The most intensively studied re smll InAs dots on GAs emitting t wvelengths round nm t low tempertures, whih n e onveniently mesured with lownoise silion single-photon detetors. A less desirle feture of the self-orgnizing tehnique is tht the dots form t rndom positions on the growth surfe. However, onsiderle progress hs een mde reently to ontrol the dot position within the devie struture (Fig. 1) y ptterning nnometre-sized pits on the growth surfe 22,23. As InGAs hs lower-energy ndgp thn GAs, the quntum dot forms potentil trp for eletrons nd holes. If suffiiently smll, the dot ontins just few quntized levels in the ondution nd vlene nds, eh of whih holds two eletrons or holes of opposite spin. Illumintion y pioseond lser pulse exites eletrons nd holes, whih rpidly relx to the lowest-lying energy sttes either side of the ndgp. A quntum dot n thus pture two eletrons nd two holes to form the iexiton stte, whih deys y rditive sde, s shown shemtilly in Fig. 2. One of the trpped eletrons 216 nture photonis VOL 1 APRIL

3 Box 1 Photon-orreltion mesurements Devie emission Bemsplitter Detetor 1 g (2) (τ) Detetor Dely, τ (ns) Figure B1 Mesuring the orreltion., Shemti of the set-up used for photon-orreltion mesurements., Seond-order orreltion funtion of the exiton emission of single dot in pillr mirovity. Reprodued with pemission from ref. 41. Copyright (2005) OSA. The photon sttistis of light n e studied y mens of the seond-order orreltion funtion, g (2) (τ), whih desries the orreltion etween the intensity of the light field, I, with tht fter dely τ nd is given y 100 : g (2) (τ )= <I(t)I(t+τ)> <I(t)> 2. This funtion n e mesured diretly using the Hnury-Brown nd Twiss 101 interferometer, omprising 50:50 emsplitter nd two single-photon detetors, shown in the figure. For delys muh less thn the verge time etween detetion events (tht is, for low intensities), the distriution in the delys etween liks in eh of the two detetors is proportionl to g (2) (τ). For ontinuous light soure with rndom emission times, suh s n idel lser or LED, g (2) (τ) = 1. It shows there is no orreltion in the emission time of ny two photons from the soure. A soure for whih g (2) (τ = 0)>1 is desried s unhed s there is n enhned proility of two photons eing emitted within short time intervl. Photons emitted y quntum light soures re typilly ntiunhed, (g (2) (τ = 0)<1) nd tend to e seprted in time. Of prtiulr interest in ommunition nd omputing systems re pulsed light soures, for whih the emission ours t times defined y n externl lok. In this se g (2) (τ) onsists of series of peks seprted y lok period. For n idel single-photon soure, the pek t zero time dely is sent, g (2) (τ = 0) = 0; s the soure nnot produe more thn one photon per exittion period, lerly the two detetors nnot fire simultneously. The figure shows g (2) (τ) reorded for resonnt pulsed optil exittion of the X emission of single quntum dot in pillr mirovity. Notie the lmost omplete sene of the pek t zero dely: the definitive signture of single-photon soure. The noise seen t τ = 0 demonstrtes tht the rte of two-photon emission is more thn 50 times less thn tht of n idel lser with the sme verge intensity. The unhing ehviour oserved for the finite dely peks is explined y intermittent trpping of hrge rrier in the dot 102. This tre ws tken for qusi-resonnt lser exittion of the dot, whih voids reting rriers in the surrounding semiondutor. For higher-energy lser exittion, the suppression in g (2) (0) is typilly redued inditing osionl two-photon pulses due to emission from the lyers surrounding the dot, ut this n e minimized with reful smple design. reomines with one of the holes nd genertes first photon (lled the iexiton photon, X 2 ). This leves single eletron hole pir in the dot (the exiton stte), whih susequently lso reomines to generte seond (exiton, X) photon. The iexiton nd exiton photons hve distint energies, s n e seen in the low temperture photoluminesene spetrum of Fig. 2, owing to the different Coulom energies of their initil nd finl sttes. Often numer of other weker lines n lso e seen owing to reomintion of hrged exitons, whih form intermittently when the dot ptures n extr eletron or hole 24. Lrger quntum dots, with severl onfined eletron nd hole levels, hve riher optil signture owing to the lrge numer of exiton omplexes tht n e onfined. High-resolution spetrosopy revels tht the X 2 nd X trnsitions of dot re in ft oth doulets with linerly polrized omponents prllel to the [110] nd [1 10] xes of the semiondutor rystl, lelled here H nd V, respetively 25,26. The origin of this polriztion splitting is n symmetry in the eletron hole exhnge intertion of the dot, whih produes splitting of the exiton spin sttes. The symmetry derives from n elongtion of the dot long one rystl xis nd inuilt strin in the rystl. It mixes the exiton eigensttes of symmetri dot, with totl zimuthl spin J z = +1 nd 1, into symmetri nd ntisymmetri omintions, whih ouple to two H- or two V-polrized photons, respetively, s shown in Fig. 2. The exiton stte of the dot hs typil lifetime of out one nnoseond, whih is due purely to rditive dey. As this is muh longer thn the durtion of the exiting lser pulse, or the lifetime of the photo-exited rrier popultion in the surrounding semiondutor, only one X photon n e emitted nture photonis VOL 1 APRIL

4 2 μm 1.5 μm 1 μm d e f 0 7 nm 500nm Figure 3 Snning-eletron-mirosope imges of semiondutor vities.,, Pillr mirovities., mirodisks. d f, Photoni-ndgp defet vities. The strutures were frited t:, University of ürzurg;,,e, CNRS-LPN (UPR-20); d, Univ. Cmridge; f, UCSB/ETHZ. (Imge soures nd permissions:, Ref. 56., Ref. 51, opyright (2005) APS. d, Ref. 47, opyright (2006) AIP. e,f, Ref. 48) per lser pulse. This n e proved, s first reported 27 y Peter Mihler, At Immoglu nd their ollegues in Snt Brr, y mesuring the seond-order orreltion funtion, g (2) (τ) of the exiton photoluminesene 28,29 (text ox). In ft eh of the exiton omplexes of the dot genertes t most one photon per exittion yle, whih lso llows single-photon emission from the iexiton or hrged exiton trnsitions 30. Cross-orreltion mesurements etween the X nd X 2 photons onfirm the time orreltion expeted for the sde in Fig. 2, tht is, the X photon follows the X 2 one. Indeed the shpe of the ross-orreltion funtion for oth ontinuous-wve nd pulsed exittion n e urtely desried with simple rte-eqution model nd the experimentlly mesured X nd X 2 dey rtes 34. SEMICONDUCTOR MICROCAVITIES A mjor dvntge of using self-ssemled quntum dots for single-photon genertion is tht they n e esily inorported into vities using stndrd semiondutor growth nd proessing tehniques. Cvity effets re useful for direting the emission from the dot into n experiment or pplition, s well s for modifying the photon-emission dynmis 35,36. Purell 37 predited enhned spontneous emission from soure in vity when the soure energy oinides with tht of the vity mode, owing to the greter density of optil sttes into whih it n emit. For n idel vity, in whih the emitter is loted t the mximum of the eletri field with its dipole ligned with the lol eletri field, the enhnement in dey rte is given y the Purell ftor, F p = (3/4π 2 ) (λ/n) 3 Q/ V, where λ is the wvelength of the emission, n is the refrtive index, Q is the qulity ftor ( mesure of the time photon is trpped in the vity) nd V is the effetive mode volume. Thus high photon-olletion effiieny, nd simultneously fst rditive dey, requires smll vities with highly refleting mirrors nd high degree of struturl perfetion. Furthermore, without ontrolling the lotion of the dot in the vity, s disussed elow, it my e diffiult to hieve the full enhnement predited y the Purell formul. Figure 3 shows imges of some of the single-quntum-dot vity strutures tht hve proved most suessful. Pillr mirovities, formed y ething ylindril pillrs into semiondutor Brgg mirrors pled either side of the dot lyer, hve shown lrge Purell enhnements nd hve highly diretionl emission profile, thus mking good single-photon soures Purell ftors of round six hve een mesured diretly 40,41, through the rte of vityenhned rditive dey ompred with tht of dot without vity, implying oupling to the vity mode of β = (F p 1)/F p > 83%, if we ssume the leky modes re unffeted y the vity. However, the experimentlly determined photon-olletion effiieny, whih is more pertinent prmeter for pplitions, is typilly round 10%, due to the ft tht not ll the vity mode n e oupled into n experiment nd tht there is sttering of the mode y the rough pillr edges. e n expet tht the photon-olletion effiieny will inrese with improvements to the proessing tehnology or new designs of mirovity. Another mens of forming vity is to eth series of holes in suspended sl of semiondutor, so s to form lterl vrition in the refrtive index, whih retes foridden energy gp for photoni modes in whih light nnot propgte 42. Photons n then e trpped in entrl irregulrity in this struture: usully n unethed portion of the sl. Suh photoni-ndgp defet vities hve een frited in silion with Q vlues pprohing 10 6 (refs 43 nd 44). High-qulity tive vities hve lso een demonstrted in GAs ontining InAs quntum dots A rditive lifetime of 86 ps, orresponding to Purell ftor of F p 12, hs een reported 47, nd very reently lifetime of 60 ps ws mesured for vity in the strong-oupling regime 48. If the Q-vlue is suffiiently lrge, the system enters the strongoupling regime, where the exittion osilltes oherently etween n exiton in the dot nd photon in the vity. The spetrl signture of strong oupling, n ntirossing etween the dot line nd the vity mode, hs een oserved for quntum dots in pillr mirovities 49, photoni-ndgp defet vities 50, mirodisks 51 nd mirospheres 52. It hs een demonstrted for tom vities tht strong oupling llows the deterministi genertion of single photons 53,54. Single-photon 218 nture photonis VOL 1 APRIL

5 Photon ounters t 1 t 2 Non-polrizing emsplitter 2 ns 2 ns + t Single-mode fire Retrorefletors or Opposite output proility Dely offset (ns) Figure 4 Two-photon interferene., If the two photons re indistinguishle, the two outomes resulting in one photon in either rm interfere destrutively. This results in the two photons lwys exiting the emsplitter together., Shemti of n experiment using two photons emitted suessively from quntum dot., Experimentl dt showing suppression of the o-inidene rte in when the dely etween input photons is zero owing to two-photon interferene 60. Copyright (2002) Nture, ourtesy of Y. Ymmoto, Stnford University. soures in the strong-oupling regime n e expeted to hve very-high extrtion effiienies nd to e time-ndwidth limited 55. Enourgingly, single-photon emission hs een reported reently for dot in strongly oupled pillr mirovity 56. Another interesting reent development is the ility to lote single quntum dot within the vity, s this ensures the lrgest possile oupling nd removes kground emission, s well s other undesirle effets due to other dots in the vity. Aove we disussed tehniques to ontrol the dot position on the growth surfe. The other pproh is to position the vity round the dot. One tehnique omines mirophotoluminesene spetrosopy to lote the dot position, with in situ lser photolithogrphy to pttern mrkers on the wfer surfe 57. An lterntive involves growing vertil stk of dots so tht their lotion n e reveled y snning the wfer surfe 58, s shown in Fig. 3f. Reently this tehnique hs llowed lrger oupling energies for single dot in photoni-ndgp defet vity 48. PHOTON INDISTINGUISHABILITY Cvity effets re importnt for rendering different photons from the soure indistinguishle, whih is essentil for mny pplitions in quntum informtion. hen two identil photons re inident simultneously on the opposite input ports of 50:50 emsplitter, they will lwys exit through the sme output port 59, s shown shemtilly in Fig. 4. This ours euse of destrutive interferene in the proility mplitude of the finl stte in whih one photon exits through eh output port. The mplitude of the se where oth photons re refleted extly nels with tht where oth re trnsmitted, due to the π/2 phse hnge on refletion, provided the two photons re entirely identil. Two-photon interferene of two single photons, emitted suessively from quntum dot in wekly oupled pillr mirovity, ws first reported y the Stnford group 60. Figure 4 shows shemti of their experiment. Notie the redution of the o-inidene ount rte mesured etween detetors in either output port, when the two photons re injeted simultneously (Fig. 4). The dip does not extend ompletely to zero, inditing tht the two photons sometimes exit the emsplitter in opposite ports. The mesured redution in the o-inidene rte t zero dely of 69% implies n overlp for the single-photon wvepkets of 0.81, fter orreting for the imperfet single-photon visiility of the interferometer. Two-photon interferene dips of 66% nd 75% hve een reported y Bennett et l. 61 nd Vuroutsis et l. 62 Similr results hve een otined for single dot in photoni-ndgp defet vity 63. This two-photon interferene visiility is limited y the finite oherene time of the photons emitted y the quntum dot 64, whih renders them distinguishle. The depth of the dip in Fig. 4 depends on the rtio of the rditive dey time to the oherene time of the dot, tht is R = 2τ dey /τ oh. hen this rtio is equl to unity, the oherene time is limited y rditive dey nd the soure hs perfet two-photon interferene. The most suessful pproh thus fr hs een to extend τ oh y resonnt optil exittion of the dot nd redue τ dey using the Purell effet in pillr mirovity, to give vlues of R 1.5. In the future, higher visiilities my e hieved with lrger Purell enhnement, using single-dot vity in the strong-oupling regime or with eletril gting desried in the next setion. A soure of indistinguishle single photons ws used y Fttl et l. 65,66 to generte entnglement etween post-seleted pirs. This involves simply rotting the polriztion of one of the photons inident nture photonis VOL 1 APRIL

6 A Al p-ohmi ontt Emission InAs quntum dot C X 2 Cvity lyer { p+ GAs B Eletroluminesene n-ohmi ontt n+ Brgg mirror X + X X 2 X Insultor Contt metl Sustrte/uffer 95.1 μa 12.0 μa D E g (2) (τ) Eletroluminesene g (2) (τ) X Dely (ns) Time (ns) μa Clulted velength (nm) Mesured Dely (ns) Figure 5 Eletrilly driven single-photon emission. A, Shemti of single-photon LED. B, Eletroluminesene spetr of the devie. Notie the spetr re dominted y the exiton X nd iexiton X 2 lines, whih hve liner nd qudrti dependene on drive urrent, respetively. Other wek lines re due to hrged exitons. C, Seond-order orreltion funtion reorded for the exiton () nd iexiton () emission lines. D, Time-resolved eletroluminesene from devie operting with 1.07 GHz repetition rte. E, Modelled () nd mesured () seond-order orreltion funtion of the iexiton eletroluminesene t 1.07 GHz. (Adpted with permission from ref. 71, opyright (2005) AIP, nd ref. 73, opyright (2005) APS.) on the finl emsplitter in Fig. 4 y 90 o. By post-seleting the results where the two photons rrive t the emsplitter t the sme time nd where there is one photon in eh output rm (lelled 1 nd 2), the mesured pirs should orrespond to the Bell stte: ψ = 1 ( H 1 V 2 > V 1 H 2 >). (1) 2 Note tht only if the two photons re indistinguishle, nd thus the entnglement is only in the photon polriztion, n the two terms in eqution (1) interfere. Anlysis of the density mtrix pulished y Fttl et l. 65 revels fidelity of the post-seleted pirs to the stte in eqution (1) of 0.69, eyond the lssil limit of 0.5. This soure of entngled pirs differs in n importnt wy from tht sed on the iexiton sde desried elow. Post-seletion implies tht the photons re destroyed when this sheme sueeds. This is prolem for some quntum-informtion pplitions suh s LOQC, ut ould e usefully pplied to quntum key distriution 65. SINGLE-PHOTON LEDS An erly proposl for n eletril single-photon soure y Kim et l. 67 ws sed on ething semiondutor heterostruture tht hd Coulom lokde. However, the light emission from this ethed struture ws too wek to llow the seond-order orreltion funtion to e studied. Reently, enourging progress hs een mde towrds the reliztion of single-photon soure sed on quntizing lterl eletril-injetion urrent 68,69. However, the most suessful pproh so fr hs een to integrte self-ssemled quntum dots into onventionl p-i-n doped juntions. In the first report of eletrilly driven single-photon emission y Yun et l. 70, the eletroluminesene of single dot ws isolted y forming mirometre-dimeter emission perture in the opque top ontt of the p-i-n diode. Figure 5A shows n improved emissionperture single-photon LED fter Bennett et l. 71, whih inorportes n optil vity formed etween high-refletivity Brgg mirror nd the semiondutor ir interfe in the perture. This struture forms wek vity, whih enhnes the mesured olletion effiieny tenfold ompred with devies without vity 72. Single-photon pulses re generted y exiting the diode with trin of short voltge pulses. The seond-order orreltion funtion g (2) (τ) of either the X or X 2 eletroluminesene (Fig. 5C) shows the suppression of the zero-dely pek inditive of single-photon emission 71. The finite rte of multiphoton pulses is due mostly to kground emission from lyers other thn the dot, whih is lso seen for non-resonnt optil exittion. Suh eletril ontts lso llow the temporl hrteristis of the single-photon soure to e tilored. By pplying negtive is to the diode etween the eletril injetion pulses, Bennett et l. 73 redued the jitter in the photon-emission time to less thn 100 ps. This llowed the repetition rte of the single-photon soure to e inresed to 220 nture photonis VOL 1 APRIL

7 A B C Degree of orreltion C 0.6 o 0.6 o o S = 0 μev S = 25 μev Errors (mgnitude) Rel prt Imginry prt Dely period (/12.5 ns) Figure 6 Genertion of entngled photons y quntum dot. A, Degree of orreltion mesured for dot with exiton polriztion splitting S = 0 µev in liner (), digonl () nd irulr () polriztion ses s funtion of the dely etween the X nd X 2 photons (in units of the repetition yle). The orreltion is defi ned s the rte of o-polrized pirs minus the rte of ross-polrized pirs divided y the totl rte. Notie tht the vlues t fi nite dely show no orreltion, s expeted for pirs emitted in different lser exittion yles. More interesting re the peks lose to zero time dely, orresponding to X nd X 2 photons emitted from the sme sde. The presene of strong orreltions for ll three types of mesurement for the dot with zero exiton splitting n only e explined if the X nd X 2 polriztions re entngled. B, Degree of orreltions mesured for the dot in A sujet to n in-plne mgneti fi eld so s to produe n exiton polriztion splitting of S = 25 µev. Notie tht the orreltion in digonl nd irulr ses hs vnished, inditing only lssil orreltions t fi nite splitting. C, Two-photon density mtrix of the devie emission in A long with errors lulted from the errors on the orreltion mesurements. The strong off-digonl terms pper owing to entnglement. (,, Adpted with permission from ref. 92. Copyright (2006) IOP.) 1.07 GHz (Fig. 5D) while retining good single-photon emission hrteristis (Fig. 5E). Suh eletril gting ould provide tehnique for produing time-ndwidth-limited single-photons from quntum dots. Another promising pproh is to perture the urrent flowing through the devie 74,75. This is hieved y growing thin AlAs lyer within the intrinsi region of the p-i-n juntion nd lter exposing the mes to wet oxidtion in furne, onverting the AlAs lyer round the outer edge of the mes to insulting AlO x. By reful ontrol of the oxidtion time, mirometre-dimeter onduting perture n e formed within the insulting ring of AlO x. Suh strutures hve the dvntge of exiting just single dot within the struture, therey reduing the mount of kground emission. The oxide nnulus lso onfines the optil mode lterlly within the struture, potentilly llowing high photon-extrtion effiieny. Altering the nnostruture or mterils tht omprise the quntum dot llows onsiderle ontrol over the emission wvelength nd other hrteristis. Most of the experimentl work done so fr hs onentrted on smll InAs quntum dots emitting t round nm, s these hve well understood optil properties nd n e deteted with low-noise silion singlephoton detetors. On the other hnd the shllow onfinement potentils of this system men they emit only t low tempertures. At shorter wvelengths optilly pumped single-photon emission hs een demonstrted t round 350 nm using GN/AlGN (ref. 76), 500 nm using CdSe/ZnSSe (ref. 77) nd 682 nm using InP GInP (ref. 78) quntum dots. GN/AlGN nd CdSe/ZnSSe quntum dots hve een shown to operte t 200 K. It is very importnt for quntum ommunitions to develop soures t longer wvelengths in the fire-opti trnsmission nds t 1.3 μm nd 1.55 μm. This my e hieved using InAs/GAs heterostrutures y depositing more InAs to form lrger quntum dots. These lrger dots offer deeper onfinement potentils thn those t 900 nm nd thus often emit t room temperture 79. Optilly pumped single-photon emission t teleom wvelengths hs een hieved using numer of tehniques to prepre low densities of longer-wvelength dots, inluding imodl-growth mode in moleulr-em epitxy to form low densities of lrge dots 80, ultrlowgrowth-rte moleulr-em epitxy 81 nd metl orgni hemil vpour deposition 82. Reently, the first eletrilly driven singlephoton soure t teleom wvelength hs een demonstrted 83. GENERATION OF ENTANGLED PHOTONS By olleting oth the X 2 nd X photons emitted y the iexiton sde, single quntum dot my lso e used s soure of photon pirs. Polriztion-orreltion mesurements on these pirs reveled tht the two photons were lssilly orrelted with the sme liner polriztion This ours euse the sde n proeed y mens of one of two intermedite exiton spin sttes, s desried ove nd shown in Fig. 2, one of whih ouples to two H- nd the other to two V-polrized photons. The emission is thus sttistil mixture of H X2 H X > nd V X2 V X >, nture photonis VOL 1 APRIL

8 lthough exiton spin sttering during the sde (disussed elow) ensures there re lso some ross-polrized pirs. The spin splitting 87,88 of the exiton stte of the dot distinguishes the H- nd V-polrized pirs nd prevents the emission of entngled pirs predited y Benson et l. 89 If this splitting ould e removed, the H nd V omponents would interfere in ppropritely designed experiments. The emitted two-photon stte should then e written s superposition of nd VV, whih n e rest in either the digonl (spnned y D, A) or irulr (σ +, σ - ) polriztion ses, tht is: Φ + = 1 ( H X2 H X > + V X2 V X >) 2 = 1 ( D X2 D X > + Α X2 Α X >) 2 = 1 ( σ + X2 σ - X > + σ + X2 σ - X >). (2) 2 Equl weighting of the nd VV terms ssumes the soure to e unpolrized, s indited y experimentl mesurements. Eqution (2) suggests tht, for zero exiton spin splitting, the iexiton sde genertes entngled photon pirs, similr to those seen for toms 90. Entnglement of the X or X 2 photons ws reently oserved experimentlly for the first time y Stevenson, Young nd o-workers 91,92, using two different shemes to nel the exiton spin splitting. An lterntive pproh y Akopin et l. 93 using dots with finite exiton splitting, post-selets photons emitted in nrrow spetrl nd where the two polriztion lines overlp. The exiton spin splitting depends on the exiton-emission energy, tending to zero for InAs dots emitting lose to 1.4 ev nd then inverting for higher emission energies 94,95. These orrespond to shllow quntum dots for whih the rrier wvefuntions extend into the rrier mteril reduing the eletron hole exhnge. Zero splitting n e hieved y either reful ontrol of the growth onditions to hieve dots emitting lose to the desired energy, or y nneling smples emitting t lower energies 94. The exiton spin splitting my e ontinuously tuned y pplying mgneti field in the plne of the dot 96. It hs een oserved tht the signtures of entnglement then pper only when the exiton spin splitting is lose to zero 91. Other promising shemes to tune the exiton spin splitting re now emerging, inluding pplition of strin 97 nd n eletri field 98,99. Figure 6A plots polriztion orreltions reported y Young et l. 92 for dot with zero exiton spin splitting (hieved y ontrol of the growth onditions). Pirs emitted in the sme sde (tht is, with zero dely) show very striking positive orreltion (o-polriztion) mesuring in either, retiliner or digonl ses nd ntiorreltion (ross-polriztion) when mesuring in irulr sis. This is extly the ehviour expeted for the entngled stte of eqution (2). In ontrst, dot with finite splitting shows polriztion orreltion for the retiliner sis only, with no orreltion for digonl or irulr mesurements (Fig. 6B). The strong orreltions seen for ll three ses in Fig. 6A ould not e produed y ny lssil light soure or mixture of lssil soures nd is proof tht the soure genertes entngled photons. The mesured 92 two-photon density mtrix (Fig. 6C) projets onto the expeted 1/ 2 ( H X2 H X > + V X2 V X >) stte with fidelity (tht is, proility) of ± 0.022, exeeding the lssil limit (0.5) y 9 stndrd devitions. Two proesses ontriute to the wrongly orrelted pirs, whih impir the fidelity of the entngled photon soure. The first of these is due to kground emission from lyers in the smple other thn the dot. This kground emission, whih is unpolrized nd dilutes the entngled photons from the dot, limited the fidelity oserved in the first report 91 of triggered entngled photon pirs from quntum dot nd hs een susequently redued using etter smple design 92. The seond mehnism, whih is n intrinsi feture of the dot, is exiton spin sttering during the iexiton sde. It is interesting tht this proess does not seem to depend strongly on the exiton spin splitting. It my e redued y suppressing the sttering using resonnt exittion or lterntively y using vity effets to redue the time required for the rditive sde. OUTLOOK The pst severl yers hve seen remrkle progress in quntum light genertion using semiondutor devies. However, despite onsiderle progress mny hllenges still remin. The struturl integrity of vities must ontinue to improve, therey enhning qulity ftors. This, omined with the ility to relily position single dots within the vity, will further enhne photonolletion effiienies nd the Ri energy in the strong-oupling regime. It is lso importnt to relize ll the enefits of these vity effets in more prtil eletrilly driven soures. Menwhile ndstruture engineering of the quntum dots will llow wider rnge of wvelengths to e essed for oth single nd entngled photon soures, s well s strutures tht n operte t higher tempertures. Tehniques for fine tuning the hrteristis of individul emitters will lso e importnt. One of the most interesting spets of semiondutor quntum optis is tht we my e le to use quntum dots not only s quntum light emitters, ut lso s the logi nd memory elements, whih re required in quntum informtion proessing. Although LOQC is slle theoretilly, quntum omputing with photons would e muh esier with useful single-photon nonlinerity. Suh nonlinerity my e hieved with quntum dot in vity in the strong-oupling regime. Enourgingly, strong oupling of single quntum dot with vrious types of vity hs lredy een oserved in the spetrl domin. Eventully it my even e possile to integrte photon emission, logi, memory nd detetion elements into single semiondutor hips to form photoni integrted iruit for quntum informtion proessing. doi: /nphoton Referenes 1. Gisin, N., Riordy, G., Tittel,. & Zinden, H. Quntum ryptogrphy. Rev. Mod Physis 74, (2001). 2. Dusek, M., Lutkenhus, N. & Hendryh, M. 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Aknowledgements The uthor would like to thnk Mrk Stevenson, Roert Young, Anthony Bennett nd Mrtin rd for their omments during the preprtion of the mnusript nd the UK Deprtment of Trde nd Industry Optil Systems for Digitl Age, Engineering nd Physil Sienes Reserh Counil nd Europen Commission Future nd Emerging Tehnologies rm of the 1st progrmme for supporting reserh on quntum light soures. nture photonis VOL 1 APRIL