Experiments on single nitrogen vacancy (N V) centres in

Transcription

1 Anisotropi intertions of single spin nd drk-spin spetrosopy in dimond R. J. EPSTEIN, F. M. MENDOZA, Y. K. KATO AND D. D. AWSCHALOM* Center for Spintronis nd Quntum Computtion, University of Cliforni, Snt Brr, Cliforni 936, USA *e-mil: Pulished online: 6 Otoer 25; doi:.38/nphys4 Experiments on single nitrogen vny (N V) entres in dimond, whih inlude eletron spin resonne, Ri osilltions 2, single-shot spin redout 3 nd two-quit opertions with nery 3 C nuler spin 4, show the potentil of this spin system for solid-stte quntum informtion proessing. Moreover, N V entre ensemles n hve spin-oherene times exeeding 5 μs t room temperture 5. We hve developed n ngle-resolved mgneto-photoluminesene mirosope pprtus to investigte the nisotropi eletron-spin intertions of single N V entres t room temperture. We oserve negtive peks in the photoluminesene s funtion of oth mgneti-field mgnitude nd ngle tht re explined y oherent spin preession nd nisotropi relxtion t spin-level nti-rossings. In ddition, preise field lignment unmsks the resonnt oupling to neighouring drk nitrogen spins, otherwise undeteted y photoluminesene. These results demonstrte the pility of our spetrosopi tehnique for mesuring smll numers of drk spins y mens of single right spin under mient onditions. The N V defet pir, with trigonl symmetry 6, hs n nisotropi eletron-spin hmiltonin owing to spin spin nd spin orit intertions 7. Consequently, the degrees of spin-level mixing nd oupling to nery impurity spins re very sensitive to the orienttion of n pplied mgneti field, whih hs not een ontrolled in experiments on single N V entres. Figure depits the tomi struture nd relevnt energy levels of the (negtively hrged) N V entre. The triplet ( 3 A) ground stte 8 hs zero-field splitting etween the m S = nd m S =± spin sulevels, where m S is the quntum numer of the spin sulevel, quntized long the N V symmetry xis, rystl xis. Zero-field spin splittings hve lso een mesured in the triplet ( 3 E) exited stte ut there is no onsensus on the rrngement of sulevels 2 5. Linerly polrized optil exittion of the 3 A 3 E trnsition preferentilly pumps the spin system into the ground-stte sulevel 6. In ddition, the verge photonemission rte is sustntilly smller for trnsitions involving the ± levels thn for the level 3, whih enles the spin stte to e determined y the photoluminesene intensity I PL.Both ofthelttertwoeffets hve een ttriuted to spin-dependent intersystem rossing to the singlet ( A) level,7. The single-rystl smples investigted here re ommerilly ville (Sumitomo Eletri Industries) high-temperture highpressure dimond with two polished prllel () surfes nd nominl dimensions of.4 mm.4 mm. mm. They ontin nitrogen impurities with densities of 9 2 m 3,mesured y ultrviolet sorption 8. N V entres re nturlly present with sustntilly lower densities rnging from to 3 m 3.For ensemle mesurements, smples re irrdited with.7-mev eletronswithdoseof5 7 m 3 nd susequently nneled t 9 Cfor2htoinrese the N V entre onentrtion 6. The phonon-rodened 3 E 3 A trnsition of the N V entre is deteted y mens of non-resonnt photoluminesene mirosopy (see Methods). For exmple, Fig. is sptil imge of the spetrlly integrted photoluminesene from dimond smple with the lser foused roughly μm elowthe surfe. Multiple resolution-limited fetures re oserved in the 2 μm 2 μm field. In order to determine tht given feture is due to single emitter, histogrm is plotted of the time τ etween onseutive photon detetion events using Hnury Brown nd Twiss detetion geometry 9, yielding the experimentl intensity orreltion funtion g (2) (τ). Figure shows the dt from olour entre lelled NV. The vlue of g (2) () is elow.5, proving tht NV is single-olour entre 2. In ddition, the rise of g (2) (τ) ove unity with inresing τ is inditive of intersystem rossing to the A metstle stte 2,2. These single-photon emitters re further hrterized y optilly deteted eletron spin resonne (ESR; see Methods). Figure d ontins dt from NV with zero pplied mgneti field. In this se, the ± ground-stte levels re degenerte so tht only one resonne (m S = ±) is oserved t 2.87 GHz, the hrteristi zero-field splitting of N V entres. The dt refitwithlorentzinofmhzfull-widththlf-mximum (solid line), whih is omprle to reported vlues in similr dimond smples. Strin-dependent optil mesurements on ensemles of N V entres hve indited tht eletri dipole trnsitions re llowed for dipoles in the plne perpendiulr to the symmetry xis 6. Figure 2 depits n N V entre with trnsition dipoles X [ 2] nd Y [ ] in () plne. The exittion is long [] for ll mesurements, therefore I PL depends on the lser polriztion ngle 94 nture physis VOL NOVEMBER Nture Pulishing Group

2 3 E V A N.94 ev ± 3 A μm d 2 g (2) (τ) τ 5 5 τ (ns) νmw Figure Chrteriztion of single N V entres., The tomi struture nd relevnt energy levels. The green ond depits the N V symmetry xis., The sptil imge of I PL on liner olour sle, showing the emission from severl N V entres; NV NV4 (left to right) re mrked., The intensity orreltion funtion g (2) (τ) versusτ for NV, inditing single photon emission. d, Optilly deteted ESR for NV. I PL versus mirowve frequeny ν MW (irles) with lorentzin fit (solid line). The lser power is mwfor nd 37 μwfor nd d. + [] [] [] Y X α 2 ν (GHz) NV NV2 NV3 9 5 NV NV2 NV φ ( ) 5, Figure 2 Polriztion nd mgneti-field nisotropies., Mesurement geometry inditing trnsition dipoles X nd Y., Normlized I PL (rdil xis) versus the lser polriztion ngle φ for NV, NV2 nd NV3. Polriztion long [ ] orresponds to φ = nd dt t φ nd φ +8 re identil., Upper pnel: lulted ground-stte spin splitting ν s funtion of B for θ = 6 (solid lines) nd 54.7 (dshed lines). Middle pnel: overlp α 2 of eh spin level with z tthesmetwo ngles. Lower pnel: I PL versus B for NV, NV2 nd NV3, with ngle etween B nd []. The lser power is 37 μwfor nd mw for. nture physis VOL NOVEMBER Nture Pulishing Group

3 2 NV I PL (ounts ms ) ,,25 I PL (ounts ms ) 8 5 NV I PL (ounts ms ) 2 6 NV ,,,,3,6 d A (r. units) NV4 LAC NV 5-G θ ( ) Figure 3 Controlled level mixing y mens of mgneti-field lignment., I PL versus B for NV t speified mgneti-field ngles θ.,zoomofdtin (points) with fits (lines) to model desried in the text. Dt for θ = re tken with smller field steps nd fit with n ngle of.2 to ount for residul spin mixing (see the text)., I PL versus B for NV4 (points) nd fits (lines) t speified field ngles. d, Normlized mplitudes A (points) of LAC nd 5-G peks versus θ with fits (lines). Lser power is mw for NV nd 2.9 mw for NV4. φ owing to unequl exittion of the two dipoles. The dependene of I PL on φ is mesured for 2 N V entres nd shows either vertil or horizontl loes, s exemplified for three N V entres in Fig. 2. The mesured nisotropies, defined s the rtio I PL (φ = )/I PL (φ = 9 ),reroughly2:nd:2onverge;simplenisotropy lultion gives 3:, 3:, :3 nd :3 for the N V symmetry xis long [], [ ], [ ] nd [ ], respetively (see Methods). The mesured dt re modified y the presene of polrized kground photoluminesene (sutrted from the dt) nd smll dip, most visile for NV2 t φ =,whihvriesindepth from entre to entre. Nevertheless, omprison of the mesured nd lulted nisotropies enles the numer of possile orienttions of given entre to e redued from four to two. The doule degenery of the polriztion nisotropy is lifted y pplition of mgneti field B. The upper pnel of Fig. 2 shows the ground-stte spin levels s funtion of B (the mplitude of B) lulted using the hmiltonin 7 H = gμ B B S+D(S 2 z S(S+)/3),whereμ B is the Bohr mgneton, g = 2. is the eletron g-ftor, S is the totl eletron spin with mgnitude S = ndd = 2.88 GHz is the ground-stte spin splitting. A level nti-rossing (LAC) ner, G is predited fornn VentrewithsymmetryxistsmllngletoB (6 ; solid lines), ut not for lrge ngle (54.7 ; dshed lines). The middle pnel shows α 2,theoverlpof z with eh spin level, m S =α z + β z + γ + z,where β 2 nd γ 2 re the other respetive overlps nd the susript z denotes the [] sis; the evolution of α 2 with B, lulted for oth ngles, illustrtes the mixing of spin sttes nd will e relevnt in modelling the dt. The lowerpnelisplotofi PL s funtion of B, withnngleof etween B nd [], for the sme three N V entres s in Fig. 2. Wheres NV nd NV2 hve similr polriztion dependenes, theirfielddependenesshowthtthesymmetryxisofnv(nv2) is (non-)prllel to B. For NV,the negtive pek t, G oinideswiththelultedlac.inddition,nvshowspek t 5 G, the origin of whih is less ler. In order to investigte these peks further, I PL is mesured s funtion of B with B tseriesofnglesθ in the ( ) plne; seletion of suh dt from NV is shown in Fig. 3. As B pprohes the [] diretion (θ ), the LAC pek nrrows, s expeted from ensemle mesurements 22,23.Atsuffiiently smll ngles, however, the LAC pek mplitude dereses for NV (Fig. 3) or even vnishes for some entres, suh s NV4 (Fig. 3). This is in ontrst to the ensemle mesurements 22,23 tht showed mximum in the LAC pek mplitude t θ =. Aording to the hmiltonin ove, however, spin mixing should vnish t θ =. The presene of residul spin mixing t θ = hs een ttriuted to strin nd nuler intertions 24,whihvryfrom entre to entre. 96 nture physis VOL NOVEMBER Nture Pulishing Group

4 I PL (r. units) N V entre ensemles 5, μw 6.2 NV4 8. NV 3 μw Figure 4 Resonnt oupling of single spin to neighouring spins., I PL versus B for n ensemle of N V entres t two field ngles. Inset: higher-resolution sns round 5 G showing the nitrogen hyperfine struture., A single N V entre (NV4) oupling to severl nitrogen entres. I PL versus B t two indited field ngles with 3 μw lser power., I PL versus B t two indited lser powers for NV, showing rodening of nitrogen peks with inresed power. For (inset), nd, smll liner kground is sutrted from the dt. The LAC n e modelled for smll vlues of θ y onsidering nd s pseudo-spin-/2 sttes. With preferentil popultion of z, the + level is ignored euse it hs negligile overlp with z (see Fig. 2, middle pnel). We then hve n effetive hmiltonin H = gμ B (B B ) s, where B ounts for the zero-field spin splitting nd s is the pseudo-spin opertor. The Bloh equtions for B in the ( ) plne re tkentoe ds x dt = Ω zs y s x, T 2 ds y dt = Ω zs x Ω x s z s y T 2, ds z dt = Ω xs y s z T +Γ, where h = gμ B (B B ), h is the redued Plnk onstnt, = (Ω x, Ω y, Ω z ) is the Lrmor preession vetor, x [ 2], y [ ], B z [],Γ is the rte of optil spin orienttion long z, ndt nd T 2 re effetive spin relxtion times tht depend on Γ (see Methods). In this model, the spin relxtion is nisotropi in tht T nd T 2 re fixed reltive to the rystl xes rther thn the mgneti field. The stedy-stte solution for s z is s z = T Γ (+Ω 2 z T2) 2 +Ωx 2T. T 2 +Ωz 2T2 2 We then tke I PL = n + n = (/2 + s z ) + (/2 s z ),where nd (n nd n ) re the photoluminesene rtes (ouption () proilities) for the z nd z levels, respetively. This simple model desries the experimentl dt for wide rnge of ngles nd mgneti fields, where the sme fit prmeters re used for ll ngles (Fig. 3, lines). The fits yield T = 64 ns nd T 2 = ns for NV4 using lser power of 2.9 mw (Fig. 3) nd T = 3 ns nd T 2 = 23 ns for power of 9 μw (not shown). The results indite tht the lser introdues sustntil nisotropi spin relxtion y mens of exittion out of the ground-stte mnifold. This soure of deoherene n e mitigted through pulsed exittion 4. The 5-G pek evolves similrly to the LAC pek ut over roder ngulr rnge. It hs nerly the sme mplitude nd width t given field ngle for ll N V entres investigted with suitle orienttion. In ddition, the pek hs een oserved in ll four smples mesured. The evolution of the 5-G pek with θ nd B n e resonly ounted for in the model y postulting n LACintheexitedstte,sisexpetedtoourtsomefieldowing to the presene of zero-field spin splittings 2 4. Figure 3d shows the normlized mplitudes A of the 5-G nd LAC (,-G) peks s funtion of θ. Fits of the model to this dt (red lines) nd to the field sns (fits not shown) yield T = 36 ns nd T 2 =.8 ns for n exited-stte LAC t 5 G. SimilrdtretkenonensemlesofN VentresinFig.4, where the 5-G pek is found to redue in mplitude y 5% t θ =. In ddition, higher-resolution field sns round 5 G (Fig. 4, inset) show quintuplet of peks hrteristi of the hyperfine struture of sustitutionl nitrogen (N S ) entres 25. These peks pper when the mgneti field tunes the eletron spin splitting of N V entres into resonne with the mny surrounding nture physis VOL NOVEMBER Nture Pulishing Group

5 N S entres, resulting in enhned ross-relxtion y mens of the mgneti dipole intertion Notly, the N S pek mplitudes diminish s θ inreses, suggesting tht the 5-G pek is ssoited with derese in spin polriztion, like the LAC pek. The ove results point to regime ( θ < ) where the depolrizing effets of the 5-G pek re mitigted, showing the oupling of single N V entre to its neighouring N S spins. Figure 4 shows two field sns of I PL for NV4 t θ = nd ; the N S resonnes eome visile with suffiiently smll ngle etween B nd []. Figure4showssimilrdtforNVt θ = with powers of 3 nd 9 μw; the N S peks roden nd diminish in reltive mgnitude t higher power, possily resulting from ioniztion of the N S entres 29. The depths of the N S peks, differing for NV4 nd NV, re sensitive to the prtiulr sptil distriution of nery nitrogen spins. Finlly, it is worth noting tht the N S entres re drk in tht they re not diretly deteted y photoluminesene. By mesuring single N V entre, the numer of N S spins tht n e proed is deresed y orders of mgnitude reltive to the ensemle mesurements. Furthermore, this drk-spin spetrosopy tehnique is in priniple pplile to vriety of prmgneti defets in dimond. With higher purity smples nd single-ion implnttion 3, these results ould mke possile the long-rnge oupling of two individully ddressle N V entres onneted y hin of drk spins, enling experimentl tests of spin-lttie theories nd quntum informtion proessing shemes. METHODS EXPERIMENTAL TECHNIQUES The mesurement pprtus is sed on onfol mirosope with Hnury Brown nd Twiss detetion sheme 9. A diode-pumped solid-stte lser emitting t 532 nm is linerly polrized nd foused onto the smple with mirosope ojetive of numeril perture.73 nd working distne 4.7 mm. The liner polriztion is set to ny desired ngle y hnging the retrdne of vrile wve plte (fst xis t 45 to the initilly vertil polriztion) followed y qurter-wve plte (fst xis vertil). The lser spot is positioned on the smple in oth lterl dimensions with fst steering mirror. The photoluminesene from the smple is olleted y the sme mirosope ojetive, pssed through dihroi mirror nd 64-nm long-pss filter, nd sent through 5/5 em-splitter to two fire-oupled silion vlnhe photodiode modules. For ntiunhing mesurements, the outputs of the detetors re onneted to time-orrelted single-photon ounting module. The dt re normlized y the detetor ount rtes, time in width nd totl integrtion time to yield g (2) (τ). The dt re not orreted for kground photoluminesene. For mesurements of N V entre ensemles, photoluminesene is deteted with photodiode nd lok-in mplifier. In generl, the photoluminesene is used s feedk signl to ompenste for therml drift, enling single N V entre to e trked for severl dys. The smples re t room temperture for ll mesurements disussed in this letter. The stti mgneti field B is pplied to the smple with permnent mgnet mounted on multixis stge tht llows the distne etween the mgnetndthesmpletoedjustedysteppermotor,thereysettingb t the smple. In ddition, the polr nd zimuthl ngles of B re mnully djustle with mirometers while keeping B onstnt t the smple to etter thn %. For ESR mesurements, 25-μm-dimeter gold wire is onneted to mirowve signl genertor (with 6 db m power output) nd pled in lose proximity ( 5μm) to the lser spot. POLARIZATION ANISOTROPY CALCULATION Aording to Fermi s golden rule in the eletri dipole pproximtion, the sorption rte is proportionl to D E 2,whereD is the dipole mtrix element nd E is the exittion eletri-field vetor. The sorption nisotropy is estimted to e Y V 2 / X H 2,whereX nd Y re the dipoles (see Fig. 2) nd V [ ] nd H [] re polriztion vetors. A more urte lultion would ount for the dipole rdition pttern, the lrge numeril perture of the mirosope ojetive nd refrtion t the dimond ir oundry. However, the simple eqution ove is suffiient to explin oth the nisotropy orienttions nd degeneries tht re mesured. BLOCH EQUATION SIMPLIFICATIONS Eqution () hs een simplified y defining effetive relxtion times T nd T 2 tht depend on Γ. Expliitly, (T ) = (T z ) +2Γ,whereT z is the intrinsi relxtion time of s z. Likewise, T 2 hs similr form. As Γ is proportionl to the lser power, the eqution ove explins why T nd T 2 derese with inresing power, s oserved in the experiments. Reeived 29 July 25; epted 6 Septemer 25; pulished 6 Otoer 25. Referenes. Gruer, A. et l. Snning onfol optil mirosopy nd mgneti resonne on single defet enters. Siene 276, (997). 2. Jelezko, F., Geel, T., Pop, I., Gruer, A. & Wrhtrup, J. Oservtion of oherent osilltions in single eletron spin. Phys.Rev.Lett.92, 764 (24). 3. Jelezko, F. et l.singlespinsttesindefetenterresolvedyoptilspetrosopy.appl. Phys. Lett. 8, (22). 4. Jelezko, F. et l. 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Cross-relxtion dynmis of optilly exited N-V enters in dimond. Phys.Rev.B4, (989). 28. vn Oort, E., Stroomer, P. & Glseek, M. Low-field optilly deteted mgneti resonne of oupled triplet-doulet defetpirin dimond. Phys. Rev. B 42, (99). 29. Frrer, R. G. On the sustitutionl nitrogen donor in dimond. Solid Stte Commun. 7, (969). 3. Meijer, J. et l. Genertion of single olour enters y foussed nitrogen implnttion. Preprint t (25). Aknowledgements WethnkO.GywtforvluledisussionsndG.C.Frlowforhigh-energyeletronirrditionof severlsmples.thisworkwssupportedyafosr,darpa/marcondaro. Correspondene nd requests for mterils should e ddressed to D.D.A. Competing finnil interests Theuthorsdelrethttheyhvenoompetingfinnilinterests. Reprints nd permission informtion is ville online t 98 nture physis VOL NOVEMBER Nture Pulishing Group