Frequency cavity pulling induced by a single semiconductor quantum dot.

Transcription

1 Frequeny vity pulling inue by single semionutor quntum ot. Dniel Vlente 2,4, Jn Suffzyński 1,3, Tomsz Jkubzyk 3, Arien Dousse 1, Aristie Lemître 1, Isbelle Sgnes 1, Loï Lno 1, Pul Voisin 1, Alexi Auffèves 2, n Psle Senellrt 1 1 CNRS-LPN Lbortoire e Photonique et e Nnostrutures, Route e Nozy, 9146 Mroussis, Frnee 2 CEA/CNRS/UJF joint tem Nnophysis n Semionutors, Institut Néel-CNRS, BP 166, 2 rue es Mrtyrs, 3842 Grenoble Ceex 9, Frne 3 Institute of Experimentl Physis, Fulty of Physis, University of Wrsw, Hoż 69, PL--681 Wrszw, Poln n 4 Instituto e Físi, Universie Feerl e Mto Grosso, Cuibá MT, Brzil We investigte the emission properties of single semionutor quntum ot eterministilly ouple to onfine optil moe in the wek oupling regime. A strong pulling, broening n nrrowing of the vity moe emission is eviene when hnging the spetrl etuning between the emitter n the vity. These fetures re theoretilly ounte for by onsiering the phonon ssiste emission of the quntum ot trnsition. These observtions highlight new sitution for vity quntum eletroynmis involving spetrlly bro emitters. Progresses in nnotehnologies llow to effiiently ouple soli-stte optil resontors suh s ieletri vities or plsmoni ntenns to rtifiil toms like NV enters in imon [1], nnorystls [2] or semi-onutor quntum ots [3 ]. Suh optil mei benefit from strong light-mtter intertion n show single photon sensitivity [6 1], opening the pth to slble quntum informtion proessing on hip. However, espite their similrities with rel toms, rtifiil ones show very ifferent emission properties, ue to their oupling to the soli-stte environment they re embee in, whether phononi [11 13] or eletrostti [14 16]. This strong intertion les to broening of the emission line whih n eventully overome the vity line. Although this b emitter regime hs been mostly onsiere rwbk for prtil purposes, reent works hve suggeste tht it oul be resoure for quntum light genertion. Inee, oupling spetrlly broene emitter to high qulity ftor resontor inues Purell enhnement of mehnisms resonnt with the moe, leing to the intense emission of photons t the resontor frequeny, even when the etuning between the moe n the emitter is lrge. This vity-feeing effet hs been extensively stuie for semionutor quntum ots (QDs) [17 2] n hs been propose to buil wvelength stbilize single photon soures [21] or single emitter bse lsers [22]. Very reently, these ies hve been exploite to emonstrte nrrowbn tunble single photon soure t room temperture with NV enter ouple to n optil fiber bse vity [23]. From the funmentl point of view, this b emitter limit llows exploring sitution for vity quntum eletroynmis not investigte with rel toms so fr. In this frmework, semionutor self-ssemble QDs re prtiulrly interesting objets. Reent progresses in tehnology hve llowe to prepre the iel system of single QD presenting ontrolle oupling with single moe optil resontor [, 24]. In the present work, we stuy the emission of QD eterministilly ouple to pillr vity moe of low qulity ftor n eviene new effet ppering in this b emitter regime. Phonon ssiste emission les to pulling of the vity emission towr the QD line s well s broening or nrrowing epening on the QD-vity etuning. These observtions present similrities with the well-known vity pulling effet in lsers with thousns of toms [2 28]. They re here ttine with single emitter in the wek oupling regime. We stuy the emission of single InGAs QDs inserte in GAs/AlGAs miropillr vities n present experimentl results on two QD-pillrs vities, both operting in the wek oupling regime. The first pillr hs been obtine without eterministi tehnology: it embes severl QDs inluing lose to spetrl resonne with the vity moe but not lote t the mximum of the eletri fiel. The seon pillr hs been eterministilly fbrite using the in-situ lithogrphy tehnique. It embes QD2, lose to spetrl resonne with the vity moe, lote within nm from its enter, ensuring n optiml Purell effet (see referene [24] for etils on the pillrs fbrition). Eh pillr is non-resonntly exite in the ontinuous wve regime t 8 nm. The photoluminesene signl is ollete from the top of the pillr n nlyze with spetrometer with -1 µev spetrl resolution. Figure 1b shows the emission spetr s funtion of temperture n energy for the vity non eterministilly ouple to. Spetrlly nrrow emission lines with strong energy epenene on temperture rise from the QD emission. The broer line presenting

2 2 Brgg mirror Brgg mirror Emission through the vity hnnel QD2 b Energy Linewith Intensity (rb. u.) Energy e FIG. 1. : System uner investigtion: single QD is ouple to the onfine optil moe of miropillr vity. The emission from the vity hnnel is mesure. We stuy two pillrs: the first one embes non eterministilly ouple to the moe, wheres the seon one is eterministilly n optimlly ouple to QD2. Both pillrs operte in the wek oupling regime. b: Emission spetr mesure for vrious tempertures on, presenting poor oupling to the pillr moe. The two nrrow emission lines orrespons to the single QD emission lines n the bro emission to the vity moe. The re n blue lines re lorentzin fits to the experimentl t. -e: Chrteristis of the QD n vity system eue from emission spetrosopy: Energy (), Intensity () n Linewith (e) of the QD (blk) emission line n the vity (re) emission line. smller energy vrition with temperture orrespons to the emission within the vity moe. This emission observe even when the etuning between the QD n the moe is lrge is the so-lle vity feeing [17, 18], nmely the Purell enhnement of brobn bkgroun emission. When severl QDs re inserte in the vity without eterministi positioning, this emission prtilly rises from non resonnt QDs [17, 19] whih behve s internl white soures n llow to mesure the intrinsi hrteristis of the moe. The properties of the -vity system re extrte by routinely fitting the experimentl urves with sum of two lorentzin peks, one for the QD lines (blue), the other for the vity emission line (re). The line positions, intensities n linewiths re shown s funtion of temperture in figure 1. The QD n vity emission lines ontinuously shift to lower energies with temperture. The QD emission slightly inreses t resonne beuse of smll Purell effet while the vity line intensity oes not show hnges relte to the QD resonne. Lst, the vity linewith slightly vries ross the resonne, but only in the rnge of 2%. Note tht in ll experiments reporte here, the mesure QD emission linewith is limite by the experimentl setup resolution. Figure 2 reports signifintly ifferent fetures, observe on the eterministilly ouple QD2-vity evie. Figure 2 shows the emission intensity s funtion of energy n temperture for QD2 where three emission lines (hrge exiton (), neutrl exiton (X) n biexiton ()) re suessively brought into resonne with the vity moe through temperture tuning. Figure 2b n 2 present two emission spetr for two etunings (vertil white lines in figure 2) where vity emission linewith iffering by lmost ftor 2 is observe, showing strong epenene of the moe properties on the QD trnsitions-vity etuning. This epenene is onfirme in figure 2-f presenting the emission properties eue by fitting eh spetrum by sum of lorentzin peks. We only plot the fit results for etunings where the two lines re well resolve spetrlly. Unlike in Fig. 1, the moe energy isplys S-like temperture epenene (figure 2) in between two spetrl resonne between the QD trnsition line. Figure 2e presents the spetrlly integrte intensity emission of the QD n vity lines. For eh spetrl resonne, the inrese in the QD emission intensity orrespons to signifint erese of the moe intensity. Finlly, the vity emission linewith shown in figure 2f presents strong vritions with etuning, exeeing ftor 2.: the vity line is broer when the moe stns in between two QD lines. Observing these new fetures hs been me possible thnks to full ontrol in the QD-vity oupling: the vity istortion is observe on every eterministilly ouple QD-pillr evie [24] with qulity ftor roun 1-, the lower the Q, the lrger the istortion. In n ielly ouple QD-vity system, the vity emission is expete to rise mostly from phonon siebns in the smll etuning rnge [29]. In the following, the emission spetr of single QD exiton wekly ouple to vity moe n to the phonon bth ontinuum [29, 3] is lulte using Fermi s golen rule. Contrry to reent works [31, 32], no iret inoherent pumping of the moe is introue: we show tht the vity istortion inee rises from vity pulling effets when the QD phonon siebns minly prtiipte to vity feeing. The oupling of QD isrete stte to ousti phonons les to the pperne of emission siebns whih spre over few mev spetrl rnge [12, 13]. They result from the emission of photon ssiste by ousti phonon emission or bsorption. The initil stte is the exite quntum ot with given therml istribution for the ousti phonon bth. It eys towrs ontinuum of eletromgneti n phononi moes. The emission spetrum S QD (ω, T ) of QD in bulk t temperture T is nlytilly lulte by ext igonliztion of the inepenent boson moel Hmiltonin (see supplementry mterils). At low tempertures, the spontneous emission spetrum is given by S QD (ω, T ) =

3 Energy Intensity (rb. u.) X b 1.2 mev mev Energy 6 b Energy Intensity (rb. u.) With X 4 e 1.2 f QD2 6 X Energy Normlize Intensity Linewith g h i Theory 6 X FIG. 2. : Emission intensity s funtion of energy n temperture for the pillr ouple to QD2. b,: emission spetr extrte from the temperture flow presente in, orresponing to the two vertil white lines. Blk symbols: experimentl points. Blk lines: fit with the sum of three lorentzin peks. Re line: vity pek. Blue lines: n peks. -f: Chrteristis of the QD2-pillr evie eue by fitting the spetr with sums of lorentzin peks: Energy (top), Intensity (mile) n linewith (bottom) of the QD (blk) emission line n the vity (re) emission lines. The QD linewith whih is below the spetrl resolution for ll temperture is not shown. g: Clulte energies of the pprent QD (blk) n moe (re) lines s funtion of temperture. The re otte line in the bre vity moe energy. h: Normlize emission intensity of the QD line (blk) n the moe line (re) s funtion of temperture. i: Clulte with of the pprent vity line s funtion of temperture. Γ ZPL (ω) + Γ 1PL (T, ω). The first term Γ ZPL (ω) esribes the QD zero-phonon line (ZPL), proportionl to Dir elt funtion, whih is phenomenologilly substitute here by lorentzin. The seon term ounts for the temperture epenent one phonon line (1PL), given by Γ 1PL (T, ω) = (n(ω, T ) + 1)Γ 1PL (ω) + n(ω, T ) Γ 1PL (ω), where the first term orrespons to the emission of phonon n the seon term to bsorption. Γ 1PL (ω) is the one phonon line t zero temperture, Γ 1PL (ω) its mirror funtion with respet to the ZPL entrl energy n n(ω, T ) is the Bose-Einstein verge number of phonons with frequeny ω q = ω ω. When inserte in vity, the QD intert with n ensemble of eletromgneti moe whose ensity is given by the vity normlize spetrum S v (ω) = κ 2π [(κ/2)2 + (ω ω) 2 ] 1, where κ is the bre vity linewith n ω its frequeny. The normlize spontneous emission spetrum of the QD wekly ouple to vity is S(ω) = S v (ω) S QD (ω, T )/Γ where Γ = ω S v (ω) S QD (ω, T ). S(ω) is obtine experimentlly by olleting the emission through the vity hnnel (Fig.1). The emission spetrum presents two terms rising from the QD ZPL n 1PL. Sine the vity linewith is muh lrger thn the ZPL linewith, the first term is given by S v (ω) Γ ZPL (ω) Γ ZPL (ω). It orrespons to the QD like emission line in the experiment. The seon term stems from the QD phonon siebn filtere by the vity moe S v (ω) Γ 1PL (T, ω). It is this term tht gives rise to the vity like emission, whose behvior is now theoretilly nlyseit orrespons to the vity like emission in the experiment. Figure 3 shows the lulte spetr for vity moe with qulity ftor Q=1, positively etune by 1 mev from the QD ZPL, t 4 K. The green line in figure 3 presents the QD emission spetrum S QD (ω, T ). The min pek orrespons to the ZPL. The phonon siebn is lmost symmetril on both sies of the ZPL beuse signifint phonon popultion. The re line represents the vity spetrum S v (ω, T ). The blk urve is the lulte emission spetrum S showing two peks with vity emission line pulle towr the QD line. Moreover, the vity emission linewith is signifintly nrrower thn the bre vity spetrum. To eluite the influene of vrious prmeters on

4 4 Intensity (rb. u.) 1 1 S QD (ω) S v (ω) S(ω) 4K E moe -E QD Moe Energy Normlize moe intensity Moe linewith K Q=1 Q=3 Q= bre QD bre vity b E moe -E QD FIG. 3. Cvity pulling inue by the QD phonon bth: : Clulte emission spetr for QD-vity etuning of 1 mev t 4K for bre vity of Q=1. Green line: lulte emission spetrum S QD of the QD stte ouple to the phonon bth. Re line: vity spetrl funtion S v. Blk urve: lulte emission spetrum S of the ouple QDvity system. b-: Clulte emission hrteristi for the vity emission line s funtion of etuning with the QD line for T=2K. b: Energy of the vity line with respet to the QD energy. : Intensity of the vity line : Linewith of the vity line (log sle). Three bre vity qulity ftors re onsiere: Q=1 (blk), Q=3 (re), Q= (green). In b, the se of Q= is not shown for lrity n the blk (resp. blue) soli line is the bre QD (resp. vity) frequeny. The otte lines re the liner pproximtions (eqution 1). In, the horizontl lines show the bre vity linewith. Lines in re the normlize intensity of the vity-filtere 1PL: S v(ω) Γ 1PL(T, ω)ω/γ. the vity istortion, S is lulte s funtion of the etuning. The pprent vity energy, intensity n linewith re extrte from multi-lorentzin fit to mimi the experimentl proeure. Figure 3 presents these prmeters s funtion of etuning for three bre vity qulity ftors Q = ω /κ. The isple moe energy is plotte with respet to the QD ZPL. The blue line represents the bre vity moe. Figure 3b shows tht the vity emission is pulle towr the QD energy. This pulling is strongest when the moe Q is low. It n be shown tht the emission mximum is obtine t frequeny given by κ ω QD + κ 1P L ω κ + κ 1P L (1) pproximting the 1PL with lorentzin shpe of linewith κ 1P L n onsiering the smll etunings rnge ω ω QD << κ 1P L, κ. Note tht this simple eqution is very similr to the one giving the pulle frequeny in tomi gs lser [26]. It is plotte in figure 3.b (otte lines) for κ 1P L = 1.meV n gives goo pproximtion of the vity pulling effet for smll etunings. In prtiulr, the vity like behvior follows the bre vity behvior when the Q is high. This orrespons to se where phonon ssiste mehnisms t s built in white light soure insie the resontor. On the ontrry, strong vity pulling is expete when the Q is low, s observe in Fig. 3 n in Fig.2. The symbols in figure 3 show tht the moe intensity ereses when pprohing the resonne with the QD line, s observe experimentlly. The normlize vityfiltere 1PL emission S v (ω) Γ 1PL (T, ω)ω/γ is lso plotte (thin soli lines). A goo greement is foun with the intensity eue from the lorentzin fit. Lst, figure 3 shows the lulte vity linewith s funtion of etuning (symbols). For smll qulity ftors, the phonon siebn minly les to nrrowing of the vity line, i.e. n pprent inrese of Q. For lrger Q both pprent reution or inrese of Q re preite, epening on the slope of the phonon siebn spetrum t given etuning. Our theoretil frmework llows to ount for most of the experimentl observtions s isplye in figure 2.g-i. The QD-vity emission properties re lulte for severl QD lines ouple to the vity moe. To simplify, the QD-vity etuning is ssume liner with etuning. The mesure spetrum is the verge of spetr orresponing to the QD being either in the X, or stte. Here, equl ouption probbility of the sttes is ssume. Eh QD line experienes the optiml oupling to the vity moe n to the phonons. As observe in figure 2-f, the lulte vity moe is pulle towr the losest QD trnsition. In between two trnsitions, the moe is fe by the phonon siebns of both QD lines, resulting in signifint slope hnges in the line energy n in vity line broening. Finlly, lose to eh resonne, the inrese in the QD emission orrespons to erese in the vity line intensity, s observe experimentlly. Inee, the QD emits single photon either in the 1PL or in the ZPL, with frtion epening on the Purell effet of eh line. When the ZPL is on resonne, the ZPL Purell enhnement is lrger thn for the 1PL: the single photon is minly emitte in the ZPL, t the expense of the 1PL, feeing the vity line. While most experimentl observtions re well ounte theoretilly, we note tht our experiments show itionl fetures very lose to eh QD line resonne where the vity line presents n voie rossing with the moe. This moe pushing is espeilly ler for the resonne (see figure 2). These fetures re not reproue theoretilly using the bulk phonon ispersion. Sine the vity probes the phonon siebn emission, the voiing rossing t resonne inites the presene of isrete phonon moes. The existene of suh onfine phonon moes hs reently been propose in III-V miropillrs vities [33].

5 In onlusion, we hve eviene vity pulling effets for single rtifiil tom ouple to mirovity in the wek oupling regime. These observtions, obtine thnks to full ontrol of the emitter-vity oupling, show strong istortion of the vity spetrum inue by the phonon siebn. We note tht emission spetrosopy is ommonly use to mesure the properties of vity moe ouple to soli stte single emitter, whether the emitter is self ssemble QD, NV enter in imon or olloil QD. However, our work shows tht this tehniques n le to strong unertinties on both the eue vity linewith n spetrl position: the oupling to the soli stte environment inues new phenomen ppering in the b emitter limit for vity quntum eletroynmis. Aknowlegments This work ws prtilly supporte by the Frenh ANR P3N DELIGHT, ANR P3N CAFE, the Fontion Nnosienes e Grenoble, the ERC strting grnt QD-CQED, the CHISTERA projet SSQN, the Ntionl Siene Center in Poln (DEC- 211/1/N/ST3/436 ), n Lier grnt from The Ntionl Center for Reserh n Development in Poln. The uthors thnk Drio Gere, Robson Ferreir, Clue Fbre, Jqueline Bloh, Thoms Coureu n Piotr Kosski for isussions. lexi.uffeves@grenoble.nrs.fr psle.senellrt@lpn.nrs.fr [1] S. Shietinger, M. Brth, T. Aihele n O. Benson, Nno Lett. 9, 1694 (29) [2] A. G. Curto et l. Siene 329, 93 (21). [3] M. Pelton et l, Phys. Rev. Lett.89, (22) [4] A. Dousse, et l. Nture 466, (21) [] A. Bolto, et l., Siene 38, 118 (2) [6] P. Mihler et l. Nture 46, 968 (2). [7] P. Mihler et l Siene 29, 2282 (2) [8] A. Reinhr et l., Nture Photon. 6, 93 (211). [9] R. Bose, et l., Phys. Rev. Lett. 18, (212) [1] Loo V., et l., Phys. Rev. Lett. 19, (212) [11] Y. Shen, T. M. Sweeney, n H. Wng Phys. Rev. B 77, 3321 (28) [12] L. Besombes, K. Kheng, L. Mrsl, H. n Mriette, Phys. Rev. B 63, 137 (21) [13] E. Peter, et l., Phys. Rev. B 69, 4137 (24) [14] S. A. Empeoles, D. J. Norris, n M. G. Bweni, Phys. Rev. Lett. 77, 3873 (1996) [1] A. Berthelot, et l., Nture Physis 2, 79 (26) [16] G. Sllen et l., Nture Photonis 4, 696 (21) [17] M. Kniberet l., Phys. Rev. B 77, (28) [18] J. Suffzyński,et l., Phys. Rev. Lett. 13, 2741 (29). [19] S. Ates et l., Nture Photonis 3, (29) [2] M. Winger et l., Phys. Rev. Lett. 13, 2743 (29) [21] A. Auffèves,J.-M. Gérr, n J.-P. Poizt Phys. Rev. A 79, 3838 (29) [22] A. Auffèves,et l., Physil Review B 81, (21) [23] R. Albreht et l, Phys. Rev. Lett. 11 (213) [24] A. Dousse et l., Phys. Rev. Lett. 11, (28). [2] W. R. Bennett, Jr., Gseous Optil Msers Applie Optis, 1, (1962) [26] A. E. Siegmn, Lsers, University Siene Books, (1986). [27] W. R. Bennett, Jr., Phys. Rev. 126, 8 (1962) [28] L. Csperson n A. Yriv, Appl. Pys. Lett. 17, 29 (197) [29] I. Wilson-Re n A. Immoglu, Phys. Rev. B, 6, (22); [3] G. Trel n V. Svon,Phys. Rev. B 81, 73 (21) [31] T. Twr,et l., Opt Express. 18, 2719 (21) [32] E. el Vlle, F. P. Lussy, n C. Tejeor, Phys. Rev. B 79, (29). F. P. Lussy, E. el Vlle, n C. Tejeor Phys. Rev. B 79, 2332 (29) [33] A. Finstein, N. D. Lnzillotti-Kimur, B. Jussern, n B. Perrin, Phys. Rev. Lett. 11, 3743 (213)