Coupled donors in quantum dots: quantum size and dielectric mismatch effects

Coupled dono s in quan um do s: Quan um size and dielec ic misma ch e ec s J. L. Mo illa, A. Balles e , and J. Planelles* Depa amen de Química Física i Analí ica, Uni e si a Jaume I, Box 224, E-12080 Cas elló, Spain 共Recei ed 17 Feb ua y 2009; e ised manusc ip ecei ed 17 Ap il 2009; published 20 May 2009兲 Spa ial and dielec ic con inemen modula ions o he spon aneous emission a es, ansi ion ene gies, and cha ge-densi y dis ibu ions o a singly ionized double dono sys em 共D2 +兲in a sphe ical quan um do a e calcula ed wi hin he amewo k o he e ec i e-mass en elope unc ion app oxima ion. Dipole momen s, ene gy spli ings, ansi ion momen s, elec on-densi y dis ibu ions, and spon aneous emission a es in ol ing bonding and an ibonding lowes -lying molecula s a es a e add essed o di e en dielec ic en i onmen s, quan um do adii, and ela i e loca ions o he coupled impu i ies inside he do . The esul s indica e ha he dono molecule beha es as he e opola when he spa ial con inemen b eaks he in e sion symme y, which is pa alleled by a s ong educ ion in he exci ed-s a e adia i e li e ime. Dielec ic con inemen , ac ing on a la ge leng h scale han spa ial con inemen , may eco e he bulklike homopola cha ac e when he do is embedded in a low dielec ic cons an medium. In he weak spa ial con inemen egime, dielec ic e ec s can inc ease he co esponding bulk adia i e li e imes signi ican ly and simul aneously modula e he cha ge-densi y dis ibu ion. DOI: 10.1103/PhysRe B.79.195319 PACS numbe 共s兲: 71.55.⫺i, 73.21.La, 77.22.Ej, 03.67.Lx I. INTRODUCTION The sys em buil o wo coupled semiconduc o quan um do s 共QDs兲con aining elec ons, holes, o an exci on cons i- u es one o he simples solid s uc u es p oposed as he unc ional pa in a wide ange o de ice applica ions, in- cluding spin onics,1op oelec onics,2pho o ol aics,3and quan um in o ma ion echnologies.4,5The widesp ead in e - es in his sys em elies on he abili y o manipula e con e- nien ly i s molecula p ope ies, such as he ene gy spli ing be ween he bonding 共nodeless兲and an ibonding 共noded兲 lowes -lying molecula like s a es o he spa ial dis ibu ion o ca ie s in he sys em.6In his ega d, he asymme y o he cons i uen do s 共ei he in insic o in en ional兲has been iewed no as a law bu as an essen ial design choice o p o ide addi ional con ol o e he sys em p ope ies.5,7,8 Ad ances in single-dopan ab ica ion9–11 and cha ge de ec ion12,13 ha e led a omic scale elec onics 共pa icula ly he ield o quan um compu ing兲 o pea inc easing a en ion o ano he molecula sys em. Namely, he D2 +sys em, i.e., he sys em buil o wo coupled dono impu i ies in a semicon- duc o hos in which one o he wo excess elec ons has been ionized. This sys em encodes he logical in o ma ion ei he on he spin o on he cha ge deg ees o eedom o he emaining excess elec on.14–20 Ini ial p oposals elied on spin encoding. Howe e , di ec de ec ion o a single spin emains oday a majo challenge.21 On he con a y, a ac- ion o a single elec on cha ge can be easily de ec ed wi h s a e-o - he-a single elec on- unneling de ices.12,13 This eadou easibili y, oge he wi h he ela i e simplici y o he manipula ion o cha ge deg ees o eedom as opposed o spin, has aised in e es in cha ge qubi s, whe e he logical s a es a e ep esen ed by he wo lowes -lying elec on o bi al s a es posi ioned a he di e en dono s. All he same, he sho cohe ence imes o o bi al s a es se e ely limi he scal- abili y o cha ge qubi s,16 so ha mechanisms enhancing co- he ence would be desi able. S udies on con ined D2 +sys ems ha e been ecen ly ad- d essed in he li e a u e.22–24 Pa icula ly, Kang e al.24 ound ha he con inemen o he D2 +sys em in a sphe ical QD can g ea ly enhance he ene gy di e ences be ween he wo lowes -lying elec on s a es and mo e exci ed s a es, a o ing he iden i ica ion o he quasi- wo-le el sys em equi ed o quan um compu a ion pu poses.25 Qui e a la ge amoun o wo k has been done in he s udy o he elec onic s uc u e and ela ed p ope ies o single shallow dono s in nanoscale semiconduc o he e os uc u es.26–28 In addi ion o he well-known quan um size e ec , he in luence o he dielec ic con inemen 共com- ing om he di e en dielec ic esponse o he QD and he su ounding medium兲on he dono le els has been e ealed as a pa icula ly no iceable e ec in colloidal quan um do s as hey a e usually syn hesized in media wi h a dielec ic esponse a he di e en o ha o he do ma e ial.26,29,30 P omp ed by he impo an ole o coupled impu i ies in nano echnology, we p esen in his pape a heo e ical s udy on he molecula p ope ies o a D2 +sys em con ined in a sphe ical quan um do . We ocus on he in luence o bo h he QD size and he dielec ic misma ch on he adia i e li e- ime, he bonding-an ibonding ene gy spli ing, and he elec- on cha ge dis ibu ions in he lowes -lying D2 +molecula s a es, and analyze he dependence o he esul s on he ela- i e posi ion o he dono s inside he quan um do . The pape is o ganized as ollows. In Sec. II, we in oduce he model employed in he desc ip ion o he con ined double dono sys em and ou line he de ails o he nume ical p oce- du e used o sol e he esul ing Hamil onian. The e ec s o spa ial and dielec ic con inemen s on he double dono sys- em a e p esen ed and discussed in Sec. III. Conclusions, gi en in Sec. IV, end he pape . II. MODEL AND THEORETICAL OUTLINE The p esen s udy is ca ied ou wi hin he amewo k o he e ec i e-mass and en elope unc ion app oxima ions. Consequen ly, we employ a mac oscopic ea men o Cou- lombic in e ac ions, and use a pa ame e , he dielec ic con- PHYSICAL REVIEW B 79, 195319 共2009兲 1098-0121/2009/79共19兲/195319共6兲©2009 The Ame ican Physical Socie y195319-1 s an , o cha ac e ize he dielec ic esponse o each ma e ial in ol ed. The alidi y o such a ea men has been well es ablished o bo h doped and undoped semiconduc o he e os uc u es.31 Ou model consis s o a shallow dono pai con ined in a sphe ical quan um do wi h dielec ic con- s an ␧QD, which is in u n imme sed in a dielec ic medium wi h pe mi i i y ␧ou 共see Fig. 1兲. The co esponding e ec i e-mass Hamil onian o he bound conduc ion-band elec on eads, in a omic uni s, H=−1 2 䉮 冉 1 mⴱ共 兲䉮 冊 +V共 兲+ ␾ s共 兲+兺 i=1,2 ␾ c Ii共 , i兲. 共1兲 The i s e m on he igh -hand side o Eq. 共1兲is he gene alized kine ic-ene gy ope a o ,32 which accoun s o di e en elec on masses in di e en ma e ials. V共 兲is a s eplike unc ion ep esen ing he ini e spa ial con ining po- en ial due o he conduc ion-band o se be ween he media in ol ed. ␾ c Ii共 , i兲s ands o he Coulomb po en ial gene - a ed by he impu i y loca ed a he ixed posi ion i, including he e ec o he pola iza ion cha ges induced a he do su - ace as a consequence o he dielec ic misma ch be ween he QD and he su ounding medium. The elec on i sel also induces pola iza ion cha ges a he do bounda ies, whose e ec s a e desc ibed by he sel -pola iza ion po en ial ␾ s共 兲. When 共as is he case he e兲a␧共 兲=␧共 兲s eplike dielec ic unc ion is assumed, ␾ cand ␾ sadmi analy ical exp essions.33 In o de o educe he numbe o a iables in he s udy, we ix he QD ma e ial pa ame e s close o hose o CdS 共␧QD =5.5 and mⴱ=0.15兲共Re . 34兲unless o he wise indica ed. Since we a e no dealing wi h a speci ic su ounding me- dium, we will assume a ypical dep h o V0=4 eV o he QD con ining well and an e ec i e mass mⴱ=1 o he ex- e nal medium. Likewise, we will concen a e on dono s which a e aligned along an axis o he QD 共see Fig. 1兲, al hough he conclusions ob ained make possible o en isage he ends cha ac e izing o he con igu a ions. This acili a es he calcula ion since he axial symme y o he sys em allows us o in eg a e analy ically he angula coo dina e o he elec- on in Eq. 共1兲. Then, o ob ain elec on ene gies and wa e unc ions, we ca y ou an exac 共nume ical兲in eg a ion o 共 ␳ ,z兲coo dina es by means o a disc e iza ion scheme based on he ini e di e ences me hod. The explici exp essions o ␾ cand ␾ s oge he wi h a de ailed desc ip ion o he in eg a- ion me hod can be ound in Re . 28. III. RESULTS We s a by in es iga ing he e ec o he spa ial and di- elec ic con inemen s on he elec on cha ge dis ibu ion o he double dono lowes -lying s a es. When he cen e o mass o he dono pai is no loca ed a he do cen e 共zCM ⫽0, see Fig. 1兲, he asymme y o he QD con inemen is expec ed o b eak he in e sion symme y o hese s a es. To moni o 共and quan i y兲 he symme y b eakdown, we calcu- la e he dipola momen o he co esponding elec on cha ge dis ibu ions wi h espec o zCM, ␮ =具i兩 −zCMuz兩i典,共2兲 whe e i=1,2 labels he g ound and i s exci ed s a es o he sys em. The esul s a e shown in Fig. 2, whe e ␮ /dI−I共wi h dI−I=10 nm兲is ep esen ed o hese s a es as a unc ion o he QD adius and he dono s loca ion wi hin he do . Calcu- la ions ha e been pe o med o wo di e en su ounding dielec ic cons an s, namely, ␧ou =␧QD 共absence o dielec ic con inemen 兲and ␧ou =1 共spa ial and dielec ic con ine- men s兲. In he igu e, posi i e alues o ␮ /dI−Iindica e ha he elec on is dis ibu ed o a g ea e ex en a ound he do- no close o he QD bo de , whe eas nega i e alues indi- ca e i s p e e ence o he inne mos impu i y. F om he ␧ou =␧QD panels we can obse e ha he spa ial con inemen a o s he localiza ion o he g ound s a e in he inne dono CM RQD I2 1 I εQD εou dI−I z z ρ FIG. 1. Schema ic ep esen a ion o he sys em unde s udy: an elec on bound o wo shallow dono s sepa a ed by a dis ance dI−I wi hin a diame e o a con ining sphe ical QD wi h adius RQD and dielec ic cons an ␧QD su ounded by a dielec ic medium o pe - mi i i y ␧ou .zCM s ands o he cen e o mass o he coupled dono s. FIG. 2. 共Colo online兲Dipola momen 关Eq. 共2兲兴 o he elec on cha ge dis ibu ion o a con ined D2 +sys em wi h dI−I=10 nmasa unc ion o RQD and he sys em loca ion in he do . Le 共 igh 兲 panels co espond o he elec on in he g ound 共 i s exci ed兲s a e. In op 共bo om兲panels he QD is embedded in a ␧ou =␧QD 共␧ou =1兲dielec ic medium. The o igin has been loca ed a he QD cen e . MOVILLA, BALLESTER, AND PLANELLES PHYSICAL REVIEW B 79, 195319 共2009兲 195319-2 and he exci ed s a e in he ou e one. This end, mo e p o- nounced o low QD adii and la ge zCM alues, is a conse- quence o he la ge des abiliza ion ha he po en ial ba ie p oduces in he su oundings o he ou e mos impu i y. To minimize i s ene gy, he elec on in he g ound s a e localizes in he inne dono and, o p ese e o hogonali y, he exci ed s a e concen a es in he ou e one. In o he wo ds, nonsym- me ic spa ial con inemen b ings he homopola D2 +sys em o beha e as he e opola , leading o he spa ial sepa a ion o he wo lowes -lying elec on s a es. In he case ␧ou =1 共lowe panels in Fig. 2兲, we can see ha , excep o e y small do adii and e y la ge zCM al- ues, he pola i y o he s a es is opposi e o ha in he ab- sence o dielec ic con inemen . Now, he g ound s a e local- izes he elec on densi y in he ou e dono , whe eas he inne dono is occupied by he exci ed s a e. This e ec can be explained as o igina ed by he con ibu ion o he pola iza- ion cha ges induced by he impu i ies a he QD su ace. Impu i y o -cen e ing inc eases he nonhomogenei y o he co esponding induced cha ge dis ibu ion a he do su ace, his lack o homogenei y being esponsible o an addi ional s abiliza ion o o -cen e ed elec on loca ions.35 As a conse- quence, he o al Coulomb po en ial is deepe a he posi ion o he dono close o he su ace, so ha he g ound s a e dis ibu es p e e ably a ound i . The e o e, spa ial and dielec- ic con inemen s yield opposi e spa ial sepa a ion o he elec on s a es36 and hei in e play will de e mine he inal con igu a ion o he co esponding elec on cha ge dis ibu- ions in each case. Fo a mo e de ailed desc ip ion o his in e play, in Fig. 3共a兲we ha e depic ed ␮ /dI−I o he same sys em as in Fig. 2共dI−I=10 nm兲bu o he pa icula case o zCM=5 nm and a mo e ex ended RQD ange. Fo his alue o zCM, one o he impu i ies is loca ed a he QD cen e , a si ua ion a p io i easie o be ob ained expe imen ally han any o he . In he igu e, solid 共dashed兲cu es co espond o he g ound 共 i s exci ed兲s a e. In e es ingly, he case o pu e spa ial con ine- men 共␧ou =␧QD, hin ed lines兲shows homopola i y o la ge RQD alues, whe eas in he p esence o dielec ic misma ch 共␧ou =1, hick blue lines兲 he sys em beha es as he e opola . This is a signa u e o he di e en leng h scales in which spa ial and dielec ic con inemen s ope a e and is a conse- quence o he long ange o image cha ge Coulomb in e ac- ions. The di e en leng h scales o hese con inemen sou ces we e al eady epo ed by Goldoni e al.,37 who also in oduced he concep o emo e dielec ic ailo ing o une a will exci on-binding ene gies in semiconduc o /insula o hyb id nanos uc u es. Fo in e media e alues o RQD 关see e.g., RQD⬇14 nm in Fig. 3共a兲兴, whe e bo h spa ial and dielec ic con inemen e - ec s a e signi ican , we can obse e ha he dielec ic con- inemen compensa es, and e en in e s, he end imposed by he spa ial con inemen . Finally, o low RQD alues, he spa ial con inemen domina es and he inne dono is p e- e ed by he g ound s a e in bo h cases. The spa ial sepa a ion o he wo lowes -lying elec on s a es is mo e p onounced as he in e dono dis ance in- c eases. This is appa en in Fig. 4共a兲, which co esponds o he same sys em as in Fig. 3共wi h one o he impu i ies a he do cen e 兲bu o dI−I=15 nm. In his case, ␮ /dI−Iis plo ed as a unc ion o ␧ou o wo di e en do adii, namely, RQD=20 and 23 nm. Again, solid and dashed lines a e used o he g ound and i s exci ed s a es. As can be obse ed om he RQD=20 nm cu es, when ␧ou ⬎␧QD he dielec ic con inemen magni ies he s a es spa ial sepa a ion imposed by he spa ial con inemen 共␧ou =5.5兲. On he con- a y, his end is in e ed as ␧ou diminishes. The bulklike homopola cha ac e is eco e ed o a gi en alue o ␧ou 共3.9 in his case兲, compensa ing he e ec o he spa ial con- inemen . Finally, dielec ic misma ch e ec s domina e o low enough alues o ␧ou , yielding again a spa ial sepa a ion o he lowes -lying molecula s a es bu wi h opposi e pola - i y. This e olu ion can be seen in Fig. 4共d兲, whe e he modu- lus o he wa e unc ion ⌿共 兲 es ic ed o he azimu hal angle ␾ =0 is ep esen ed o bo h he g ound and i s ex- ci ed s a es and h ee di e en alues o he su oundings −0.4 −0.2 0 0.2 0.4 µ/d I−I 0.2 0.4 0.6 0.8 1 µ12 /µ12 bulk 1 3 5 7 ∆E/∆Ebulk 12 16 20 24 28 100 101 10−1 τ / τbulk εou =εQD εou =1 (a) (b) (c) R Q D(nm) g ound s a e 1s exci ed (d) FIG. 3. 共Colo online兲共a兲Dipola momen 关Eq. 共2兲兴 o he elec- on cha ge dis ibu ion in he g ound 共solid lines兲and i s exci ed 共dashed lines兲s a es o he con ined coupled dono sys em 共dI−I =10 nm兲wi h one o he impu i ies loca ed a he QD cen e as a unc ion o he QD adius. Thick blue lines co espond o ␧ou =1, whe eas hin ed lines co espond o ␧ou =␧QD 共absence o dielec ic con inemen 兲.共b兲Co esponding ansi ion momen s, 共c兲spli ing ene gies, and 共d兲 i s exci ed-s a e adia i e li e imes ela i e o bulk alues. COUPLED DONORS IN QUANTUM DOTS: QUANTUM SIZE…PHYSICAL REVIEW B 79, 195319 共2009兲 195319-3 pe mi i i y, i.e., ␧ou =5.5 共absence o dielec ic con ine- men 兲,␧ou =3.9 共si ua ion in which he homopola cha ac e is eco e ed兲, and ␧ou =2 共a ypical alue o o ganic capping ma e ials30兲. The case shown in Fig. 4 o RQD=23 nm ep esen s an addi ional example o he long ange o dielec ic e ec s. While in his case bulk cha ge dis ibu ions a e ha dly a - ec ed by he QD spa ial con inemen , he p ope choice o he QD en i onmen can s ill yield impo an changes in he ela i e elec onega i i y o he dono s and, he e o e, in he elec on cha ge dis ibu ions. The ene gy spli ing 共⌬E兲be ween he g ound and i s exci ed s a es is also in luenced by dielec ic and spa ial con- inemen s 关see Fig. 4共b兲兴. As de i ed om he igu e, ⌬E inc eases as he spa ial sepa a ion o he s a es is mo e p o- nounced, p esen ing a minimum, close o he bulk alue, when homopola condi ions a e uned. Con a y o ⌬E, he co esponding binding ene gies38 共Eb兲a e negligibly co e- la ed wi h he spa ial sepa a ion o he s a es 关see Fig. 4共c兲兴. This can be de i ed om he compa ison o solid and do ed cu es in he igu e, which co espond o zCM=7.5 nm 共one dono a he QD cen e 兲and zCM=0 共symme ic con ine- men 兲, espec i ely. Indeed, hough bo h cases p esen simi- la Eb alues, o zCM=0 he sys em p esen s homopola i y ega dless o ␧ou , whe eas his is no he case o zCM =7.5 nm. The e o e, Ebis negligibly in luenced by he o - cen e ing o he D2 +sys em and hen by he spa ial sepa a ion o he s a es. Con e sely, as expec ed, Ebis s ongly a ec ed by he dielec ic en i onmen , unde going a la ge inc ease as ␧ou dec eases. I is well known ha he spa ial sepa a ion o logic s a es in cha ge-based qubi ealiza ions can e icien ly educe he decohe ence o he cha ge deg ees o eedom coding he qubi , which makes possible o pe o m he cohe en quan- um logic ope a ions a a ai ly high a io.8The e o e, con- inemen is expec ed o a ec cohe ence in ou sys em. In dono -based cha ge qubi s, decohe ence caused by in e ac- ion wi h phonons occu s in ime scales ha can be made much longe han all o he ime scales in he p oblem by choosing an app op ia e dono sepa a ion.20 Then, o s udy how con inemen a ec s decohe ence in ou sys em, we will neglec in a i s app oxima ion acous ic and op ical phonon sca e ing and will only ake in o accoun decohe ence com- ing om acuum elec omagne ic luc ua ions 共 adia i e de- cay兲. The adia i e decay a e in a sphe ical quan um do can be es ima ed wi hin he dipole app oxima ion by39 ␶ −1 =9␧ou 5/2 共2␧ou +␧QD兲2 ⌬E3 3 ␲ ␧0ប4c3 ␮ 12,共3兲 whe e cis he speed o ligh in acuum, ␧0is he acuum dielec ic cons an , ␶ is he adia i e li e ime, and ␮ 12 =兩具1兩 兩2典兩2is he squa e o he dipole ansi ion momen be- ween he s a es 兩1典and 兩2典, which a e in ou case he g ound and i s exci ed s a es o he sys em. ␮ 12, ela i e o i s alue in he absence o spa ial and dielec ic con inemen s, is depic ed in Fig. 3共b兲 o he s ud- ied sys em. Again, esul s o ␧ou =␧QD and ␧ou =1 a e shown. As can be seen in he igu e, ␮ 12 dec eases as he sys em mo es away om homopola condi ions. By inspec- ion o Eq. 共3兲, one could expec ha a dec ease in ␮ 12 would help in inc easing he li e ime. Howe e , he dependence o ␶ −1 on ⌬E3canno be neglec ed in his case since, as we showed be o e, spa ial sepa a ion o he wo lowes -lying s a es is pa alleled by an inc ease in he ansi ion ene gy 关see Fig. 3共c兲兴. On balance, he in luence o ⌬Eon he adia- FIG. 4. 共Colo online兲共a兲G ound s a e 共solid lines兲and i s exci ed-s a e 共dashed lines兲dipola momen s o a dI−I=15 nm con- ined D2 +sys em wi h one dono a he QD cen e as a unc ion o ␧ou . Cu es a e shown o wo di e en QD adii. 共b兲Spli ing ene gy dependence on ␧ou o he wo QD adii s udied. 共c兲Co e- sponding g ound-s a e binding ene gies 共solid lines兲. Cu es co e- sponding o zCM=0 共do ed lines兲ha e been included o compa i- son. 共d兲Modulus o he wa e unc ion ⌿共 兲 es ic ed o he azimu hal angle ␾ =0 o he same sys em as abo e wi h RQD =20 nm and di e en alues o ␧ou . MOVILLA, BALLESTER, AND PLANELLES PHYSICAL REVIEW B 79, 195319 共2009兲 195319-4 i e li e ime is la ge han ha o ␮ 12. This can be seen in Fig. 3共d兲, whe e ␶ has been ep esen ed ela i e o ␶ bulk. Re- e ing o he esul s o ␧ou =␧QD 共whe e only he spa ial con inemen is in luencing he sys em兲, we obse e ha ␶ d ops s ongly o small alues o RQD, whe eas i eaches he bulk alue when he spa ial sepa a ion o he wo lowes - lying s a es disappea s and homopola condi ions a e eco - e ed. The esul s o ␧ou =1 a e mo e in e es ing. ␶ shows a p o ile simila o ha o ␧ou =␧QD calcula ions bu despi e spa ial sepa a ion s ill pe sis s in he whole ange o RQD unde s udy, ␶ eaches alues mo e han 1 o de o magni ude la ge han in bulk. The enhancemen o ␶ when he QD is su ounded by a low-dielec ic cons an medium is a conse- quence o he in luence o local- ield e ec s,39 which ha e been obse ed expe imen ally h ough measu emen s o ex- ci on ecombina ion a es in QDs embedded in apola sol- en s wi h low e ac i e indices.30 The d op o ␶ o small alues o RQD in Fig. 3共d兲is induced, in bo h ep esen ed cases, by he spa ial con ine- men h ough he la ge inc ease ha i yields on ⌬E. This can be con i med in Fig. 5共le panel兲whe e he adia i e li e- ime o ou sys em as a unc ion o ␧ou and he sys em loca- ion wi hin a R=14 nm QD is shown. When he o cen e - ing o he dono pai is no much p onounced 共low and medium zCM alues兲, he in luence o he spa ial con inemen is negligible and, in he absence o dielec ic misma ch, ␶ keeps close o he bulk alue. In hese condi ions, ␶ inc eases no iceably wi h espec o he bulk as ␧ou dec eases. How- e e , as he dono pai ge s close o he do su ace 共la ge zCM alues兲, he adia i e li e ime becomes domina ed by he e ec s o spa ial con inemen . ␶ expe iences a s ong educ- ion, which is only pa ially compensa ed by dec easing ␧ou . Finally, o p obe he e ec o inc easing he QD dielec ic cons an , we ha e epea ed he calcula ions o QD pa am- e e s simila o hose o Si 共␧QD=11.7 and mⴱ=0.26兲. The esul s, shown in he igh panel o Fig. 5, e idence ha in his case ␶ may inc ease up o almos 2 o de s o magni ude wi h espec o he co esponding bulk alue. IV. CONCLUDING REMARKS We ha e p obed he in luence o spa ial and dielec ic con inemen s on spon aneous emission a es, ene gy spli - ings, and cha ge-densi y dis ibu ions in he lowes -lying s a es o a D2 +double dono sys em con ined in a sphe ical quan um do . We ound ha asymme ic con inemen 共p o- duced when he dono s a e no symme ically dis ibu ed a ound he QD cen e 兲leads he o he wise homopola dono pai o beha e as he e opola , diminishing he in e dono un- nel coupling and localizing he g ound and i s exci ed s a es in di e en dono s. In his ega d, when 共as usual兲␧ou ⬍␧QD, spa ial con inemen ends o localize he g ound/ i s exci ed s a e in he inne /ou e dono , whe eas dielec ic e - ec s end o dis ibu e hem opposi ely. Howe e , hese con- inemen sou ces ope a e in di e en leng h scales. While in he la ge do size egime only dielec ic e ec s in luence he D2 +sys em, in he small do size egime spa ial con inemen e ec s domina e. This makes possible o une he unnel cou- pling s eng h and cha ge-densi y dis ibu ion in he D2 +sys- em a will, by choosing he app op ia e do size and su - ounding medium. We also ound ha bulk adia i e li e imes a e s ongly educed by spa ial con inemen due o he enhanced spli ing ene gies. On he o he hand, when spa ial con inemen e - ec s a e no longe in ol ed 共la ge do sizes兲, adia i e li e- imes may inc ease o de s o magni ude when he QDs a e embedded in low-dielec ic cons an media. Summing up, he con inemen o he D2 +sys em in a quan- um do p o ides addi ional mechanisms o mold i s p ope - ies; i is wo h o no ice he spa ial dis ibu ion o he lowes -lying s a es, he co esponding ene gy spli ings, and he adia i e li e imes. The 共wide ange兲 uning capabili y o his las p ope y could be o in e es o inc ease he ela- i ely low bulk cohe ence imes o o bi al s a es in cha ge qubi ealiza ions. We close by s essing ha con inemen migh also be use- ul o imp o e he pe o mance o op ically d i en dono - based cha ge qubi schemes.17,18 In such schemes, he deco- he ence caused by he ioniza ion and spon aneous emission o he exci ed s a es ac ing as connec ing channels be ween he logical s a es could be minimized h ough he p ope choice o QD size and dielec ic en i onmen . On one hand, quan um con inemen would li he quasidegene acy among nea -con inuum s a es, inc easing he co esponding ioniza- ion h eshold and exci a ion selec i i y. On he o he hand, he employmen o low dielec ic cons an su ounding ma- e ials would help in educing hei 共o he wise limi ing兲 spon aneous emission a es. ACKNOWLEDGMENTS Suppo om MICINN unde P ojec No. CTQ2008- 03344 and Bancaixa unde P ojec No. P1-1B2006-03 is ac- knowledged. FIG. 5. 共Colo online兲Fi s exci ed-s a e adia i e li e ime 共 ela- i e o bulk兲 o a dI−I=10 nm D2 +sys em con ined in a R =14 nm QD as a unc ion o ␧ou and he sys em loca ion wi hin he QD. 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