Optimal coupling of entangled photons into single-mode optical fibers

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1 Omal coulng o nangl hoons no sngl-mo ocal bs. ns Damn o Phscs Facul o gculu an Naual Scncs Th nvs o h Ws Ins S. ugusn ublc o Tna an Tobago W.I.. ans@ans.u... P an Sabn Saa Damn o Phscs Kng s Collg Lonon San Lonon WC LS K. o.@cl.ac.u sabn.saa@cl.ac.u bsac: W sn a conssn mulmo ho ha scbs h coulng o sngl hoons gna b collna T-I aamc on-convson no sngl-mo ocal bs. W hav calcula an analc sson o h b am hch mamzs h a hoon coun a. Fo a gvn ocal lngh an avlngh a lo lm o h b am o sasaco coulng s oban. Ocal Soc o mca OCIS cos: 9.9 Nonlna ocs; 9. Paamc ocsss ncs an lns. D. C. Bunham an D. L. Wnbg Obsvaon o smulan n aamc oucon o ocal hoon as Phs. v. L Z. Y. Ou X. Y. Zou L. J. Wang an L. Manl mn on nonclasscal ouh-o nnc Phs. v C. K. Hong an L. Manl Tho o aamc qunc on-convson o lgh Phs. v Z. Y. Ou an L. Manl Volaon o Bll s nqual an classcal obabl n a o-hoon colaon mn Phs. v. L P. G. Ka K. Mal H. Wnu. Zlng. V. Sgno an Y. H. Shh Phs. v. L C. H. Bnn G. Bassa C. Cau. Jozsa. Ps an W. K. Woos Tlong an unnon quanum sa va classcal an nsn-pools-osn channls Phs. v. L S. L. Baunsn an H. J. Kmbl Tloaon o connuous quanum vaabls Phs. v. L L. Vaman Tloaon o quanum sas Phs. v D. Boums J-W Pan K. Mal M. bl H. Wnu an. Zlng mnal quanum loaon Nau J-W Pan D. Boums H. Wnu an. Zlng mnal nanglmn sang : nanglng hoons ha nv nac Phs. v. L D. Boums J-W Pan M. Danll H. Wnu an. Zlng Phs. v. L K. J. G. a P.. Tas an G. M. Palma Paccal quanum cogah bas on ohoon nom Phs. v. L W. Tl J. Bnl H. Zbnn an N. Gsn Quanum cogah usng nangl hoons n ngm Bll sas Phs. v. L C. Kus M. Obal an H. Wnu Hgh-cnc nangl hoon a collcon n -II aamc luoscnc Phs. v S. Casllo I. P. Dgovann M. Wa an. Mgall Coulng cncs n sngl hoon on-man soucs Xv:quan-h/ F.. Bovno P. Vasco. M. Colla G. Casagnol G. D. Gus an. V. Sgno cv b coulng o nangl hoons o quanum communcaon Ocs Communcaons P an S. Saa Th Quanum Tho o aaon Oo nvs Pss ns.. P an Sabn Saa Phoon colaons an nnc n -I ocal aamc on-convson J. O. B: Quanum smclass. O

2 9.. Yav Ocal lconcs n Mon Communcaons 5 h on Oo Ss n lccal an Comu ngnng.. J. W. Gooman Inoucon o Fou Ocs McGa-Hll N Yo 968 chas. 7 an 8.. Q. Cao an S. Ch oma nalcal Dscon o Funamnal-Mo Fls o Ga-In Fbs: Bon h Gaussan omaon Jounal o Lghav Tchnolog Volum 9 Issu Ma. Vaz G. Whs an. Zlng nanglmn o h obal angula momnum sas o hoons Nau vol L. Mgall D. Bannng an S. Casllo Talong sngl-hoon an mulhoon obabls o a sngl-hoon on-man souc Phs. v Inoucon Th ocal ocss o sonanous aamc on-convson SPDC nvolvs h vual absoon an sonanous slng o an ncn um hoon n a ansan nonlna csal oucng o lo-qunc sgnal an l hoons [-]. Th as o hoons can b nangl n a mul-aam sac o qunc momnum an olazaon. In -I SPDC h hoons a qunc-nangl an h sgnal an l hoons hav aalll olazaons ohogonal o h um olazaon. nangl hoons hav bn us o monsa quanum nonlocal [5] quanum loaon [6-8] an mo cnl quanum nomaon ocssng [9-] an quanum cogah []. On o h challngs n cn accal schms such as quanum cogah an quanum communcaon s o mamz h cnc o coulng o sngl hoons no sngl-mo ocal bs. Sval mols an mns hav bn vlo o c an masu h coulng cncs o on-conv lgh no sngl-mo bs [56]. In h mol an mn o Kus. al. [] h angula sbuon o non-collna - II on-conv lgh o a gvn scal banh s calcula. Th a s o mach h angula sbuon o h hoon as o h angula h o h b mo. Bovno. al. [6] ouc a mo goous mol n hch h nnc o h coulng cnc on csal lngh an al-o nvsga. Th moanc o h-nanglmn n -I on-convson an s ossbl us as a souc n h l quanum nomaon has bn cnl scuss []. Sngl hoon on-man soucs hav also bn sgn usng an aa o -I on-convs []. In conas o vous o sn a al hocal mol scbng sngl-hoon mo coulng n h sml suaon o collna -I on-convson. Th a hoon coun a s calcula an an analc sson hch mns h conon o omum sngl-hoon coulng n sngl-mo ocal bs s oban n ms o mnal aams.. mlu o a con n sngl-mo bs Th amlu o cng hoon as a conjuga sac-m ons s n b H H h an a con ms o sgnal an l hoons an H a h Hsnbg lcc l oaos [8]. In h sa sa h gh-han-s o q. can b ss as an

3 I I I a h nacon-cu lcc l oaos a som aba bu sc con ons an an s a uncon hch scbs h sha o h um n h ansvs con; a lan-av mos scbng h lcomagnc l n h csal h as h av vcos o h sgnal an l hoons s h av vco o h ncn um hoon an a olazaon ncs. s n ou vous sus hav no nouc h cs o a chang n h lna acv n bn h csal an s suounngs. Th ncooaon o hs nc os no qualavl chang ou conclusons. W hav ho assum ha h nonlna csal s mb n a mum hos lna acv s h sam as ha o h csal. Ocal bs us n h analss a assum o hav h sam acv n as h csal. Th nal sa o h lcomagnc l consss o a cohn sa h avvco h monochomac um bam h oh mos n h vacuum sa. W a h quanz lcc l n h b as a / h h coulng cocn s a ojcon ono h aoa b mo an s n as [9] n n a saal mos ncn on h b an a h b mos. Fo snglmo bs assum a saal mo ol ha s nnn o an. W ma ho suss h b mo ncs n q. o sml h noaon. omng h ngaon ov h volum o h csal an valuang h caon valu q. smls o z z / / snc ~ 5

4 h s h lngh o h csal z z z z an h sgnal/l av vcos a n as ˆ ˆ zˆ z h = no sgnal l mos an ~ z a comonns o h av vco along h z cons scvl. s h o-mnsonal Fou ansom o. Fo gna sgnal an l hoons m a a con angl o h um an o quncs clos o h gna qunc h snc uncon n q. 5 can b aoma o un n a s-o analss. I assum ha h vgnc o h um s nglgbl ov h lngh o h csal.. h csal s sucnl hn an ha h ansvs sha o h um s gaussan can a h sha uncon as 6 Thus ~ h s h cv h o h um bam. In ms o hoon quncs a s-o analss gvs ~ sn v 7 h v s h s-o sson cocn o h nonlna csal. Th collna suaon s oban o.. Calculaon o h coulng cocn Th coulng cocn s n n q.. as h ovla ngal o h nu mos an h b mo. Fo ou calculaons n h collna gom h bs a oson along h z-as. In mns on ns o us a bam sl o saa h bams as s shon n Fg.. lns o ocal lngh s us o ocus collna sgnal an l bams ono ncal sngl-mo bs hough a 5/5 bam sl. Th a coun a s hn masu b sngl-hoon cos D an D connc o a colao. Snc h bam sl noucs consan has acos no h a con amlu ou calculaons ll also b val o hs mn. D lns Sngl mo b Nonlna Csal Sngl mo b BS Fg. : Schmac o h mnal su o mn a hoon coulng n bs D

5 ssumng ha h nu ac o h bs s a h mag lan o h lns an ha lan-av mos scb b h -l nacon-cu lcc l oaos n q. a ncn on h lns can mlo acon ho o oban h lcc l mos a h mag lan o h lns []. W oban sn cos n 8 h s h sanc om h cn o h csal o h lns an s h sanc om h lns o h mag lan. W a also assumng ha a ccula gon o h lns o aus s bng aa b h on-conv lgh. W a h b mos as Gaussan mos [] n b 9 h s h aus o h b mo. Subsung q. 8 an q. 9 n q. oban h coulng cocn as B B h an B a n as B. To-hoon coun a n sngl-mo bs Cons h suaon n hch h b s n h ocal lan o h lns... W assum ha Gaussan ls a us o slc quncs clos o h gna qunc. Thn o an o s-o n h sson o h csal h o-hoon amlu n q. 5 aomas o b a h c n c n b a g g s h m nc bn h con o sgnal an l hoons s h gna has-mach av numb g n s h gou acv n an s h

6 banh o h on-conv lgh achng h bs. To oban h coun a a h moulus squa o h ngal n q.. Tcal hoon cos hav solvng ms much lag han h cohnc m o h on-conv hoons. Th lms n h ngaon h sc o ma hn b an as cvl om o. Th ngaon gvs a la uncon hch ucs a oubl ngal o a sngl -ngal. omng h -ngal an usng h aomaon o a cal banh as - oban o a goo aomaon C 6 h C s h a coun a an. Ths aoachs a mamum hn.. Ths gvs h b aus.5 o omal coulng h s h avlngh n h b. Fo a b am qual o h algh h o h acon an o h au.. h o-hoon coun a n h b s onl 56% o h mamum. 5. Concluson W hav sn om a s-ncls calculaon a ull quanz mulmo ho o scb h coulng o sngl hoons gna b collna T-I SPDC no sngl-mo ocal bs. W hav hus ouc a accal c o mamz h coulng o sngl hoons no ocal bs. s on ou al hs s moan o quanum cogah an quanum communcaon alcaons. Fo h -I collna on-convson su h n no sgncan nnc o h coulng on h ansvs h o h um bam an csal lngh hch hav bn oban o non-collna goms. Th moan aams o h collna cas a sml h hoon avlngh h ocal lngh o h lns an h b am.