Chapter 9: Loss in Quantum Optics

Transcription

1 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy Chp 9: ss n Qunum Opcs 9. Opcl Bm pls: n Inducn Dscn phn lss n qunum pcs s n s sh fwd s n clsscl pcs. In hs scn w wll s wh hppns whn n pcl m s nud whn s suffs lss. Th smpls cnssn pcu f lss s nd wh n pcl m spl nd h suls cn usd mdl ln pcl lsss f ny nd. 9.. Clsscl Dscpn f Bm pl upps cnnuus w pcl m s ncdn n m spls s shwn lw If h mplud f h ncdn m s nd s pw s nd pw f h nsmd m P wh P hn h mplud P P nd f h flcd m w h P P m spl s cully fu-p sysm wh w npu nd w upu ps s shwn lw. Th mpluds h upu ps ld h mpluds h npu ps n h ms nl wy y h scn mx ls clld h -mx Th fm f h mx cnss pw nd pss h m sl symmy

2 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy Oun pw snc Incmn pw 9. Qunum Dscpn f Bm pl Qunum dscpn f m spl s ll m cmplcd hn h clsscl dscpn. upps w h qunum s f lh cmn n fm h npu p s shw lw W wn s wh h m spl ds. n qunum ss mpls wn n h chdn pcu. Bm spls hndld n smpl wy f n ws wh ps nsd. 9.. Bm pl n h sn Pcu In h u w h fu ps cmn h m spl. Th w npu ps nd w upu ps. smplcy h cl s wll s h hnl xs lld wh nd h m spl s lcd n h xs. Th dsucn ps f h w npu ps nd nd h ps f h w upu ps nd. Th nl s s cmn n n p. cn ny phn pc cd m nd lcld wh. xmpl snl-phn pc wuld wh d d

3 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy s cmplly lcld n h npu p nd s dpcd lw. chn s pc n lcld wuld d wh pcls num f d h ln wn h npu nd upu ps f ll ms s nc w h judcusly chsn h lcn f h m spl n h h cl nd h hnl xs h phs fcs wll cncl u nd n s lf wh h smpl mx ln f ll m On cn fy h h cmmun ln h upu ps psd

4 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy Thf h mx ln f h m spl ls pss h cmmun lns f h upu ps whn hy hld f h npu ps. Th phn flux ps f ll chnnls upps h ncmn qunum s m s wh Wh s h s n p nd p s n h cuum s Ths mns nd s h ncdn flux n p lcn m. 9.. Oun Phn lux W nd fnd h phn fluxs n h w upu ps m h s l nuh h h qunum s hs n ps h m spl. W fs lu nd f Bu Thf

5 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 5 mlly n cn shw h 9.. Oun Phn lux Clns s n h clsscl spl h ns nducd y h m spl cn sudd y ln h phn flux cln funcns. W fs clcul h phn flux cln funcn n h upu p f nd nd. Th nly nn- ms

6 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 6 W h usd h fc h h fnl sul s. Th ns n h phn flux dfnd s cn nw cmpud f upu p Th fs m n h h hnd sd psns h phn flux ns n h npu p nud y h m spl. Th scnd m psns h ns ddd y h m spl. c h hs scnd m s nn- nly cus f h cuum flucuns h cm n fm h npu p f h m spl. Thf h ns ddd y h m spl cn undsd s du h nfnc wn h npu snl n p nd h cuum flucuns nn h m spl fm h npu p. Th spcl dnsy f h phn flux ns n p s If w l hn w h sm sul s nd n h clsscl nlyss mly f h upu p n ns nd

7 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 7. Exmpl f Cnnuus W Chn : upps wh s cnnuus w chn s d nd P Th phn flux s qul P f Th phn flux ns cln f h npu s P f Th upu flux n p s. P Th ns n h flux n p s P P Th spcl dnsy f h phn flux ns n p s P P If w l hn w h sul fml fm h clsscl nlyss n h cs whn h npu hd sh ns p p p P

8 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 8 W s h whn h npu hs sh ns h upu ls hs sh ns. Exmpl f Chn Pc: upps wh d nd phns n h pc num f d Th phn num p f pcs lcn s d W h f f ls snc On cn n m fm h phn num n h nsmd pc n p d d d

9 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 9 s xpcd n lsss phns n h spl. Wh u flucuns n h phn num f h upu pc n p? d d d d hn Th flucun n h phn num n h nsmd pc s ls qul h mn phn num. Th pps f h cnnuus w chn ss nd chn s pcs sujcd lss fm h m spl pn h fc h h upu ss ls cnnuus w chn ss nd chn s pcs spcly. Ths ppy wll pn nx. 9.. Bm pl n h chdn Pcu Exmpl f Chn Pc: upps wh d nd phns n h pc num f d

10 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy W wn fnd h s l m whch s l nuh such h h pc hs y hn n ps h m spl. cll h W d d d d Th nfn cuum ny hs n nd. Th m spl ln s Thf d d d W cn w h sul s

11 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy d d d d d Th sul shws h h s l m s chn s pc n h upu p nd chn s pc n h upu p. Th mplud f h nsmd pc s scld y h nsmssn cffcn nd h mplud f h flcd pc s scld y h flcn cffcn. Chn ss hus mn chn ss whn undn pcl lss. Exmpl f um Pc: Ms qunum pcl ss wh h xcpn f chn ss nnld wn h w upu ps n m spl. Ths s s llusd y cnsdn snl phn pc ncdn fm npu p d wh d W wn fnd h s l m whch s l nuh such h h pc hs y hn n ps h m spl.

12 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy d d d d Th cuum ny hs n nd. Th m spl ln s Thf d d d d d Th qunum s l m s ln suppsn f h phn n h upu p wh cuum n h upu p wh ply nd h phn n h upu p wh cuum n h upu p wh ply. Th fnl s s n fc n nnld s. h chn s pcs d n nnld wn h w upu ps s shwn n h pus xmpl m Cmmns n ss n Qunum Opcs In h pus cns w sw h whn m suffs lss nd s nud ns ls s ddd h m n h pcss. xmpl h m spl ln mpld h f snl cmn n n p h snl ln n p s n y Th ls m n h lf hnd sd psnd ns du h cuum flucuns n n h upu p fm h npu p. W ls sw h h ddn f h ns ws ncssy n d h ps h p cmmun lns h upu. Ths sns sus h qunum

13 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy mchnclly cnssn mdl f lss n qunum pcs cn dlpd h s ndpndn f h mcscpc dls f h lss mchnsm y nsun h psn f cmmun lns. In h nx cn w dscuss such mdl. 9. Qunum Dscpn f ss f Ppn s nn-dsps nd nn-ncn wud f f f-spc w dd h lln w qun upps h ppn s n plc n mdum h hs lss. In d mdl h lss w cn dd m n h h hnd sd wh s h pw lss cffcn uns: p un lnh. Th qun lhuh clssclly cc s qunum mchnclly ncnssn. W nw h s s f h lln w qun wh lss pss h cmmun ln. Dfn chn f ls W W cn nw fnd h qul-m cmmun ln m If m hn m. W s h h cmmun ln dcys nd s n psd. Ispc f h mcscpc dls f h lss mchnsm ns s nducd dun ppn n ny lssy mdum. T mdl hs ns w nduc qunum nn ns p s fllws W mps h fllwn cmmun ln n h ns p

14 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy Th ns ps h mn lus Th n s wh spc h dnsy p dscn h ns sucs. lun s d Th cmmun ln s Th cmmun ln s psd f. Thus h cc qunum qun n h psnc f lss s In ms css n mpss ddnl cndns n h nn ns sucs h ccmpny lss Ths cndns nsu h h phn flux ys s n mh nuly xpc. Cmmn n s: In d m h n pcdu n h psnc f nn sucs xplc supps h nl s f h dn md s nd h cspndn dnsy p s. upps h nl s dscn h s sscd wh h lss s. Th s psns hs ds f fdm n whch h ny ls fm h dn md s n. Th s ds f fdm ls spnsl f njcn ns n h dn md. Th s f h cmpl sysm s hn n y h dnsy p. ll n n h sn pcu s pfmd wh spc h dnsy p. 9. Qunum Thy f ss f Cy Mds Cnsd cy s shwn lw. W ssum h cnns nly snl dn md nd h mlnn s Cy

15 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy Th cn nd dsucn y h qul-m cmmun ln â Th m dlpmn s n y h sn quns d d d d I fllws h d d n d d n n w w ssum h h cy cnns lss. In h psnc f lss spc f h mcscpc dls f h lss mchnsm h phn num shuld dcs s n n T mdl lss w y y ddn dcy ms h p quns d d d d w dn n d nd n n n n Th cn nd dsucn ps m I fllws h h qul-m cmmun ln m s If m hn m â Th cmmun ln dcys wh m. Thf u mhd f nducn lss s qunum mchnclly ncnssn. Equl-m cmmun lns lws f nu. If hy fund ld mns h n hs md ms. T mdl lss ccly w nd nduc h ns h cms wh h lss. W mdfy h cn nd dsucn p quns nd nduc nn ns sucs 5

16 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 6 d d d d Ŝ nd nn ns ps nd h nly qumns w mps n hm s h hy ssfy ln h Equns n ns d d Th qul-m cmmun ln s d d d If hn f ll m. Thf n h psnc f lss h cc p quns d d d d wh upps w wn fnd h phn num m. W h d d n n Th phn num s n T n In d n h nu sul n n n mus mps h fllwn ddnl cndn n h ns sucs Th ln nd h cmmun ln f h ns sucs mpls h w mus ls h

17 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 9.5 Wud Mdl f ss n Cs Cnsd cy cnncd wud s shwn lw. Cy Wud = W ssum h h cy hs snl dn md. Th mlnn f h dn md f clsd cy.. cy wh n wud chd s In h psnc f h wud h mlnn mus nclud h cupln wn h cy md nd h ppn md nsd h wud. Th dls f hs cupln s yu wll s wll un u unmpn. W ssum h n h psnc f h wud h cy md xpncs lss snc ny s nsfd fm h cy md h ppn md nsd h wud. In h wds h ny ls u fm h cy n h wud. W cn mdl hs lss y ddn dcy ms h sn quns f h cn nd dsucn ps nd â spcly d d d d s dscussd l h lss mus ccmpnd y ns whch cn mdld y nducn nn ns sucs d d d d Th quns dqu f dscn h cy lss du cupln wh h wud. w h w wll dscuss mcscpc mdl f h cy lss du cupln h wud wh h m clfy h n f h ns sucs. s sul f h cupln wn h cy nd h wud phns nsd h cy cn l n h wud. Th ps nd snd f h wud mds mn n h lf nd h dcns spcly. 7

18 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 8 d d Thy ssfy h fllwn qul-spc nd qul-m cmmun lns nc w nsd nly n hs wud mds whs fquncy s cls h cy fquncy w chs such h fquncy cy. Th cupln wn h cy nd h wud s n n ccun y h fllwn qun d d Th ls m dscs h cupln f h lf-mn flds n h cy. Th m hs n ddd m sn p u f h slwly yn nlp p. Th cupln cnsn mns dmnd. Th cspndn qun f h cn p s d d Cmpn Equns nd wh nd w s h hy quln pdd h lu f h cupln cnsn s. Thf h phnmnlcl nn ns sucs ld h wud ps s On cn fy h ll cmmun lns nd s nln ps Ŝ nd ssfd wh h dfnns. Th ns h ccmpns phn lss n h wud s du h cuum flucuns cmn n h cy fm h wud. Th fnl mnn qusn s hw dsc h phns ln u n h wud nd mn h h. W nw h h phn num nsd h cy dcys s n d n d h phn flux n h wud n n h h dcn mus qul h f phn lss n h cy n In d n h ln n mh cnjcu h

19 Qunum Opcs f Phncs nd Oplcncs hn n Cnll Unsy 9 Th ln s ncc. mus ls nclud h flcd p f h lf-mn fld.. h p h ds n m n h cy. w y c Th pm c nds dmnd. ln h Equn d d n ns d f susun h sul n h xpssn f w c d m h xpssn h qul-spc cmmun ln f s. c c Th lf hnd sd mus qul. Thf c mus qul. nlly w cn w h w quns dscn h cupln wn h wud nd h cy s d d Th cspndn quns f h djns d d h hs quns dpnd n nly n pm h lss. Th lu f s dmnd y h dls f h cupln wn h cy nd h wud. In nl cy cn h m hn n suc f lss.. ml lss nsd h cy dn lss wud lss. ch dsnc lss mchnsm n cn nduc n ndpndn nn ns suc.