Chapter 11: Matter-Photon Interactions and Cavity Quantum Electrodynamics
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- Carol Walsh
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1 Quu Ocs f Phcs Olccs h Cll Usy Ch : M-Ph Ics Cy Quu lcycs. A S-Clsscl Ach Pcl-l Ics I hs Ch w wll s uu hy f h cs bw ch cls lcc fl. P hl f h u c lcs wll b cssy l ssbl hy. Yu h s Ch 5 h h ss wy uz s fs chs u h sul cu ls. Bu c h fl hs b uz s lb sc csuc ch h u s sy sh h w wll. hf h scuss h fllws h cl c wh h fl wll b uu chclly bu h fl wll b clssclly. hs s h s cll s-clsscl ch. Oc w h b subl l scb h c bw h cl h fl w wll h chs u uz h fl Sc.. I uu chcs h bsc f lcc fl h c u f cl ssfs h fllw ul- cu ls wh h cl s As sul f h b cu ls fllw h us s Ch h u f cl s s by h h s s h Sch cu I h sc f lcc fl h ccl u f cl s f s A I s h ccl u h c u whch bys h ul- cu ls h b cu ls h cc sb us f h f ch f h cl c u ccc wh h z fc lw. h ccl u hus lys l scb cl-fl cs uu chcs. I h x Sc w scuss h ccl u l... Ccl Kc Mu f Ch Pcl h s bh h ccl u w s f h clsscl xss f h u f h lcc fl P
2 Quu Ocs f Phcs Olccs h Cll Usy h lcc fl c b cs c-f ss c lul c wh I u-sc h s ss lul us bcus h cs fls hl lll h c f h wc u-sc.. I fllws h W ls h A A h c l c ls b ss lul s A A A Wh h b fs c w h xss f h fl u s fllws P h sc h h h s h b u ws f wh h u f h hs Ch 5. w xl h fs whch wul b z f h w chs csuly f w z. h fs c b w s A A A A A sl cl f ch s h ch sy s hf A
3 Quu Ocs f Phcs Olccs h Cll Usy h h xss b h ss c f h c l s lu h lc f h cl s. h u f h lcc fl s h P A h l u f h cl h fl s Pl A Isly h fs w s h h h s ssc wh h cl s lcy... Quu Mchcs f Ch Pcl h Culb Gu S f w h y chc f h u. W w chs u whch h lul c f h c l s z A h xss f h l u P l lls us h f fs ccl u ssc wh h cl s A A h h l u f h cl h fl c b w cully sl f s h su f h cl ccl u h u f h ss fl Pl cll h Ch 5 h Culb u h u f h ss fl ws f wh h u f h hs. K hs h Culb u h ccl u f ch cl s s css f w s: h c u f h ch cl h u f h lul fl ssc wh h ch cl h suc f whch s h ch cl slf Quz f h Pcl Dycs h Culb Gu: h ch cl h lul fl ch s cs bc wh u ul suls h fllw ul- cu ls hs cu ls ly h h ccl u f h cl h c u s s by h h s s h Sch cu
4 Quu Ocs f Phcs Olccs h Cll Usy 4 Pcl l h Culb Gu: Assu clsscl lcc fl h Sch u f h cl s Wh h l h Sch cu c b w s. A I h s s h l s A A h b xss s l h Culb u. h us w ss wh f s ff chc f h u. hs w cs x... Quu Mchcs f Ch Pcl Aby Gu Cs h fllw u sf. A A A A w w w s by sl-lu scl fuc. h u sf ls h lcc c fls uch. ls h h u sf ffcs ly h lul c f h c l ls h ss c uch. W ssu h u h b u sf h uu s f h cl sfs s w wh s uy. A uy s cs bbls sc w xc h u sf ffc h hyscl suls y wy. f h s f h w c s fllws. Cs h s f h cl If w u sf w xc h s lu ch. hf w w hs ls Sc h cus wh h s y w s I fllws h h s s h ffc f h uy s us lcl ch f hs f h cl wfuc
5 Quu Ocs f Phcs Olccs h Cll Usy 5 w w I s hw h l sfs u h u sf w s f h Sch u w w w w h h Sch u s s f u h uy u sf. w W sll f. f w s f h Culb u whch A A A w u sf A A w w h uy sf h s s h sc w h h sf l bcs
6 Quu Ocs f Phcs Olccs h Cll Usy A w W u h h cc lu f f s h l l. If shul sul h sf l h h s h h sf l wll h h s f s h l l A w w w I h s s h sf l s A w w w Aw w w Sc h fs h sf l b ss h c y f h cl w us h Aw hs suss h h w u h c u f h cl us b l h ccl u by h b u. I h f f h l h s s suss h h ccl u s sll s by h h sf l. hf h Sch cu hf ssfs h fl cu l wh h cl s h b us shw h y by u h l f ch cl clsscl lcc fl c b w s A wh h c ccl l by A h ccl u h s s s h y u A 6
7 Quu Ocs f Phcs Olccs h Cll Usy w ly h Culb u c h ccl u b f s h su f h c u f h cl h lul u f h fl. I ff u h ccl u hs such sl. Gu Ic f h Kc Mu: h u c cul h f c lu c bh. A s hyscl bsbl us ly h f c u u sf bu s lu shul ls ch u u sf. h c u f cl f xl sssss bh hs bus. s hs cs s xc lu A Sus w fs u sf Aw A w I fllws h A A w A w w A w w Aw w Kc Mu Cu ls: I h bsc f y lcc fl ll cs f h c u cu I h sc f lcc fl bs hf h sc f c fl ff cs f h c u l cu! h Puzzl f h l: Cs h l A h l s h -lu f h uu s f h cl h Sch u U u sf h sf l ws fu b A w w w 7
8 Quu Ocs f Phcs Olccs h Cll Usy w w w hf h l s cly f u u sf. w s xc lu chs u u sf w w w w w w w w w hf h l cul s h y f h cl whch s hyscl bsbl. I y u f subcs h cbu c f h scl l f h lcc fl h bs h f h y f h cl. I h s cs h y f h cl s by h c y h l A whch s bh f lu u u sf...4 h A. Ic h scuss h us Sc shw h h f h l f cl clsscl lcc fl h Sch cu s A h sc bw h cl s h uy c-. O c h b l xl - l V h ss h cf l f sl h f cysl whch h cl ss A V h h f h y f h cl s hs cs A V O c lwys chs u whch h scl l f h lcc fl s z hs wll b ssu f w ws. I hs u h l s h s s h f h y f h cl. O c h l w s s shw blw P I P V. A A. A. A I w 8
9 Quu Ocs f Phcs Olccs h Cll Usy I h c bw h fl h cl s scb by. h bl wh h b l s h Ĥ P s cs h l y f h cl bcus s h f h c y f h cl h sc f h lcc fl. A hf h ss f Ĥ P cs h y ss f h cl. Blw w f f h l subl f uu cs...5 h. Ic: h lcc Dl l I s css f ccl s h cl w fucs.. w fucs f lcs s y lclz sc c h cl s. hf y lc A by A h c y h l. hs s cll h l-wlh x. I hs x h l s A s h lc f h cl. hs s A V O c w f u sf h c l f h c y f h l. Sus chss A. h Aw A A A w.. U hs u sf h l bcs V. w w h P I P V. I Sc h c l h lc f h cl hs b u wy Ĥ P w css h y f h cl h bsc f h fl. h I whch scbs cl-fl c s w. h b c l s cll h lcc l l. 9
10 Quu Ocs f Phcs Olccs h Cll Usy. A Quu Mchcl Ach Pcl-l Ics h fl s bul fully uu chcl hy f cl-fl c s h uz f h lcc fl h clus f h fl y h l. W hs s by s h scuss h fllws. b l w clu h cl h scuss. W wll s f clsscl l h w wll uz bh h cl s wll s h fl ycs. h chs f h cls h s lcy cs scly. h ch sy c b w s. h cl clfl l us clu h c y f h cls. A h l us ls clu h y f h fl.. O h h h h l shul ls clu h l y wh s h lcc scl l. hs us u b h cs. us hs w fs h h lcc fl c b cs s lul ss cs wh S h lul c f h fl y bcs h lul fl y s us h l Culb c y f h ch cls clu Culb slf-c. Sc w h ly clu hs c y h..
11 Quu Ocs f Phcs Olccs h Cll Usy h l y b s. h clsscl xss f h l clfl l s hf.. A I c b shw h h b l ss h l y f h cl-fl sys s - s h l y f sys f cls fl uh b. I s css f ccl s s s h ycs f sl cl.. lc wul l xclu Culb slf-cs f h sc sc hy fs bu c b lz wy f s cful. I such css y w h b l f sl cl h fl s.. V A wh V s h sc Culb l f ll h h cls whs ycs h b clu h l hs h cls ssu b sy. ls h ly h ss lcc fl s h xss f h fl y. I shul b h y h b l s u. x w wll uz h b l. h uz f h cl ycs fllws h s h s scuss l. W sul h fllw ul- cu uls bw h cl s h ccl u s Bf w uz h fl w slc u h s c chc s h Culb u whch h lul c l s z. h lcc fl c b uz fllw h ss scuss Ch 5. h fl bls bc s. h sul fully uu chcl l s.. V A I h Sch cu h l s.. V A I h Sch cu h l s clly - bcus h l f y s w clu h sc... h. Ic: h lcc Dl l Cs h l.. V A I s css f ccl s h cl wfuc.. wfucs f lc s wll lclz sc c h s. hf y lc h A by A h c y h l wh s h
12 Quu Ocs f Phcs Olccs h Cll Usy s f h cl. hs s cll h l-wlh x. I hs x h l h Sch cu s.. V A w w wll f u sf h lcc l l. Sus s uu s f h cl-fl sys. U u sf s by h uy h w s s w Sc h l w ss h l y f h cl-fl sys s xc lu us b u- w w w whch ls w llw h s-clsscl ch Sc..5 w ssu A. h clcul f h w l s b cy sc h cs bh h cl s s wll s h fl c suc s. h fl sw s.... w V h ls ss h l slf-y f h cl. I ss bcus h l wlh x fls f s wh y l wcs. I wh fllws w wll h l slf-y sc usls h l... V h b l hs h s... V I P I P O y ls w h b l h sb cu
13 Quu Ocs f Phcs Olccs h Cll Usy... V I P I P h b l wll b us hs Ch. h h lcc fl h b l s clly ss. W wll h subsc h f hs Ch.. A w-l Sys Ic wh Cy Cs h fl w ll sys s cls cy whch sus sl f fucy. h l s I P wh V P I h c f h l I Ĥ c b w subl f. cll h h lcc fl h Sch cu s U hf U h c f h l c b w s I I I cl cl W ssu h h y ss f P Ĥ h f y hf I I I fllws h Cy
14 Quu Ocs f Phcs Olccs h Cll Usy 4 I wh. U.. lb Sc h lb sc w csss f ll ss f h y fl cl xl f w-ll sys s hs h cy h s f h cb sys s w s... Clss l h clss l s fl fl cl... A Isl w-l Sys s sslss Cy Cs w ll sys cul sl s lsslss cl cy. h l s h sc l fllws f h w x. h b l ss clly sl sys. I us h ss s f h f I f h ss h cs s cs h s.. cl u s fl ub s chc f s s f h l hus s s sc Ĥ c s w s. x y hs ls fls. w y h l su s s b
15 Quu Ocs f Phcs Olccs h Cll Usy 5 b b b If w w b s f Ĥ wh lu h w us h. hs ls h fllw w us b b b P lz.. us b. h w us b c b w x f s b b h u b f s bf Cs f Z Du: Assu h x b s w lus h cs cs... h b s f ss h cs s csu h s f ss s f h l Ĥ. h ly s s wh y. hs s h u s f h sys. Quu b Osclls: Sus s l s wh h cl h y ll hs h cy. hf W f. W s f
16 Quu Ocs f Phcs Olccs h Cll Usy 6 s cs h s f h sys sclls bw s cs h cl h u y ll s h h bsbs f s. C h b sul sclsscl sul b l wh w-ll sys subc clsscl xhb ul sclls h h h c by cs w c cclu h h sclsscl b fucy h sh f h clsscl fl. I h fully uu sul w h h b fucy l h su f h ub f hs h fl. Qus: Wh f chs. Wh s? Vcuu b Osclls: Cs h cs wh.. h fl s lly h cuu s. W s cs hs wh cll cuu b sclls. h cuu b fucy s ssu. I hs cs h cl h u y ll s h sus ss h bsbs f s. Cy b Sl: A sys css f w-ll s lsslss cy h -c cs.. cl-fl c hs h fllw y ss s ssu
17 Quu Ocs f Phcs Olccs h Cll Usy 7 Ss s Wh h c bw h cl h fl s s h y scu s s fllws φ φ φ φ φ φ Ss s h c lfs h cy bw h ss sls h w s. hs s cll b sl. hs s cll cuu b sl. h u f h cuu b sl s...4 Ocl ss s Gl ul Cs y ll cul cuu f hh y lls c wh h cy
18 Quu Ocs f Phcs Olccs h Cll Usy 8 Sus h cl s lly h lw y ll h hs s h cy. S h l s f h sys s. h s h hh y lls s by h s Gl ul I h h s s l h ub f hs h cy. w cs y ll cul cuu f lw y lls c wh h cy Sus h cl s lly h hh y ll h hs s h cy. S h l s f h sys s. h s h lw y lls s by h s Gl ul I h h s s l lus h ub f hs h cy. h s clus cbus f bh sul sus ss csss. h fc h suls f h uu chcl s wh h sul s b hyc us wll bf h uu hy f ws l..4 Sus ss f w-l Sys Sc W h s h us Sc h wh h fl ss cuu c us s Gl ul clcul s s. I h xls cs h h fl s ws sl s bu h ssbl fl ss f h cl bl cuu. Ah usful xl s wh h cl fl s s sl s bu h h fl ss bl cuu. hs s h cs wh s h f sc. Cs w ll sys c wh f sc. cll h f sc h lcc fl c b x s
19 Quu Ocs f Phcs Olccs h Cll Usy 9 V V. W ssu h h w ll sys s lc h such h ly h z-c f h fl hs -z l x l. h l s M M V V wh V z M. Sus h cl s lly h hh y ll h s s h cuu s. hf l h fl s cul cs y f h ss whch h cl s h lw y ll h s susly h y f h y s fl Sc h fl ss f cuu c us s Gl ul. h sw s D z V z V V I. h uy D s h sy f s.. h ub f s u lu u fucy l f sc fucy s by c D h sus ss f sc s hf l h h sy f ss f sc. h h sy f ss c b sfcly f us cscl sucus such s hc cysls ccs hby l h sus ss. I fc wh h hl f subly s sucus h sus ss c b hc sl fl c h sus ss f sc clly suss. z y x
20 Quu Ocs f Phcs Olccs h Cll Usy.5 Dycs h Psc f W Dchc f w-l Sys Cul Cy M h lyss h us sc uc h xc ss f h cl-fl l. Dchc s xc ucly sy h l sus h ss h s f h sys wul clls h. I h sc f chc hs w s: Us subl bss s x h sy b W h sb cu h f s usful wh h chc s uch fs h h cuu b sl cs f w chc h l s lly lcbl usful bu s s s s h f..5. h Dsy Mx Ach Sus h sy x f h sys css f w ll sys c wh sl f cy s. Sus h l s s. hf h l s G h l s s sbl ssu h h lb sc l h bl csss f ly w ss. O c hf xss h sy h bss css f ly hs w ss. A h x s h u f h sy s O h x ls f h b u wh sc h bss ss bs
21 Quu Ocs f Phcs Olccs h Cll Usy W h clu h ffcs f chc h b us h ff-l cs f h sy x. W h ssu h chc cllss y sus bw h ss. h slu f h sy x us subc h l c ssu z u s cs s wh As h ff-l cs f h sy x z.5. Dchc h sb Pcu A h ffcs f chc h sb cu uu chclly css wy us s c. W s f h -c l f w ll sys c w h fllw sb us f W w h chc s h ff l cs f h sy x z. S w y l chc hlclly by fy h us f cy s s shw blw wh h cy s sy h uu chcl csscy f h us. s hs h Mully h b w us b h cu ll s h f fs
22 Quu Ocs f Phcs Olccs h Cll Usy Bu sc h sul c b cc. O c s uu chcl csscy f h us by s sucs h us f wh h xl fcs c bu cssy sc hy wll h lb sl Scs h fllw. As lwys w h ssus s s c h w lb Sc. b Sys s cu wh h s s wh. c A B B A h slu f h us s W w f h lus f A B s fllws. W fs ully h fs u by h sc u f h h s h " " "
23 Quu Ocs f Phcs Olccs h Cll Usy W h bh ss f h b u A A " " " hs ls A W w ully h fs u by h sc u f h lf s h B hf B lly w f cu " " I s h cu l w us h " " " Slly c shw h I s css f ccl s wh chc s fs h h f ch f h uls c us h fllw xs A B " " "
24 Quu Ocs f Phcs Olccs h Cll Usy 4.5. Dycs h Psc f S Dchc f w-l Sys Cul Cy M W w cs w ll sys c wh sl f s cy. h l s l w sw h h bsc f chc h xc ss s f h l cul b b. w cs h cs wh chc s l. I h sc f chc h sb us S f h u f Bcus f fs chc s xc ch s sy s lu y fs. Bu w fc u h fs c bf w f h sy s lu. W w h f h u f s z hs s Cy
25 Quu Ocs f Phcs Olccs h Cll Usy 5 W us h b lu f h u f h fl Cs h lu f h sc h h h s c b f wh h by h w ll sys c b f wh h ch h cy fucy u c wh h w-ll sys ls cll fucy ull. W wll hs fucy shf. W w h s s cll h ffl. h u f h c b b slly. W flly h s s wh w h f w w s sucs s s h cl fucs f h s sucs s s s s h cu s s s
26 Quu Ocs f Phcs Olccs h Cll Usy 6 Ph ub u: Us s s w c u f h h ub s s h h h h s ss sul ss. h ss sul bs. h sus ss s h h s s s cs u wh w s. S h s s z-. h s l s s l lu sc s s f ll s. s hs xlcly h us f h fl s f h h l. hs cu s s s l l w w lu s s s s Slly s A hf w f s s h sw s h sus ss. Sc h ls h h ub u s z c f z- h ub s suc s s s s s A w h h ub u s h cl f h h ub s suc s
27 Quu Ocs f Phcs Olccs h Cll Usy h b cl fuc shws h h y css sul ss sul bs sus ss cbus sh s h h ub. hs fc wll b us l us h flucus ls..6 - ss W w clu - ss h us f w-ll sys. W wll w h sb cu. S f h -c l f w ll sys O c w h fllw sb us f h us ss f h b us uu chclly css? us chc Mully h b u by slf h b w us f c bh b h u lyss s cc. W fy h l u z- s suc s fllws h s hf cu ls c b us s s. h b u ls Mully h b u by slf ssu c 7
28 Quu Ocs f Phcs Olccs h Cll Usy If w w w us h c c lx hus - ss s h sh s bh. hs shul c s sus sc ss ccus ly. W ls w hs s ssbl ly f h u f s.7 xl Pu A xl u usully hh w ls c b us sf cls f h lw y ll h hh y ll. hs s ch h ll sch s shw blw. h lx f ll ll s ssu b y fs s h ll cls sf by h u f h lw ll h us ll lx ll ly. Pu I h sc f u h us f h w-ll sys P P P s h s suc h ls h s h u css s cl fuc c b fu us h s hs s w us h cs f h sul s 8
29 Quu Ocs f Phcs Olccs h Cll Usy 9 h us f h uls P P lus h us f chcs cl h sc f sl w-ll sys..8 A w l Sys Ic wh Cy : h ull S f us Cs h fl w ll sys s cls cy whch sus sl f fucy. h l s W clu h ffcs f cy lss lx chc u h sb us. h sul us P P Cy Wu z =
30 Quu Ocs f Phcs Olccs h Cll Usy S S z b S z b S h hs c u f h cy scb by h us u u z b z b S z b z b S h b us csu h cl s f us scb h uu bh f w-ll sys cl cy..9 Cy hc Sus ss h Pucll ffc I h sc f s chc w sw h h sus ss cls cy s by h l Sc. U h cul c b l by cs h sz f h cy hf h lu. W ssu h h w-ll sys s such h hs -z l x l wh ly h z-c f h cy fl. W ls ssu h h Cy
31 Quu Ocs f Phcs Olccs h Cll Usy cy fl s lz h z-c h lc f h w ll sys. Df lu V s U. U V h h sus ss sc.. bcs Cy z V I s s c h cy sus ss h sus ss f sc. z sc D h sus ss h cy wll b l D V h sul b s l h chc s uch sh h h s cuu b fucy ls uch sh h h cy h lf.. Blw w cs wh hs wh h cy h lf bcs sh h h chc ls uch sh h h s cuu b fucy.. W cs w ll sys s cy cul wu s shw blw. h ss cul s bw h cy fl h w ll sys bu bw h cy fl h wu. As sul f hs cul h cy bcs hybz wh h s f h wu. Cy z = Wu I h fs clcul s w wll h cul bw h cy fl h w-ll sys ly cs l s ub clcul h sus ss. Cs fs h sb u f h cy fl
32 Quu Ocs f Phcs Olccs h Cll Usy z b W w h z b h subsc hs b uc h f h fl xlcly c h h s f h h lf c. W h slu f l s h l bw h h s h cy fl s z b z b Us h lu f h cy fl clcul b l f l s w b h b u xsss h l bw h s f h h lf s. W us I h Sch cu h b u shws h h cy s u f wu s f ff fucs h c h cy s f whl h l. h xss b ls shws h h wu s wh fucs cls h sc fucy f h cls cy h s. W w clcul h sus ss. h c f h l c b w s h l s f h sys s l
33 Quu Ocs f Phcs Olccs h Cll Usy h fl s cul cs y f h ss whch h cl s h lw y ll h s susly h y f h wu s h h c fl Us s Gl ul h sus ss bcs Cy h sus ss sc.. s 6 V z Cy W c c h cy sus ss h sus ss f sc. D z sc h sus ss h cy wll b l D V 6 h hc xss by h xss b s cll Pucll hc. W c ls w h c f Pucll hc s f h cy uly fc Q D V Q 6 A l Q cy wh sll lu V c hc sus ss s by fcs s l s 5-. I h l cs wh h chc h cy h lf cbl bh uch sh h h s b fucy h fllw sul c b wh ll l ff Cy h l fucy c b f h clx l h fl sul s V z Cy
34 Quu Ocs f Phcs Olccs h Cll Usy I c b s h h b xss ucs h cc suls h w ls scuss l.. W S Cul s Quu Cy lcycs h b scuss shws h -h cs cy c b cz s fllws: S Cul : uu chcl chc bw s f f s. W Cul : uu chcl chc bw s f f s. I hs cs c lly b scb s f sul sus ss.. A Cllc f w-l Syss Ic wh Cy Cs cllc f w-ll syss c wh sl s cy scb by h l wh Cy Wu z = If w f 4
35 Quu Ocs f Phcs Olccs h Cll Usy 5 h wh hs fs h l c b w h fllw fl f h ly fc hs b wh w wh h b l s h h su uls h cs f w-ll syss h cs f sl w-ll sys. h sb us s h us sc uch. h l s f h sys s scf by scfy h l s f ll h w-ll syss s wll s h s f h. xl f h sy f h -h w-ll sys s h h sy f h full sys s by
Chapter 8: Propagating Quantum States of Radiation
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Chapter 5: Quantization of Radiation in Cavities and Free Space
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