Chapter 8: Propagating Quantum States of Radiation

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1 Quum Opcs f hcs Oplccs h R Cll Us Chp 8: p Quum Ss f R 8. lcmc Ms Wu I hs chp w wll cs pp quum ss f wus fs f spc. Cs h u shw lw f lcc wu. W ssum h h wu hs l lh qul h -c wll ssum l. Th lcc cs s fuc f l h w pps h cs. Th w qu s c W fs f h ms f h ffl p W ssum ms f h fm wh c Th ms ll h ss m h pp c. N h Df Th ssfs Cl Cl C

2 Quum Opcs f hcs Oplccs h R Cll Us. c Nml f h Tss Ms:. Ohl f h Tss Ms: m m. Ohl f h Ms: m m. O c p h c pl ms f h ms s fllws q Th l f mpls q q ssum pc u c h -c fs h fllw qulc p q Th q p Tl f h fl s q p..

3 Quum Opcs f hcs Oplccs h R Cll Us 3 8. l Qu s f w l h fls cm ps mps h fllw cmmu ls h fl mplus m m p q Df p q p q N h p p q q W h fllw cmmu l f h c suc ps m m Th ml cms Th ml s h fllw m pc f h fl c suc ps 8.3 Slwl V lp ppm I m css f pccl s s s fls h wh c u pcul wc p l sl ss m. Tpcll h ss m s h lws m I hs Chp w wll l wh l sl ss m s w wll p h ss m fm w ws. h sl m w cs h s usull -- lshp w h wc h fquc h huh f h sps l qull h s l s shw h u. Supps

4 Quum Opcs f hcs Oplccs h R Cll Us 4 O c Tl p h wc h hh f ! 3! wh h up lc h sps ll h hh spss f s Sc h wh s c u qull w c w s I s c fc u h fs m pc f h p f -c f fls h p s p f m. W h O c w wh

5 Quum Opcs f hcs Oplccs h R Cll Us 5 Smll ls Th qus h js cll h slwl lps sc h fs spl m pcs h fc u. W c ls w h fls s Wh h p s ] [ 8.3. w lw Th pw flw p sc h -c s h p S

6 Quum Opcs f hcs Oplccs h R Cll Us 6 S.. Us h c c. R w S If s h cuum cu S h S c w s S wh s f ] [ Sc S s h p f flw p sc h qu mus h p f ph s.. um phs p u lh. N w lk h pps f h p m l Th C Dsuc Ops Th p ssfs h qul m cmmu l ] [ s ] [

7 Quum Opcs f hcs Oplccs h R Cll Us 7 lhuh h cmmu l s cl l fuc spc c ppm s p kps m h h wh f h ppm l fuc spc s f h f. Smms h pss f s w s l s ] [ u s l. Ths c sc h s -- lshp w. T c l h Thf ] [ N h Nw u h h Sch p cs ph ppml h lc h p ss ph h lc. Rcll h ] [ Th quum s csps sl ph lcl h lc. s h h p cs sl ph s supps f ff wcs

8 Quum Opcs f hcs Oplccs h R Cll Us 8 Nw w wll s wh hpps wh ks h s s s ph ff lc Supps If succssfull s h ph c h fs sp h shul h sm s h cuum s h puc shul. S w lu Th sul lls us h c s ph l h sm lc whch ws c. Th ps c s sl ph h lc. Rcll h h l fuc h cms fm h cmmu l hs fc sm f spl wh f h f h s wh. S h ph c s lcl spc f s f h f h s wh Tm-Dpc: Th Tll W qu W w su h m pc f h p. If lus s Th ls m s - l f h p hs m pc. I h cs f -c f fls hs m-pc. Bu h cs f fls c wh m c m-p. I h fs m h h h s us h Tl ps f h wc 3 3 3! h s u sfm w

9 Quum Opcs f hcs Oplccs h R Cll Us 9 ] [ ! Th ms s h cks h h h s sc h ffcs f sps ll s h sc m scs h ffc f cs. I h cs f -c -sps wu f w ls S u qu cms Slu s Ch h umm l O c ls w h slu s Th pss mpls h h slu l m s sl s f slu l m Tm-Dpc: Th s ppch O c ls us h s qu s hw h p hs m. W h m

10 Quum Opcs f hcs Oplccs h R Cll Us Th m-pc f h p s h s l. T s hs cll h h s p s Th csp Sch ps Th m-pc f h suc p s Thf O qull N h Ths s cus w h s m-p pl h f f h p. Nw w c w S h s p csp h p s fc. -c wu f wh h l s f -c -sps wu f wh w ls h w s s s h Th s h sm sul s h l sl h ll w qu f c -sps wu

11 Quum Opcs f hcs Oplccs h R Cll Us qul-spc Cmmu Rls W kw h -sps -c wu w c f smpl pss f h qul-spc cmmu l Us h qul m cmmu l w Spc Gl Th scuss s ls l f-spc pp f w ssum h sps l f f spc c c 3 h h cs f f spc Th ss ms c chs s css h ms wll h ps pl ws wh f ss s pp h c. If w w cs m wh f s h ss c h w wul cs ppp f spc ms such s m-guss ms whch cs h ms wul c h ss c wh sc f hs cc c s smll scs f s h c smpl plc h ss m h lu Op W h s h h flw p sc s S Th ph flu p s hf Th p u pus lss wh h ss m pfl. s h um f phs pss p sc lc m h Ds Op Sc h ph flu p s Th ph s p p f h um f phs p u lh mus hf

12 Quum Opcs f hcs Oplccs h R Cll Us h Num Op O c f ph um ps f pp pcks w ws. Th ph um p lc f ph pcks s f s N Th p N csps cu phs pcks whl s f lc. Th p N csps h ph um msums m phc. Th ph um p m f pcks c ls f s N Th p N csps h um f phs h ph pck s. -c -sps wu f w h hf N N N Sc s chs N N S f -c -sps wu h ph um p f pck s h sm whh cus phs s ps s h pck psss f cus h phs s h pck. Sc h s lss f phs h sc f cs h ph um p f ph pcks s p up hw s h cu. 8.4 p Quum Ss I h fllw Scs w wll cs sm smpl pp quum ss. W wll lws l wh -sps -c mum f whch ssfs Slu f h qu s

13 Quum Opcs f hcs Oplccs h R Cll Us 8.4. h Num cks W f s Th qul m cmmu ls Th ph s p s Sl-h cks: Cs h s Th s pss sl ph lcl m wh up lc. I s ph pck cus s l supps f sl ph um ss wh ff wcs W c f u m u ppl h s p Thf s s f h ph s p. Th lu s cl wh wul h pc f lcl ph. Th s s ppl ml. Th s s ml lcl. Wh f w w csuc s csp ll f sl ph pck h s s shpl lcl ls whs s s ppl ml hf m lsc. Cs h s Th m f h s s wh lu 3

14 Quum Opcs f hcs Oplccs h R Cll Us " " " = " " " w. Th s s ph s p s sc s l supps f ph s ss. W c clcul h lu f h ph s f h s s fllws " " " O w h fl sul s m ll h suc ps pp h pss ws h h us h cmmu ls. N h " " " " " " " " Th sul mpls " " " Thus h ph s s su spc wh pl su. W l kw h cc us f /sc. ls h. Th ph flu s hf whch hs h 4

15 Quum Opcs f hcs Oplccs h R Cll Us 5 ~ wh ~ s h u sfm f. Thf s l supps f sl ph ss f ff wcs ch wc h l supps s wh ~. W wll w hs ss s Tm-Dpc: Wh f w lu? I m w pc h sl ph pck h ll sc. ssfs Smll Thf. Sc f ll Thf m h ph s hs m fw. Mul-h cks: I csuc pcks c phs w c l s fllws. Cs h s! O c shw h f. us clcul h ph s

16 Quum Opcs f hcs Oplccs h R Cll Us! Th cmpu s c u shf h m h lf us h cmmu ls. Th sw s 8.4. Ch S h cks Cs h s f lw f cmpl fuc ps f p T T h S : T T T T T s ml T T T T T T c T T T T T Thf s s f h p. s fc ll ch s pck. Th lus f h ph s p h ph flu p Jus lk cls c ch ss ch s pck s l supps f ph um pcks. Th s cs c um. Supps N h N s h ph um h s. T s hs w us h p f h l um f phs lc N clcul h ph um f h s 6

17 Quum Opcs f hcs Oplccs h R Cll Us 7 N N Thus s ch s pck wh ph um qul N. Wh u ph um flucus? W s fm N N N T T N Thf N N N N Th s ph um s qul h m s pc f ch ss Cuus-W CW Ch Ss cuus m f lh s cls cmm pc h ulsh pulss pcks. Supps w w csuc ch s csp cuus lcmc w f phs pw.. flw/sc qul. Th ph flu s h s p f lc. W f cmpl fuc s

18 Quum Opcs f hcs Oplccs h R Cll Us 8 Th. cuus w f cs pw wll h f lu f h ph um. Th ph flu s ls Th flu s p f h lc. h lu Ns: W w lu h s h ph flu f h cuus w ch s. W kw h flu s. Blw w clcul h flu-flu cc fuc T T Is T T w ch p. Th lf h s fuh smplfs Th ph flu s cc fuc s h wh

19 Quum Opcs f hcs Oplccs h R Cll Us 9 h Th s h ph flu s l cl m. Th spcl s f h ph flu s s S S s fl hs lu qul h m ph flu. Thf h ph flu f cuus w ch ss hs sh s chcscs. I fc s ffcul shw h h s ph flu s cl sh s. Ths s s sul. I ss h ps s lc s phs cuus w ch s f wll s h ph l ms cmpll ucl Tm Dpc f p Ss h Sch cu Cs sl ph pck m wh W w f h s l m. Rcll h Th s s fu s fllws

20 Quum Opcs f hcs Oplccs h R Cll Us N h w h h f cuum h. Th sul shws h m h wpck hs m fw spc. s h mpl cs ch s pck m W w f h s l m. W Quu Ops Quu Ns f p Ss Th quu ps f pp ss f s N h ulk h quu ps f c fls quu ps f pp fls h us f s squ f lh. s mpl cs ch s wh Th lu f h quu s Tm = Tm

21 Quum Opcs f hcs Oplccs h R Cll Us Rcll h Smll S w cs Th lu f h quu s s Th qus sk s wh s h quu s? s u wll s s mful lu qus such s. Is w lk h quu s cl fucs. W ssum s f ch s f 4 Thf h quu s cl fuc s 4 Smll c shw h

22 Quum Opcs f hcs Oplccs h R Cll Us 4 I l f ch s 4 l h cus w h s h f ch ss s c h m squ quu flucus qull 4 f quu. pp ch ss h quu s cls l-cl wh wh ppl 4 f quu.

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