Photon Statistics. photons/s. Light beam stream of photons Difference with classical waves relies on different statistical properties
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1 hoo Sascs Lgh beam sream of phoos Dfferece wh classcal waves reles o dffere sascal properes Average cou rae correspods o Iesy of lgh beam Acual cou rae flucuaes from measureme o measureme The pulse aure of he phoo cou s he evdece of he dscreeess of phoo? Or cosequece of deecor properes? Deeco of a lgh beam low esy by meas of phoomulpler ube MT or a avalache phoodode AD IA N / phoos/s Average umber of phoos hrough a cross-seco u me cous/s Average umber of cous regsered by deecor coug me L5/
2 IA hoo Coug phoos/s N / cous/s Ma cou rae deermed by recovery me of deecor «dead me» ~ ms 0 6 0% 0 W J ev Hz m cm - 6,40 8, , ,0340,600-9,480 4, , , ,360-5, ,3360 -,9860-5,400-6, ,0,9860-3,400-4, HeNe mw aeuaed by 0-6 ev W 0 9 3, 0 9,6 0 9 phoos/s s 30 cm 0,s 3cm 3,phoos 0,3phoos,8 0,6 L5/
3 Cohere lgh sasc Sasc of cohere lgh s osso dsrbuo p ep! robably for phoos Idepede radom eves oo mea square devao elave amplude of flucuaos L5/3
4 Classfcao by sascs A cohere beam of cosa esy s represeed by osso sascs Iesy flucuao Super-ossoa sascs Sub-ossoa dsrbuo o-classc lgh beam Sub ossoa ossoa Super ossoa No classc erfecly cohere lgh arally cohere, ucohere, hermal emsso L5/4
5 Super-ossoa lgh L5/5 Blackbody emsso, e.g. hermal radao a equlbrum / ep 3 T k ω c π ω ω = W ω B T / / B B T k E T k E = ep ep Bose-Ese dsrbuo ep T k d d B / T k ω B e d d d d Every me a esy flucuao s prese Super-ossoa dsrbuo. Mos of epermeal lgh sources
6 Super-ossoa lgh Every me a esy flucuao s prese Super-ossoa dsrbuo. Mos of epermeal lgh sources Blackbody emsso, e.g. hermal radao a equlbrum = W ω T ω π c = ω 3 = ep ω / k B T ep ω / k B T Wave Nose Typcal of he dscree parcle aure of he lgh L5/6
7 Super-ossoa lgh Lgh from a sgle specral le of a dscharge lamp, chaoc lgh, has a paral coherece due o he phase jumps coseque o he collsos, he oal esy flucuae me aroud he mea value. Thermal radao Off-Equlbrum E a e Ī I c E c E a IA phoos/s hoo flu o cosa due o flucuaos o a me scale of he order of coherece me c If c addoal flucuaos are sgfca Quaum + hermal + coherece Oherwse coherece flucuaos dsappear he average L5/7
8 Super-ossoa lgh Lgh from a sgle specral le of a dscharge lamp, chaoc lgh, has a paral coherece due o he phase jumps coseque o he collsos, he oal esy flucuae me aroud he mea value. Thermal radao Off-Equlbrum W W W W Frs corbuo ' d' = Quaum Nose Secod corbuo hermal + coherece ose = Classcal/Wave Nose W cou rae deeco me erval If o esy flucuaos ad cosa me, would rever o a ossoa L5/8
9 Sub-ossoa lgh Sub-ossoa lgh s «more sable» ha perfecly cohere beam. No classcal equvalece Typcal quasc sae epreseed by umber sae > Fock saes 0 Mamum phase deermao Mmum esy deermao I 0 L5/9
10 Degradao of phoo sascs by losses Loss sources he deeco processes degrades he regulary of he phoo flu makg dffcul he observao of sub-ossoa lgh effce colleco opcs oly a fraco of he lgh emed from he source s colleced; losses he opcal compoes absorpo, scaerg, or reflecos from he surfaces; 3 effcecy he deeco process mperfec quaum effcecy. L5/0
11 Sem-classcal heory of phoodeeco hoomulpler: Esseal process geerao of prmary elecros o he cahode such ha I =I +. Emsso probably of a phoo-elecro shor me erval. Neglgble probably for emsso of phoo-elecros ', ' 0 ', ' I ' 0 ', ' I ' ' ' 3. Eves a dffere mes are depede, ' ', ' ', ', ' I ' ', ' I ' ' 0, ' ', ' d d ', ' I ', ', Cha of recursve equaos ' L5/
12 Sem-classcal heory of phoodeeco d d ', ' I ', ' hoomulpler: Esseal process geerao of prmary elecros o he cahode, Cha of recursve equaos d, ' d' ep ep 0 ' I '' d'' d ep d', ' such ha I =I + ', ', ' I ' ' I '' d'', ' I ' d d ' I '' d'' I ' I ' d' ep I ' I ' d' d d ', ', ' I ',0 0 0 I, I ' d' 0 0, ep I ' d' ep I,, I ' d'! ep,0 0 I ' d' L5/
13 Sem-classcal heory of phoodeeco hoomulpler: Esseal process geerao of prmary elecros o he cahode, I ' d'! ep I ' d' A se of measuremes yelds dffere values I ca flucuae wh sarg me I, ep I,! Average of he cou probably over a large umber sarg mes esemble average = me average L5/3
14 Sem-classcal heory of phoodeeco hoomulpler: Esseal process geerao of prmary elecros o he cahode I, ep I,! Cosa esy I, I I! ep Classcal sable wave equvale o quaum mechacal cohere sae Also for chaoc lgh f r >> c Chaoc lgh wh r << c I, p I I I e I I adom walk case I Sgle mode of a hermal source L5/4
15 Quaum heory of phoodeeco N deeced phoo. If = he N=. If = he N = =N 3. If << he N =N whaever lgh los phoos N N Varace of umber of phoo-cous Varace of umber of phoos Deecor s quaum effcecy = key eleme o fahfully measure lgh radao sasc Ay opcal loss lgh deeco process ca be see lke a casual samplg a beam-spler. Opcal losses deerme a degradao of he regulary of phoo flu. L5/5
16 IA hoo Coug phoos/s N / cous/s Ma cou rae deermed by recovery me of deecor «dead me» ~ ms 0 6 0% 0 W J ev Hz m cm - 6,40 8, , ,0340,600-9,480 4, , , ,360-5,9980-3,3360 -,9860-6,400 3, ,9860-3,400-4, HeNe mw aeuaed by 0-6 ev W 0 9 3, 0 9,6 0 9 phoos/s s 30 cm 0,s 3cm 3,phoos 0,3phoos,8 0,6 L5/6
17 ose L L L Sho-ose phoododes hoo flu > 0 6 pho/s phoodode reverse bas V 0 L ose e e e L L L L hoocurre esposvy 0 0
18 e e e Sho-ose phoododes ose L ose. ossoa beam =>. =ef <> Weer-Kche ose f s =e L f <> Whe ose Sho-Nose s Classcal flucuao compoe elecrc ose of he crcu, mechacal ose of he laser cavy, wave flucuao always prese A hgh frequey, deecor respose lm / D L5/8
19 ose f=e L f <> Sho-ose phoododes T:sapphre ±3 Mhz Nd:YAG 66mW@064m Badwdh 00kHz log dbm 0 0 ower referred o a sadard value of mw mw Lear relaoshp Classcal ose ca be reduced Quaum=sho ose cao mmze DC compoes lke dark curre ad badwdh Nose eaer Boh orgae from source ad deeco Opmze produco ad deeco Balaced deecor Negave feedback compesae for flucuao oly classcal corbuo Sgal from he wo decal deecors are subraced. All classcal flucuao are washed ou L5/9
20 Sho-ose phoododes He:Ne Badwdh deecor 00kHz 0.43 A/W Deecor esposvy 50 W Load essace. Deecor s quaum effcecy. Average phoocurre 3. MS curre flucuao 00kHz 4. Nose power dbm afer amplfcao 0dB 00kHz e V 0.43 A W 0.84 Quaum effcecy 0.43 A W 0 W 4. 3mA rms ef e A Average hoocurre MS Curre Flucuao ose L e W rms Nose power 0 Ampl 0 3 ose 0 ose 6.90 W 9. 6 dbm Amplfed Nose power dbm L5/0
21 Observao of sub-ossoa sascs Lgh source wh sub-ossoa sascs Hgh quaum effcecy deecor ~ N Emsso a ev 53.7 m Sascs of emed elecros s ossoa Bu a small cahode volage se of Hg emsso or Space charge regme Sub-ossoa dsrbuo for carrers aode curre Very small devao from ossoa for phoo sascs due o low 0.5% deeco effcecy poor phoo colleco ad quaum effcecy of he deeco sysem Eced sae lfeme much shorer ha me scale of he elecrcal curre flucuao used for geerao of aomc ecao Space charge regme Low V 0,6% MC Tech, BEA Saleh, J.Op.SocB, L5/
22 Observao of sub-ossoa sascs Lgh source wh sub-ossoa sascs Hgh quaum effcecy deecor ~ N LED or laser dodes have go much beer effcecy. Elecrcal ose deermed by hermal ose of he ressece ca be reduced well below he sho ose. V kb T / e k b T~5meV AlGaAs LED 875m Drve curre srogly sub-ossoa If LED effcecy s hgh log db 30 dbm 0 0 mw L5/
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