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Publié par | ruprecht-karls-universitat_heidelberg |
Publié le | 01 janvier 2009 |
Nombre de lectures | 7 |
Langue | English |
Extrait
Dissertation
submittedtothe
CombinedFacultiesfortheNaturalSciencesandforMathematics
oftheRuperto-CarolaUniversityofHeidelberg,Germany
forthedegreeof
DoctorofNaturalSciences
putforwardby
Diplom-PhysikerRobertFleischhaker
borninLimburganderLahn,Germany
Oralexamination:October28th,2009
Lightpropagationin
denseandchiralmedia
Referees:
Priv.-Doz.Dr.J.Evers
Prof.Dr.M.Weidemu¨ller
Zusammenfassung
DieelektromagnetischenEigenschaftenvonLichtwerdeninderQuantenoptikmeist
aufdieelektrischeKomponentereduziert.EinMedium,dassowohlmitderelek-
trischenalsauchmitdermagnetischenKomponentewechselwirkt,wa¨rejedochaus
technologischerSichtsehrinteressant.EinvorkurzemvorgeschlagenerAnsatz,um
diemagnetischeAntwortzuversta¨rken,basiertaufhoherDichtesowieinduzierter
Chiralita¨t.EineKombinationvonbeidemistjedochexperimentellzurZeitnicht
umsetzbar.
DieseArbeituntersuchtLichtpropagationindichtenundinchiralenMedien,wobei
beideKonzeptegetrenntundinexperimentellzuga¨nglichenParameterbereichenbe-
handeltwerden.ImEinzelnenanalysierenwireinsog.Closed-LoopSystem,demon-
striereneinSchemazurKontrollederGruppengeschwindigkeitimUV-Bereich,zei-
gen,wieparametrischeProzesseinderLichtpropagationverwendetwerdenko¨nnen
underla¨uterndenEinusshoherGasdichteaufeinenverlangsamtenLichtpuls.Wir
leitendieWellengleichungfu¨rMedienmitinduzierterChiralita¨therundlo¨sensieauf
BasisderallgemeinenMediumsantwort.IneinemkonkretesBeispielverwendenwir
dieerarbeitetenKonzepte,umLichtpropagationmitchiralerWechselwirkungzuun-
tersuchen.Dabeistellenwirfest,dasseinchiralesMediumdieoptimaleUmsetzung
einesClosed-LoopPhasenkontrollschemasermo¨glichtundsodieDynamikeinesver-
langsamtenLichtpulseswa¨hrendderPropagationkontrolliertwerdenkann.Außer-
demzeigenunsereErgebnisse,dassbereitsmitheutigenexperimentellenMethoden
Parametererreichbarsind,beidenendiemagnetischeKomponentedesProbefelds
relevantwird.
Abstract
Inquantumoptics,theelectromagneticcharacteroflightismostlyreducedtoits
electriccomponent.Technologicallyinteresting,amediuminteractingwithboththe
electricandmagneticcomponenthasrecentlybeenproposed.Butthesuggested
combinationofhighdensityandinducedchiralitytoenhancethemagneticresponse
isbeyondthelimitsofcurrentexperiments.
Thisthesisstudieslightpropagationindenseandchiralmedia,assessingbothcon-
ceptsseparatelyandinmoreaccessibleparameterranges.Inthiscontext,weanalyze
aso-calledclosed-loopsystem,demonstrateaschemeforgroupvelocitycontrolin
theUVrange,showhowtoutilizeparametricprocessesforlightpropagation,and
explaineectsduetohighdensityonaslowlightpulse.Wederivethewaveequation
formediawithinducedchiralityandsolveitonthelevelofgeneralmediumresponse
coecients.Thisisthenfollowedbyaspecicexample,inwhichthedevelopedcon-
ceptsareappliedtostudylightpropagationwithchiralinteractions.Wendthat
achiralmediumisanidealimplementationofaclosed-loop-phasecontrolscheme
andshowthatthedynamicsofaslowlightpulsecanbecontrolledthroughoutprop-
agationtime.Furthermore,ourresultsdemonstratethatthemagneticprobeeld
componentcanbecomerelevantforparametersachievableincurrentexperiments.
v
Withintheframeworkofthisthesis,thefollowingarticleswerepublishedinrefereed
journals:
•M.Mahmoudi,R.Fleischhaker,M.Sahrai,andJ.Evers,
Groupvelocitycontrolintheultravioletdomainviainteractingdark-stateres-
onances,
J.Phys.B:At.Mol.Opt.Phys.41,025504(2008).
•R.FleischhakerandJ.Evers,
NonlineareectsinpulsepropagationthroughDoppler-broadenedclosed-loop
atomicmedia,
Phys.Rev.A.77,043805(2008).
•R.FleischhakerandJ.Evers,
Four-wavemixingenhancedwhite-lightcavity,
PhysRev.A78,051802(R)(2008).
Articlessubmittedforpublicationinrefereedjournals:
•R.FleischhakerandJ.Evers,
Lightpropagationinchiralmedia,
arXiv:0906.5301[quant-ph](2009),
submittedtoPhys.Rev.A.
Articlesinpreparation:
•R.Fleischhaker,T.N.Dey,andJ.Evers,
Phasemodulationinducedbycooperativeeectsinelectromagneticallyinduced
transparency,
arXiv:0902.0752[quant-ph](2009).
•R.FleischhakerandJ.Evers,
Maxwell-Blochequationsinchiralmedia:Anumericalintegrationscheme,
inpreparation.
iv
Contents
Introduction
ICoherentcontrolinadiluteatomicvapor
1Nonlineareectsinpulsepropagationthroughclosed-loop
atomicmedia
1.1Introduction................................
1.2Theoreticalanalysis...........................
1.2.1Hamiltonian............................
1.2.2Masterequation.........................
1.2.3Time-dependentsolution....................
1.2.4Physicalinterpretation......................
1.2.5Linearandnonlinearsusceptibility...............
1.2.6Dopplerbroadening.......................
1.2.7Buergasandpressurebroadening...............
1.3Results...................................
1.3.1WithoutDopplerbroadening..................
1.3.2IncludingDopplerbroadening..................
1.4Conclusion................................
1.AAppendix.................................
2Groupvelocitycontrolviainteractingdark-stateresonances
2.1Introduction................................
2.2Analyticalconsiderations........................
2.2.1Themodelsystem........................
2.2.2Observables............................
iiv
11
71
911912122232425262727282922343
5335737393
CONTENTS
2.3Results...................................40
2.3.1Withoutinteractingdarkstateresonance...........40
2.3.2Withinteractingdarkstateresonance.............41
2.3.3Withinteractingdarkstateresonanceandincoherentpumping42
2.3.4Dressed-stateanalysis......................46
2.3.5Doppleraveraging........................47
2.3.6Numericalvericationoftheanalyticalresults........49
2.4Conclusion................................50
IIParametricprocessesandcooperativeeectsin
lightpropagation51
3Four-wavemixingenhancedwhite-lightcavity53
3.1Introduction................................53
3.2Bandwidthofanopticalcavity.....................56
3.2.1Emptycavity...........................56
3.2.2White-lightcavitycondition...................56
3.3Lightpropagationeects........................57
3.3.1Relationtonegativegroupvelocity...............57
3.3.2Parametricprocesses.......................57
3.3.3Eectivesusceptibility......................58
3.4Results..................................58
3.4.1Groupindexandeectivesusceptibility............58
3.4.2Bandwidthenhancement.....................59
3.5Conclusion................................62
4Phasemodulationinducedbycooperativeeectsin
electromagneticallyinducedtransparency63
4.1Introduction................................63
4.2Susceptibility...............................65
4.2.1Equationsofmotionincludinglocaleldcorrection......65
4.2.2Transparencywindow......................66
4.3Pulsepropagationdynamics......................67
4.4Results..................................68
4.4.1Numericalexample........................68
iiiv
CONTENTS
4.4.2Scalingofphasemodulation...................68
4.4.3Underlyingmechanismofenergytransfer...........70
4.4.4Comparisontononlinearself-phasemodulation........71
4.5Conclusion................................71
IIICrosscouplingofelectricandmagneticlaser
eldcomponent:Chiralmedia73
5Lightpropagationinchiralmedia75
5.1Introduction................................75
5.2Chiralcrosscoupling...........................76
5.3Lightpropagationinchiralmedia....................78
5.3.1Waveequationfortheelectricandmagneticeldcomponent78
5.3.2Solutionofthewaveequations.................79
5.4Prerequisitesforachiralatomicmedium................80
5.5Conclusion................................81
6Chiralcontrolofpropagationdynamics83
6.1Introduction................................83
6.2Modelsystem...............................84
6.2.1Chiralenhancementofmagneticresponse...........85
6.2.2Phasedependence........................85
6.2.3Mediumresponsecoecients..................86
6.3Pulsepropagationwithphasecontrol..................88
6.3.1Reducedgroupvelocity.....................88
6.3.2Constantphase..........................90
6.3.3Phaseswitching..........................91
6.4Conclusion................................92
Conclusion95
AAppendix:Numericalalgorithm99
A.1Equationsofmotionindimensionlessform...............99
A.2Discretizationscheme..........................100
Bibliography103
xi
Introduction
SincetheworkofJ.C.Maxwell[1]andH.R.Hertz[2]weknowthatlightisaform
ofelectromagneticradiation.Assuchitcanbedescribedasanelectromagnetic
wavecomposedofoscillatingelectricandmagneticeldcomponents.According
toMaxwell’sequations[3],thesetwocomponentscontinuallygenerateeachother
whiletheelectromagneticwavepropagates.Achangeoftheelectriceldinducesa
magnetic