Fast light， slow light， and phase singularities a connection to generalized weak value.pdf

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1、Fastlight,slowlight,andphasesingularities:aconnectiontogeneralizedweakvaluesD.R.Solli,1C.F.McCormick,1R.Y.Chiao,1S.Popescu,2,3andJ.M.Hickmann1,41DepartmentofPhysics,UniversityofCalifornia,Berkeley,CA94720-7300.2UnivBristol,HHWillsPhysLab,BristolBS81TL,Avon,England.3HewlettPackardLabs,BristolBS126QZ

2、,Avon,England.4DepartamentodeF´ısica,UniversidadeFederaldeAlagoas,CidadeUniversitaria,57072-970,Macei´o,AL,Brazil.´AbstractWedemonstratethatAharonov-Albert-Vaidman(AAV)weakvalueshaveadirectrelationshipwiththeresponsefunctionofasystem,andhaveamuchwiderrangeofapplicabilityinboththeclassicalandquantum

3、domainsthanpreviouslythought.Usingthisidea,wehavebuiltanopticalsystem,basedonabirefringentphotoniccrystal,withaninfinitenumberofweakvalues.Inthissystem,thepropagationspeedofapolarizedlightpulsedisplaysbothsuperluminalandslowlightbehaviorwithasharptransitionbetweenthetworegimes.Weshowthatthissystem's

4、responsepossessestwo-dimensional,vortex-antivortexphasesingularities.Importantconsequencesforopticalsignalprocessingarediscussed.arXiv:quant-ph/0310048v17Oct20031Theroleofmeasurementinquantummechanicshasposedchallengesforphysicistsfornearlyacentury.Standardquantummechanicsrepresentsidealmeasurement

5、sastheactionofaHilbert-spaceoperatoronastate.Inanidealor“strong”measurement,theoperatorcompletelycollapsesthestateintoaneigenstate,withanexpectationvaluewithintherangeoftheoperator'seigenval-ues.Strongmeasurementsyieldmaximalinformationaboutthestateofthesystemandcorrespondtomostlaboratorymeasuremen

6、ts.Contrarytotraditionalquantummeasurementtheory,certainexperimentscanreturnresultsthatarefarbeyondtherangeofanobservable'seigenvalues[1].Theseso-called“weak”measurementsbarelyperturbthestate,andhavebeenlessstudiedinquantummechanicsbecausetheyyieldverylittleinformation.Intheirseminalwork,Aharonov,A

7、lbertandVaidman(AAV)showedthatpara-doxicalresultscanbeobtainedifonepreselectsaninitialstate,performsaweakmeasurement,andsubsequentlyastandardstrongmeasurementwhichpostselectsaparticularfinalstate.Al-thoughth