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1、Quantumeffectsinone-photonandtwo-photoninterferenceL.MandelDepartmentofPhysicsandAstronomy,UniversityofRochester,Rochester,NewYork14627Afterintroducingsomebasicde®nitions,thearticledescribesseveralopticalinterferenceexperimentsinwhichquantumeffectsappear.Ananalysis
2、oftheseexperimentsleadstosomenewandimprovedmeasurementtechniquesandtoabetterunderstandingofthequantumstate.[S0034-6861(99)02102-9]I.INTRODUCTIONWenowturntointerferenceeffectsthatarede®nedintermsofanensembleaverage.Letusstartbydistin-Althoughinterferenceisintrinsica
3、llyaclassicalwaveguishingbetweensecond-orderorone-photon,andphenomenon,thesuperpositionprinciplewhichunder-fourth-orderortwo-photoninterferenceexperiments.Inliesallinterferenceisalsoattheheartofquantumme-thesimplestandmostfamiliartypeofexperiment,onechanics.Feynman
4、hasreferredtointerferenceasreallyphotodetector,sayD1,isusedrepeatedlytomeasure``theonlymystery''ofquantummechanics.Further-theprobabilityP1(x1)ofdetectingaphotoninsomemore,insomeinterferenceexperimentsweencountershorttimeintervalasafunctionofpositionx1[seeFig.1(a)]
5、.Interferenceischaracterizedbythe(often,butnottheideaofquantumentanglement,whichhasalsobeennecessarily,periodic)dependenceofP1(x1)ontheop-describedasreallytheonlyquantummystery.ClearlyticalpathlengthsSAD1andSBD1oronthecorrespond-interferenceconfrontsuswithsomequite
6、basicques-ingphaseshiftsfA1andfB1.BecauseP1(x1)dependstionsofinterpretation.Despiteitslonghistory,goingonthesecondpoweroftheoptical®eldandonthede-backtoThomasYoungatthebeginningofthe19thcen-tectionofonephotonatatime,werefertothisastury,opticalinterferencestillchall
7、engesourunderstand-second-order,orone-photon,interference.Sometimesing,andthelastwordonthesubjectprobablyhasnottwophotodetectorsD1andD2locatedatx1andx2areyetbeenwritten.Withthedevelopmentofexperimentalusedincoincidencerepeatedlytomeasurethejointtechniquesforfastand
8、sensitivemeasurementsoflight,probabilityP2(x1,x2)ofdetectingonephotonatx1andithasbecomepossibletocarryoutmanyoftheGedan-oneatx2withinashorttime[s
