A possible way to look at the last and future even

arXiv:quant-ph/0107079v116Jul2001HEP/123-qedApossiblewaytolookat[e-mail](07.06.2001)AbstractInviewofathree-dimensionalpicture(3D)ofprobabilitytofindaparticleataplaneofthefrequencyandthetime(PTF)becomesthatprocessofabsorp-tionandprocessofradiationfortwo-levelsystemhavedifferentdirectiononthetime.Bothprocessesareinthepastorinthefuturedependingonnamedtransitionduetoreversiblemodelofthetwo-levelatom.Theopportunitytoknowthelasthistoryoftheresonanteventfortheabsorptionprocessisforquantuminterferenceinteractionorfortheresonantradiation.Onthecontrary,topredicttheresonanteventinthefutureispossibleonlybyusenearresonantatom-fieldabsorptionorbyuseradiationatafixedtime.Theproblemoflifetimeforaparticleisenteredthroughtimeofspontaneousra-diationconnectedwithtrajectoryofthequantumtransition.Itisofferedtoconnectatrajectoryofaparticleduringquantumtransitionswithdistribu-tionofprobabilitytofindaparticle.Theconceptionofthespectralhistoryforeventsduetoprobabilitydistributionisintroducedfornextdiscussion.31.70.,32.80.TypesetusingREVTEX1Theprobabilitytofindaparticleontheupperenergylevelwithintwo-levelsystemisthefunctionoftwovariablessuchasthetimeτandthefrequencyω.WeconsiderP(τ,ω)asthefunctionofprobabilityinsystemofaxiscoordinatesτandω,whereweshalltodiscuss3Dpicturesofprobability-time-frequency(PTF).Suchimagesunderliepresentwork.Onthemtheconnectionbetweeneventsiswellvisible.ThefunctionP(τ,ω)ofprobabilityisadistribution,whichhasdirectconnectionwithobservablestructuresofspectrallinesandthatremindssimilardistributionoftheEMsignaltheory[1].Betweentheseperformancesofprocessesexiststheproblemofrecognitionforeventswhichoccursinanatom,butareregisteredinthelaboratory[2].Realmodelcanbewellimagineifweshallstopmoreinsomephysicalparameters.Forthenearresonantabsorptionproblemisusuallydifficulttoimaginewhythereisanabsorption,ifthereisnoexactresonance.Itisnecessarywelltoimaginewherearefrequenciesbordersofsuchinteraction.Theaccountofspectralwidthconcernsalsotothis.Thisisimortantonlyforlongpulsesorcontinuouswave(cw)-lasers.Besidestobelieveinanatureofspontaneousradiationinsystemnothavinginteractionswithanything,exceptwithafield,isdifficult.Thisconcernstonoradiatingtransitionstoo.TheRabifrequencyΩνmeasuredin(MHz)is:Ων=d1,2·E0¯h(1)whered1,2-isthematrixdipolemomentumandE-istheamplitudeofEMwave.ThereisthefrequencyΩ,thatmakearoundoscillationsbetweentwolevels.Eachroundconsistonwellknownprocessesoftheabsorptionandtheemissionduetocw-laserexcitationwiththefieldE=E0·cos(ω·τ)(2)Therefore,wecanconsideronlytheabsorptionprocessortheradiationprocesswiththefrequencymeasuredin(rad./s):Ω=2πΩν/2=πΩν.Weshallnotice,thatconsideringRabifrequencyasvariedparameter,weshouldoperateintensityIofthecw-laserinspaceoflaboratorybyusetheknownrelation:Ων=const·√I(3)Thefrequencytuningconditionsforthequantuminterferenceare:E(τ)=E0[cos(ω1τ)+cos(ω2τ)](4)Δω2=ω2−ω0(5)whereweset:Δω1=ω0−ω1(6)ForthequantuminterferenceperturbationoftheupperenergylevelW2[Fig.1],therearetwosymmetricalfrequencies,sowecanusetherelationforexactsolution:2Δω2=Δω1=Δω(7)Let’sonceagainaddresstothewellknownprocessofanatom-fieldinteraction,whereforeventswithaparticleexistawellknownformulafortheprobability,containingtheRabifrequencyΩ:P1=4Ω24Ω2+Δω2#sin2τ2√4Ω2+Δω2(8)Thetransitionprobabilityforthequantuminterferenceeffectis[2]:P2=sinΩΔω·sin(Δωτ)2(9)TheexperimentconditioninthevisiblerangeofaspectrumfortheLithiumatomwaschosen.ThecorrespondencebetweenRabifrequenciesandfinestructuresatthesameenergylevelareshowninthe[Fig.1].WhentheamplitudeofthelaserwaveEisabout8,7Volt/cmtheintensityofthelaserisaboutI=100mW/cm2andΩ≃1000MHz.rad.,thatcorrespondstotheRabifrequencyΩν≃318MHzandtheintensity375mW/cm2.BecausethegivenvaluefortheRabifrequencyisabout1GHz.rad,wecantocompareitforLithium,wherethedistancebetween2P1/2and2P3/2fortwoisotopesisabove(2π)10GHzandthefrequencyω0∼=2,8·106GHz.rad..Otherrealparameteristhefrequencyω0ofthelaserwithwhichispossibleverypreciselytooperate.Forreallaserssuchasthedye-laser(Coherent,Model899-21)withtemperaturestabilizedreferencecell,thefrequencydriftisonly50MHz/hourwith500kHzlinewidth.Forthequartzrodresonatorstructureofthebroadbanddye-laser,SpectraPhysics,375Dwithspecialprocedure[3]forasinglemodeoperationaresultingtemperaturesensitivitywasabout90MHz/0C.Withrespecttotherefractioncoefficientofairatemperaturesensitivityisabout410MHz/oC.Forsemiconductorslaserssuchasthe6202modelofNewFocusdiodelaserorfortheEOSIdiodelaser,thelinewidthisabout100KHzandtheaveragepower6mW,thestabilityparametersattheneededwavelengtharebetter.ThereforeitisrealtoscananatomictransitionwithaccuracyaboutΔω=20MHzImaginingrealconditionsforthetwo-levelmodelofLithiumatomat(2S−2P),lookata3DpictureofprobabilityP1[Fig.2].TheprobabilityP1forthequantumtransitionisonefunctionasknownsinc2and,aswellknownfromthetheory,itisdependonthetimetoo,asthedeltafunction.Whenweusethisprobabilityatthesmallrangeofthetime(usuallynamedastheprobabilityoftransition)welosetheinformationaboutthetimepictureforthequantumprocess