Rb87能级图

Rubidium87DLineDataDanielA.SteckTheoreticalDivision(T-8),MSB285LosAlamosNationalLaboratoryLosAlamos,NM8754525September2001(revision1.6,14October2003)1IntroductionInthisreferencewepresentmanyofthephysicalandopticalpropertiesof87Rbthatarerelevanttovariousquantumopticsexperiments.Inparticular,wegiveparametersthatareusefulintreatingthemechanicaleffectsoflighton87Rbatoms.Themeasurednumbersaregivenwiththeiroriginalreferences,andthecalculatednumbersarepresentedwithanoverviewoftheircalculationalongwithreferencestomorecomprehensivediscussionsoftheirunderlyingtheory.Wealsopresentadetaileddiscussionofthecalculationoffluorescencescatteringrates,becausethistopicisoftennottreatedcarefullyintheliterature.Thecurrentversionofthisdocumentisavailableat“CesiumDLineData”and“SodiumDLineData.”[e-mail].287RbPhysicalandOpticalPropertiesSomeusefulfundamentalphysicalconstantsaregiveninTable1.Thevaluesgivenarethe1998CODATArecommendedvalues,aslistedin[1].Someoftheoverallphysicalpropertiesof87RbaregiveninTable2.87Rbhas37electrons,onlyoneofwhichisintheoutermostshell.87Rbisnotastableisotopeofrubidium,decayingtoβ−+87Srwithatotaldisintegrationenergyof0.283MeV[2](theonlystableisotopeis85Rb),buthasanextremelyslowdecayrate,thusmakingiteffectivelystable.Thisistheonlyisotopeweconsiderinthisreference.Themassistakenfromthehigh-precisionmeasurementof[3],andthedensity,meltingpoint,boilingpoint,andheatcapacities(forthenaturallyoccurringformofRb)aretakenfrom[2].Thevaporpressureat25◦CandthevaporpressurecurveinFig.1aretakenfromthevapor-pressuremodelgivenby[4],whichislog10Pv=−94.04826−1961.258T−0.03771687T+42.57526log10T(solidphase)log10Pv=15.88253−4529.635T+0.00058663T−2.99138log10T(liquidphase),(1)wherePvisthevaporpressureintorr,andTisthetemperatureinK.Thismodelshouldbeviewedasaroughguideratherthanasourceofprecisevapor-pressurevalues.Theionizationlimitistheminimumenergyrequiredtoionizea87Rbatom;thisvalueistakenfromRef.[5].Theopticalpropertiesofthe87RbDlinearegiveninTables3and4.ThepropertiesaregivenseparatelyforeachofthetwoD-linecomponents;theD2line(the52S1/2−→52P3/2transition)propertiesaregiveninTable3,andtheopticalpropertiesoftheD1line(the52S1/2−→52P1/2transition)aregiveninTable4.Ofthesetwocomponents,theD2transitionisofmuchmorerelevancetocurrentquantumandatomopticsexperiments,287RBPHYSICALANDOPTICALPROPERTIES2becauseithasacyclingtransitionthatisusedforcoolingandtrapping87Rb.Thefrequenciesω0oftheD2andD1transitionsweremeasuredin[6]and[7],respectively(seealso[8,9]formoreinformationontheD1transitionmeasurement);thevacuumwavelengthsλandthewavenumberskLarethendeterminedviathefollowingrelations:λ=2πcω0kL=2πλ.(2)Theairwavelengthλair=λ/nassumesindexofrefractionofn=1.00026821,correspondingtodryairatapressureof760torrandatemperatureof22◦C.TheindexofrefractioniscalculatedfromtheEdl´enformula[10]:nair=1+
8342.13+2406030130−κ2+1599738.9−κ2×0.00138823P1+0.003671T−f5.722−0.0457κ2×10−8.(3)Here,Pistheairpressureintorr,Tisthetemperaturein◦C,κisthevacuumwavenumberkL/2πinµm−1,andfisthepartialpressureofwatervaporintheair,intorr.Thisformulaisappropriateforlaboratoryconditionsandhasanestimateduncertaintyof≤10−8.Thelifetimesaretakenfromarecentmeasurementemployingbeam-gas-laserspectroscopy[11].InvertingthelifetimegivesthespontaneousdecayrateΓ(EinsteinAcoefficient),whichisalsothenatural(homogenous)linewidth(asanangularfrequency)oftheemittedradiation.Thespontaneousemissionrateisameasureoftherelativeintensityofaspectralline.Commonly,therelativeintensityisreportedasanabsorptionoscillatorstrengthf,whichisrelatedtothedecayrateby[12]Γ=e2ω202π0mec32J+12J+1f(4)foraJ−→Jfine-structuretransition,wheremeistheelectronmass.Therecoilvelocityvristhechangeinthe87Rbatomicvelocitywhenabsorbingoremittingaresonantphoton,andisgivenbyvr=¯hkLm.(5)Therecoilenergy¯hωrisdefinedasthekineticenergyofanatommovingwithvelocityv=vr,whichis¯hωr=¯h2k2L2m.(6)TheDopplershiftofanincidentlightfieldoffrequencyωLduetomotionoftheatomis∆ωd=vatomcωL(7)forsmallatomicvelocitiesrelativetoc.Foranatomicvelocityvatom=vr,theDopplershiftissimply2ωr.Finally,ifonewishestocreateastandingwavethatismovingwithrespecttothelabframe,thetwotraveling-wavecomponentsmusthaveafrequencydifferencedeterminedbytherelationvsw=∆ωsw2πλ2,(8)because∆ωsw/2πisthebeatfrequencyofthetwowaves,andλ/2isthespatialperiodicityofthestandingwave.Forastandingwavevelocityofvr,Eq.(8)gives∆ωsw=4ωr.Twotemperaturesthatareusefulincoolingandtrappingexperimentsarealsogivenhere.Therecoiltemperatureisthetemperaturecorrespondingtoanensemblewithaone-dimensionalrmsmomentumofonephotonrecoil¯hkL:Tr=¯h2k2LmkB.(9)3HYPERFINESTRUCTURE3TheDopplertemperature,TD=¯hΓ2kB,(10)isthelowesttemperaturetowhichoneexpectstobeabletocooltwo-levelatomsinopticalmolasses,duetoabalanceofDopplercoolingandrecoilheating[13].Ofcourse,inZeeman-degenerateatoms,sub-Dopplercoolingmechanismspermittemperaturessubstantiallybelowthislimit[14].3HyperfineStructure3.1EnergyLevelSplittingsThe52S1/2−→52P3/2and52S1/2−→52P1/2transitionsarethecomp