Spectroscopy of the a^3Sigma_u^+ state and the cou

arXiv:0708.0931v2[physics.atom-ph]5Oct2007Spectroscopyofthea3Σ+ustateandthecouplingtotheX1Σ+gstateofK2A.PashovDepartmentofPhysics,SofiaUniversity,5JamesBourchierboulevard,1164Sofia,BulgariaP.PopovDepartmentofPhysics,TechnicalUniversityofVarna,ul.Studentska2,9010Varna,BulgariaH.Kn¨ockelandE.TiemannInstitutf¨urQuantenoptik,LeibnizUniversit¨atHannover,Welfengarten1,30167Hannover,Germany(Dated:Received:date/Revisedversion:date)WereportonhighresolutionFourier-transformspectroscopyoffluorescencetothea3Σ+ustateinducedbytwo-photonortwo-stepexcitationfromtheX1Σ+gstatetothe23ΠgstateinthemoleculeK2.ThesespectroscopicdataarecombinedwithrecentresultsofFeshbachresonancesandtwo-colorphotoassociationspectraforderivingthepotentialcurvesofX1Σ+ganda3Σ+uuptotheasymptote.ThepreciserelativepositionofthetripletlevelswithrespecttothesingletlevelswasachievedbyincludingtheexcitationenergiesfromtheX1Σ+gstatetothe23Πgstateandthefrequenciesofthefluorescencedowntothea3Σ+ustateinthesimultaneousfitofbothpotentials.Thederivedprecisepotentialcurvesallowforreliablemodelingofcoldcollisionsofpairsofpotassiumatomsintheir2Sgroundstate.PACSnumbers:31.50.Bc,33.20.Kf,33.20.Vq,33.50.DqI.INTRODUCTIONContrarytotheheteronuclearalkalidiatomicmolecules(e.g.[1,2,3]),thelowesttripletstatea3Σ+uofthehomonuclearonesismuchlessaccuratelycharacterized.Theexperimentaldatainthiscaseareeitherfragmentaryorfromlowresolutionspectroscopy.Thesituationcanbeunderstoodmainlybythepresenceofthegerade/ungeradesymmetryinthehomonucleardiatomicswhichmakesthespectroscopictechniqueswithsingle-photonexcitationinapplicable.Ontheotherhandthedemandforaccuratedataonbothstates,X1Σ+ganda3Σ+u,correlatedtothelowests+sasymptoteofthealkalies,ishighbecauseoftheveryactiveresearchinthefieldofultracoldcollisionsonalkalispecies.Thefirstspectroscopicobservationofthea3Σ+ustateinK2withpartiallyresolvedrotationalstructurewasre-portedinRef.[4].There,bluefluorescencetothea3Σ+ustatewasinducedwiththeoptical-opticaldoublereso-nance(OODR)techniqueandresolvedwitha0.85mdualgratingmonochromator.Thehighestobservedvi-brationallevelofthegroundtripletstatein39K2wasv=17.Inafurtherpaper[5]thesamegroupreportedadditionalOODRmeasurementsonthea3Σ+ustateinordertoresolvetheproblemthatthederivedpotentialcurveofthea3Σ+ustatecrossedthatoftheX1Σ+gstatetakenfromRef.[6].Thepapercontainsafewtermener-giesoflowvibrationallevelsofthea3Σ+ustatewithotherrotationalquantumnumbersthanthelevelsobservedin[4].ThelowestatomicasymptoteofK2wasstudiedbyWangetal[7]throughtwo-colorphotoassociationspec-troscopyofultracold39Katoms.Intherangebetween1500and4600MHzbelowtheasymptoteatotalof12termenergiesofnearasymptoticlevelswithhightripletcharacterweredetermined.Thustheanalysisofthea3Σ+ustatelevelstructurepresentedinthesethreepub-lications[4,5,7]couldbeperformedassinglechannelcasesignoringthesinglet-tripletmixingduetothehy-perfineinteractionswiththeX1Σ+gstate.Inanothergroupofpapers[8,9,10,11,12]s-andp-waveFeshbachresonancesin40Kweremeasuredandjustrecentlys-waveFeshbachresonancesin39Kwerere-ported[13]followedbyanapplicationforsuccessfulBose-Einsteincondensationof39K[14].Bose-Einsteinconden-sationwasobservedearlierfortheisotope41KbyMod-ugnoetal.[15]leadingtoanindependentestimateofthetripletscatteringlengthofthatisotope.IntheirrecentworkChuetal.[16]examinedseriesoftwo-steptwo-colorandtwo-photonsingle-colorlaserexcitationsinK2whichweredevotedtoastudyofits23Πgstate.Alongwiththemainsubjectoftheirstudy,theauthorsobservedalsolaserinducedfluorescencetothetripleta3Σ+ustate.Unfortunately,thiswasdoneatlowresolutionandthusgavenoadditionalspectroscopicdataforareliablecharacterizationofthea3Σ+ustate.ThepurposeofourpresentstudyistorecordhighresolutionspectraforthelowesttripletstateinK2andtoconstructpotentialenergycurvesaccurateenoughtomodelcoldcollisionsbetweentwopotassiumatomsinthecoupledsystemofX1Σ+ganda3Σ+ustates.Wewillinvestigatetheimportanceofthesinglet-tripletmixingforrelativelydeeplyboundandasymptoticvibrationallevels,sinceourexperienceontheheavieralkalicom-poundshasshownthatbyignoringitoneisnotabletoreproducesatisfactorilythewholesetofexperimen-talobservations(seee.g.[1]).Finally,thepresenceofaccurateexperimentaldataforseveralpotassiumiso-topesgivestheopportunitytolookforthepossiblebreak-downoftheBorn-Oppenheimerapproximationand,con-2sequently,thewidelyusedmass-scalingforcoldcollisions.II.EXPERIMENTTheexperimentalsetupfortheproductionofK2moleculesissimilartothatdescribedinourpreviouspa-pers[1,2].Asinglesectionheat-pipewasfilledwithabout10gofpotassium(naturalisotopiccomposition)andheatedtoabout600K.Arwasusedasbuffergasatapressureofabout1-2mbar.ForexcitationofthepotassiummoleculesweappliedthelaserlineslistedinRef.[16]andthenusedaFourier-transformspectrometertoresolvetheinducedfluores-cencetothea3Σ+ustatewithatypicalresolutionof0.05cm−1.Twodiodelaserheadswithanexternalgratingcavity(DL100fromToptica)andtheaccompanyingelec-tronicsweresuppliedwithlaserdiodesdeliveringabout50mWat850nmor100mWat980nm,respectively.Thelasersweresuperimposedcollinearlybyadichroiticmirrorandfocusedi