ﬂuorescence detection to study two photon transitions in atomicrubidium A laser system spectroscopy with combined absorption, polarization rotationand Technology Journal of Applied Researchand

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Availableonlineatwww.sciencedirect.com

Journal of Applied Research and Technology

www.jart.ccadet.unam.mx JournalofAppliedResearchandTechnology13(2015)543–550

Original

A laser spectroscopy system with combined absorption, polarization rotation and fluorescence detection to study two photon transitions in atomic

rubidium

Oscar López-Hernández

^a

, Santiago Hernández-Gómez

^a

, Francisco Sebastián Ponciano-Ojeda

^a

, Cristian Mojica-Casique

^a

, Ricardo Colín-Rodríguez

^a

, Jesús Flores-Mijangos

^a

, Daniel Sahagún

^b

,

Fernando Ramírez-Martínez

^a,∗

, José Jiménez-Mier

^a

aInstitutodeCienciasNucleares,UniversidadNacionalAutónomadeMéxico,CircuitoExteriors/n,CiudadUniversitaria,Del.Coyoacan,México,D.F., CP04510,Mexico

bInstitutodeFísica,UniversidadNacionalAutónomadeMéxico,CircuitoExteriors/n,CiudadUniversitaria,Del.Coyoacan,México,D.F.,CP04510,Mexico

Received28March2015;accepted18September2015 Availableonline19November2015

Abstract

Thedesignandconstructionofanexperimentalsystemforstudyingtwophotonspectroscopyprocessesinatomicrubidiumispresented.It isdesignedtomeasureabsorptionandpolarizationrotationinducedbyanyofthetwolaserbeamsandalsothevisiblefluorescencethatresults fromdecay oftheexcitedstates.Twohome-builtdiodelasersareusedtoproducethe opticalfieldsthatlaterinteractwithroomtemperature rubidiumatoms.Usingcounterpropagatingbeamsallowsvelocityselectionofthegroupsofatomsthatinteractwithbothlaserbeams.Thesystem wastestedinthe5S→5P3/2→5Djladderenergylevelconfigurationofatomicrubidium.Bluefluorescence(420nm)thatresultsfromdecay oftheintermediate6Pjstatesisfilteredandthenmeasuredwithaphotomultipliertube.Absorptionandfluorescencespectraprovidemutually complementaryinformationabouttheinteractionbetweentherubidiumatomsandthetwoopticalfields.

Keywords:Laserspectroscopy;Two-photontransition;Rubidium

1. Introduction

High-resolutionlaser spectroscopy freeof Dopplerbroad- eninghas madesubstantial progressthrough thestudy of the interactionbetweentwoopticalfieldsandanatomicmedium, suchas analkali metalvapor.Thisprogresshas alsobrought improvementinlaserstabilizationtechniquesthatarecommonly usedinatommanipulationsuch aslasercoolingandtrapping (Metcalf &Van der Straten, 1999).The combination of pre- ciselycontrolledexperimentsandthedevelopmentoftheoretical modelsisakeyfactorinthe advanceof high-resolutionlaser spectroscopy.The agreement betweenexperiment andtheory

∗Correspondingauthor.

E-mailaddress:[email protected](F.Ramírez-Martínez).

PeerReviewundertheresponsibilityofUniversidadNacionalAutónomade México.

is quite satisfactory under many experimental circumstances (Harrisetal.,2006;Himsworth&Freegarde,2010;Noh,Moon,

&Jhe,2010;Pearmanetal.,2002;Smith&Hughes,2004).For thepurposesofthisarticle,onecanbroadlyclassifytheexperi- mentsthatuseatomictransitionsinducedbytwophotonsintwo groups.Inthefirstone,theeffectofthelightatominteraction is observed inthe modification of the light as it is transmit- tedthroughtheatomicmedium(Auzinsh,Budker,&Rochester, 2010).Therearechangesinbothabsorptionandpolarizationof aprobelightbeamasitpassesthroughanatomicmediuminter- actingwithopticalfields.Inthesecondgroupofexperiments,the lightproducesexcitedstatesintheatomsthatcanbedetected,for instance,bylookingattheatomicfluorescence.Intheseexperi- mentsonemeasurestheatomicpopulationintheexcitedstates.

The5S→5Djtwo-photonexcitationinatomicrubidiumpro- videsverygoodexamplesofbothtypesofexperiments.Absorp- tion of a probe beam inthe 5 S→5 P3/2→5 D5/2 stepwise

http://dx.doi.org/10.1016/j.jart.2015.09.006

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excitationallowsthestudyofelectromagneticallyinducedtrans- parency(EIT)inaDopplerbroadenedmedium(Badger,Hughes,

&Adams,2001;Drampyan,Pustelny,&Gawlik,2009;Fulton, Shepherd,Moseley,Sinclair,&Dunn,1995;Gea-Banacloche, Li,Jin,&Xiao,1995;Li,Jin,&Xiao,1995;McGloin,Dunn,

& Fulton, 2000; Moon, Lee, & Kim, 2005; Moon & Noh, 2011a,2011b;Noh&Moon,2012;Sargsyan,Bason,Sarkisyan, Mohapatra, & Adams, 2010; Sargsyan, Sarkisyan, Krohn, Keaveney,&Adams,2010;Wielandy&Gaeta,1998;Xiao,Li, Jin,&Gea-Banacloche,1995).Examplesoffluorescencedetec- tioninthisstepwiseexcitationarethetwo-photonexperiments performedeitherwithasinglefrequencyor twodifferentfre- quencies(Hamid,C¸etintas¸,&C¸elik,2003;Nez,Biraben,Felder,

&Millerioux,1993,1994;Ryan,Westling,&Metcalf, 1993;

Sanguinetti,Mure,&Minguzzi,2007;Touahrietal.,1997),elec- tronshelving(Thoumanyetal.,2009),frequencyup-conversion (Meijer,White,Smeets,Jeppesen,&Scholten,2006),fourwave mixing(Akulshin,McLean,Sidorov,&Hannaford,2009),direct frequencycombspectroscopy(Marian,Stowe,Felinto,&Ye, 2005).Thesetypes of experimentshavealso been developed for advanced undergraduate laboratories (Jacques, Hingant, Allafort,Pigeard,&Roch,2009;Olson&Mayer,2009;Olson, Carlson,&Mayer,2006).Inthisworkwepresentatwo-photon spectroscopysetupinatomicrubidiuminwhichit ispossible tosimultaneouslydetecttheabsorptionand/orrotationofpolar- izationofoneofthe twoexcitationlightcomponents andthe fluorescenceofanspontaneousdecaychannel.Detectionofthe fluorescencelightprovidescomplementaryinformationtothe oneobtainedbyperformingvelocity-selectivepolarizationspec- troscopyofroomtemperaturerubidiumatoms(Colín-Rodríguez et al., 2015; Flores-Mijangos, Ramírez-Martínez, Colín- Rodríguez, Hernández-Hernández, & Jiménez-Mier, 2014;

Hernández-Hernándezetal.,2009).Thispaperisstructuredas follows. In Section 2 we review the5 S,5 P3/2, 5 Dj ladder systemin atomicrubidium,including the fluorescence decay paths.InSection3wepresenttheexperimentalsetup.Details abouttheconstructionofourdiodelasersandthefluorescence detectionsystemarealsogiven.Examplesofexperimentalspec- tra obtained with thissetup are shown inSection 4.Finally, conclusionsarepresentedinSection5.

2. The5S→5P3/2→5Djtwo-photontransitionin atomicrubidium

To understand the different spectroscopyexperiments that areperformedinoursetupwepresentanenergyleveldiagram ofatomicrubidiuminFigure1.Thevaluesofthetotalangular momentaFandhyperfine structuresplittingsshownhereper- tainto⁸⁵Rb,andasimilardiagramcanbeobtained for⁸⁷Rb.

Inoursetup(seebelow)acontinuouswave(CW)diodelaserat 780nmisusedtoexciteroomtemperatureatomsfromoneof thehyperfinecomponentsofthe5Sgroundstateintothe5P3/2

state(therubidiumD2line).AsecondCWdiodelaserbeamat 776nm,counterpropagatingwiththefirstone,providesapho- tonforexcitationintothe5Dj(j=3/2,5/2)hyperfinemanifolds.

Afterthistwo-stepexcitationtheatomsinthe5Djstatedecay backtothegroundstate.Oneofthedecaypathsisbycascade

Figure1.Energy-leveldiagramforthe5S1/2→5P3/2→5D3/2ofatomic⁸⁵Rb, includingthehyperfinestates.

emissionofanIRphoton(5␮m)intothe6Pjstate,followedby emissionofa420nmphoton.Detectionoftheexcitationprocess canbemadebymeasuringchangesintheabsorptionorrotation of the linear polarization of one of the laser beams (Flores- Mijangos etal., 2014; Hernández-Hernández et al., 2009) or bydetectionoftheemissionofa420nmfluorescencephoton.

The hyperfinesplitting ofthe 5S1/2state inatomicrubidium is largerthanthe D2 line Dopplerwidthatroomtemperature (≈500MHz).Therefore,thetotalangularmomentumFofthe initial stepin ourexcitationladder is welldefined.However, thehyperfinesplittingofboth5P3/2and5Djstatesissmaller thantheD2Dopplerwidth.Ifthefrequencyofoneofthetwo lasers is fixed,then byscanning the frequencyof the second laseronecanperformvelocityselective(Flores-Mijangosetal., 2014;Hernández-Hernándezetal.,2009)spectroscopyresult- inginlinesthatarenotbroadenedbytheDopplereffect.The resonantfrequencyν2 andthe velocityofthe groupofatoms that simultaneouslyinteractwithbothlaserbeamsisgivenby thesolutionofthesetofequations

ν_a=ν1

1−v

c

νb=ν2

1+v

c

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whereνaisoneoftheatomicresonantfrequenciesofthe5S→5 P3/2hyperfinemanifold,νbisanatomicresonantfrequencyof the5P3/2→5Djmanifoldandν1isthefixedfrequencyofone ofthelasers.Hereitisimportanttomentionthatthetransitions mustbeallowedbytheelectricdipoleselectionruleF=0,±1.

Inoursystemweusebalanceddetectiontomeasuretheabsorp- tionandpolarizationofthe780nmbeamusedinthefirststep oftheexcitation.Weaddaphotomultipliertubetothesystem

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780 nm

M M

BS

Rb M

PD2

PD1 PBS BS

L1 L2 Fluorescence420 nm λ/2

Rb

BS Filter

PMT

M

PBS PD1

PD2

Polarization spectroscopy

780 nm probe beam 776 nm beam

Two-photon spectroscopy and Fluorescence detection

A B

λ/4

776 nm M

λ/4 λ/2

Figure2.Thetwo-photonspectroscopysetup.(A)Polarizationspectroscopy setupforthe780nmlaser(ECDL)(Harrisetal.,2006;Pearmanetal.,2002).(B) Thetwo-photonspectrometerthatincludessystemsfordetectingtheabsorption andpolarizationrotationofthe780nmlightcomponentandthe420nmdecay fluorescence.Both780nmand776nmareexternalcavitydiodelasers(ECDL).

λ/2,halfwaveplate;λ/4,quarterwaveplate;PMT,photomultipliertube;L1and L2,lensesforfluorescencecollection;PD1andPD2,Siphotodiodes;M,mirror;

BS,beamsplittingglassslide;PBS,polarizingbeamssplittercube.

inordertodetectemissionof420nmphotons.Thesemeasure- mentsofabsorption,polarizationandfluorescencearemadeas functionsofthefrequencyofoneofthetwolasers,withthefre- quencyof theotherlaserfixed. Inonetypeofexperimentthe absorptionofthe780nmlaserismeasuredasitsfrequencyis scanned.Onethenobservestheeffectofthe passivelylocked 776nmlightcomponentontopofabroadDopplerabsorption well.In thisconfigurationoneobtainsanelectromagnetically inducedtransparencysignal(Gea-Banaclocheetal.,1995;Olson

&Mayer,2009).Inasecond typeofexperiment,polarization spectroscopy(Harrisetal.,2006;Pearmanetal.,2002)isused to lock the frequency of the 780nm laser to the maximum F→F+1cyclictransition,andthefrequencyofthe776nmlaser isscanned.Inthiscaseoneobtainsvelocity-selectiveabsorption andpolarizationspectra(Colín-Rodríguezetal.,2015).Forthese twocasesdetectionofthe420nmfluorescenceemissiontakes placeonlywhenthefrequencyofthelasersresonantlyexcites the5Djstateforatomswithaspecificvelocity,anditappears ontopofaflatbackground

3. Experimentalsetup

The experimentalsystem that was constructed is depicted schematically in Figure 2. Two external cavity diode lasers (ECDL) are used to produce the two-photon transition in an atomic rubidium cell kept at room temperature. The

spectrometerisshownintherighthandsidebox,denotedas(B), ofFigure2.The780nmprobebeamislinearlypolarized,and itspolarizationdirectioniscontrolledwithahalfwaveplate.The 776nmbeamiscircularlypolarizedwithaquarterwaveplate, andbothbeamscounterpropagatealongacommercialrubidium cell(TryadTechnology)mountedinsideanambientlightisola- tionandmagneticfieldshieldingsetup.Aphotomultipliertube withafilterandlensassembly(seebelow)isusedtodetectthe fluorescencelight.Amicroscopeslideatnearnormalincidence isusedtosendpartoftheprobebeamintothebalanceddetec- tion arrayafter ithascrossedthrough theRb cell. Thissetup canthereforeregistersimultaneouslyboththebluefluorescence detectedbythephotomultipliertubeandthevariationsinduced intheabsorptionanddirectionofpolarizationofthe780nmlaser componentasaresultoftheinteractionofbothbeamswiththe atomicmedium.Also,aportionof the780nmlaser issentto apolarizationspectrometer(Harrisetal.,2006;Pearmanetal., 2002)showninFigure2(A).Thisspectrometercanbeusedto monitorthefrequencyofthe780nmlaserwhenitisscanning, butitcanalsobeusedtolockthefrequencyofthislaserwhen the otherlaser isscanned.Bothdiodelasersarebasedon the Littrow-mountdesignof Arnold,Wilson, andBoshier(1998).

Wealsoincludean outputmirrorthat maintainsthe emission direction fixed (Hawthorn, Weber, & Scholten, 2001). Laser diodeswhosenominalemissionwavelengthis785nm(Hitachi HL7851G, 50mW outputpower) are mounted incollimating tubes(ThorlabsLT110P-B)containinganasphericcollimating lens(f=6.24mm,N.A.=0.40).Thecollimatingtubeisfixedto amodifiedmirrormount(NewportU100-P)inordertoprovide mechanical stability for the diode. The laser beam thenfalls ontoaholographic,1800lines/mmdiffractiongrating(Edmund NT43-775,12.7mm×12.7mm×6mm).Thediffractiongrat- ing is fixed withtwo-sided tape to a45^◦ wedge so that the first-order diffractionis fed back into the diode.The grating is oriented with its grooves along the vertical direction, and the collimatingtubeis rotated untilthe polarization direction of the free-running diodeis also vertical. The grating wedge isattachedtotheL-shapedpartof themodifiedmirrormount (Arnoldetal.,1998).Precisionscrewsinthefixedarmof the modifiedmirrormountprovide verticalandhorizontaladjust- ment of the grating, which are used to optimize the grating feedbackandalsotocoarselytunetheemissionfrequency.Two piezoelectric actuators placed betweenthe horizontalcontrol precisionscrew and theL-pieceare used for scanning of the laser’s emission frequency. Controlof these piezoelectrics is doneviaexternalpowersources.Thezeroth-orderbeamfrom thegrating(outputbeam)isreflectedonabroadbanddielectric mirror(Newport05D20BD.2,12.7mmindiameterand3mm thick),whichismountedonanotherwedgefixedtotheL-piece.

Thisexitmirrorfixtureiswhatallowsthebroadtuningof the laseremissionfrequencywithoutchangingthebeamdirection (Hawthornetal.,2001).Athermistor(10k)placednearthe collimatingtubeisusedtomeasurethelaserdiodetemperature throughoutits operation. Themodified mirror mountis itself attachedtoacopperplatethatrestsonathermo-electriccooler (Marlow DT-3-2.5) that is used for temperature control. The laserdiodecurrentandtemperaturearesetandmonitoredwith

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Figure3.Magneticfieldshieldingandambientlightisolationsetup.

acontrol card(ILX-Lightwave LDC-3916370) mounted in a multi-cardcrate(ILX-LightwaveLDC-3908).Thetwo-photon polarization spectroscopy (Carr,Adams, &Weatherill, 2012) andfluorescence detectionsystemare shownin Figure2(B).

Asexplainedabove,beams derivedfrom780nm and776nm ECDLsaresuperposedinacounter-propagatingconfiguration insideaRbspectroscopycell.The780nmprobelightcompo- nentispreparedinalinearlypolarizedstate,whilethe776nm pump beamcrosses through the cellinacircularly polarized state. In this configuration, optical pumping effects induced by the circularly polarized pump beam create an imbalance inthe atomic populationssensed bythe two opposing circu- lar polarizations in which the linearly polarized probe beam canbedecomposed.Thisgeneratesabirefringenteffectinthe absorptionoftheprobebeam.Toregisterthiseffect,oursetup incorporates aglassslide placed at nearnormal incidence in thepathoftheprobebeamafterithascrossedthroughtheRb cell. Thesmall portionof thebeam pickedbythisslide isin turnregisteredbyabalanceddetectionsystemcomposedbya polarizingbeamcube(PBS)andtwoThorlabsFDS100Siphoto- diodes(PD1andPD2).Ahalfwaveplate(λ/2)inthepathofthe probebeamisusedtosetthedirectionofthepolarizationofthis beamata45^◦anglewithrespecttothereflection/transmission axesofthePBS.Inthismanner,awayfromresonancethesig- nalsregisteredbythe twophotodiodes,PD1andPD2in(B), arebalancedandtheirdifferenceisequaltozero.Ontheother hand,whentheatomicmediumbecomesbirefringentasaresult ofitsinteractionwiththetwolightcomponents,thedifference ofthesignalsgivenbythesephotodiodesgeneratesdispersion- likesignalscenteredintheatomictwo-photonresonances.This setupisparticularlyusefulbecausethedispersion-likeelectronic signals generated as a result of the birefringenceinduced in the atomicmediumcanbe used forlocking thefrequencyof thesecondlasertotransitionsinthe5P3/2→5D5/2manifold (Carr et al., 2012). In addition, when the frequencies of the two laserbeams areresonant withthe two-photontransitions andatomsare successfully pumpedinto any of the sublevels ofthe5D3/2manifold,asaresultofthecascadedspontaneous decay,avisible420nmfluorescencesignalisproduced. Con- sequently,the spectrometerpresentedinFigure2(B)includes

afluorescencedetectionsystemoptimizedforthiswavelength.

ThefluorescencedetectionsystemusesaHamamatsu1P28pho- tomultiplier tube(PMT) that has aspectral response ranging from 185 to650nmwithits maximumsensitivityat340nm.

To operate the PMT we utilize the high voltage source of a Pacific Precision Instruments photometer (model 110) anda Keithley Instruments, model 428-PROG, programmable cur- rent amplifier. To reduce the amount of noise entering into ourdetectionsystemandtoseparatethefluorescencefromthe intensenear-infraredexcitationlightcomponents,theresponse wavelength bandwidthof the PMTis restricted by means of a band-pass interference filter (CVILaser Optics F10-420.0- 0-1.00,λc=420nm,FWHM=10±2nm).Tocharacterizeand optimizetheoperationofthePMTandfiltercombinationforthe detectionoffluorescencewithwavelengths∼420nm,thePMT wasmountedontheoutputportoftheActonSpectra-Pro2150i spectrometerreplacingthenear-infraredInGaAsdetectororigi- nallyattachedtoit.AwhiteLEDwasthenusedtomeasurethe spectralresponseofthePMT.Standardphosphorus-basedLEDs startemittingradiationatwavelengthsslightlyabove400nmand stop ataround 750nm;onthe otherhand,the PMTresponse startingaslowas185nmisperfectlycapableofdetectingthe lower endof the LED emission andcuts downthe spectrum forwavelengthsabove650nm.Thebluefilterwasthenplaced in thelight entrance portof the PMTmount andatransmis- sionspectrawithaFWHMofapproximately7nmcenteredin 421nm was measured. This measurementshows that the fil- terhaspracticallyzerotransmittancebelow412nmandabove 430nm,whichisconsistentwiththeinformationprovidedby themanufacturerofthefilter.Therefore,thecombinationofthe PMTandbluefilterconstitutesanexcellentsystemforisolating the420nmfluorescencelightfromthenear-infraredexcitation lightcomponentsandtoreduceambientlightcontributionsout oftheregionofinterest.Toreduceambientlightcontributions inthefluorescencedetectionsystemevenfurther,particularly within thehightransmissionregionofthefilter,andtoshield theatomsfromstraymagneticfields,theRbcellinwhichthe two-photoninteractionoccurswas mountedinsidethehouse- madeholderasshowninFigure3.Thecellisfirstwrappedin alayerof␮-metal,thencoveredbya1/2thicklayerofblack

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pipeinsulationfoamandallthisisheldinsideasectionof2in diameterstandardplastictubing.Asecondlayerof␮-metalis addedaroundthetubeandtheextremesoftheresultingcylin- derareclosedbycaps.Holesinthecenterofthesecapsallow theexcitationlaserbeamstocrossthroughthecellbutrestrict asmuchaspossibletheentranceoflightfromtheroom.A1

transverseapertureonthesideofthissetupandcoincidingwith thelongitudinalcenterofthecellallowsfortheattachmentof a1Thorlabslenstube.Thistubeincludesapairoflensesfor collectingthefluorescencelight andconcentrating itontothe photocathodeof thePMT.Finally,the bluefilter islocatedin thepiecethatattachestheendofthelenstubetothemountof thePMT.Thetwo-photonspectroscopysystemincorporatesthe polarization spectroscopysetup(Harris etal., 2006;Pearman etal.,2002) showninblock (A)of Figure2.Thissetupalso includesabalanceddetectionsystemcomposedofapolarizing beamsplittercubeandtwophotodiodesformeasuringtherota- tionofthepolarizationvectorofaweaklaserlightcomponent (dashedlineinFig.2(A))wheninteractingwithaRbvaporin thepresenceofamoreintense,circularlypolarizedandcounter- propagatingbeamderivedfromthesamelasersource.Asmall portionofthe780nmlightisthenalsosentintothissectionof thesystemthat allowsustoidentify thehyperfine transitions andcrossoversintheD2lineofatomicrubidiumandtolockthe 780nmlasertoagiventransitionorcross-overfeatureoftheD2

lineofRb.

4. Resultsanddiscussion

Todemonstratetheoperationofthelaserspectroscopysys- tem, in this section we show spectra recorded by means of the two-photon spectroscopy system described in Section 3 andshownschematicallyinFigure2.Thespectrapresentedin Figures4 and 5 were recorded withthe 780nm laser locked tothe 5S1/2,F=3→5 P3/2,F=4 cyclingtransitionof ⁸⁵Rb whilethe frequencyof the 776nmlaser wasscanning across theresonancesof the5P3/2→5 D3/2manifold.The graphin Figure4correspondstothesignalgeneratedinthe420nmfluo- rescencedetectionsystem.ThetopandbottomplotsinFigure5 arerespectivelytherotationofthepolarizationandthechanges intheabsorptioninducedintheprobebeamasaresultofthe presenceof the pumpbeam.The topplot isobtained bytak- ing the difference between the signals recorded by the two photodiodesofthe balanceddetectionsystemincluded inour two-photonspectroscopysetup.Ontheotherhand,theabsorp- tionsignalcorrespondstothesumof thesignalsrecordedby thesephotodiodes.Voigt profile fitsof the fluorescencereso- nancesshowninFigure4 indicatefullwidthsof6.8MHzfor anyoftheobservedlines.Thisresultisconsistentwithconsid- eringthatthewidthofthelinesislimitedbythelinewidthofthe ECDLsutilizedinthisexperiment,whichhavebeenindepen- dentlymeasuredtobeoftheorderof5MHz.Theperformanceof ourlasersiscurrentlylimitedbynoiseinthecurrentsuppliedto thediodes,butultra-low-noisecurrentsuppliesnowadayscom- merciallyavailablecouldbeusedtoliftthislimitationandobtain the width of the resonant two-photontransition. Considering solelytransitionsallowedbytheelectricdipoleselectionrules

Figure4. Thefluorescencesignalobtainedwiththe780nmlaserlockedtothe 5S1/2,F=3→5P3/2,F=4cyclingtransitionof⁸⁵Rbandthefrequencyofthe 776nmlaserscanningacrosstheresonancesofthe5P3/2→5D3/2manifold.

Theseparationofthepeaksisconsistentwiththehyperfinestructureofthe5 D3/2state.Thetwodominatingfeatures(F=4,3)correspondtoatomswith zerovelocitycomponentalongthedirectionofpropagationoftheexcitation beamsandbeingexcitedthroughthe5P3/2,F=4sublevel.Velocitygroupsof atomsmovinginthedirectionofthe780nmbeamareresonantwiththe5S1/2, F=3→5P3/2,F=3,2transitionsandcanthenbepumpedintothe5D3/2, F=2,1sublevels.

startingfromthe5P3/2,F=4sublevel,itwouldbeexpectedto observeonlyresonancesatthefrequenciesoftheF=4→F=4 andF=4→F=3transitions.Theseareindeedthetwodom- inatingcontributionsthat canbeidentifiedinallthe recorded

Figure5.Thepolarizationrotation(top)andthechangesinthetotalabsorption (bottom)inducedinthe780nmbeamobtainedwiththe780nmlaserlockedto the5S1/2,F=3→5P3/2,F=4cyclingtransitionof⁸⁵Rbandthefrequencyof the776nmlaserscanningacrosstheresonancesofthe5P3/2→5D3/2manifold.

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Figure6.Fluorescence(top)andabsorption(bottom)signalsobtainedwiththe780nmlaserscanningacrosstheDopplerbroadenedD2lineof⁸⁵Rbandthefrequency ofthe776nmlaserpassivelystabilizedtotheDopplershiftedresonancesofthe5P3/2→5D3/2manifold.Thedispersioninthemiddlepanelcorrespondstothe one-colorpolarizationspectroscopyshowninblock(A)ofFigure2.SaturatedabsorptionfeaturesintheDopplerwellcanbeidentifiedwiththeD2cyclingtransition (a)andcross-over(c1andc2)featuresintheone-colorpolarizationspectra.Areductionintheabsorptionofthe780nmlightisobservedwhenevertheDopplershifts inducedinbothlightcomponentsmakeavelocitygroupresonantwiththetwo-photontransitions,producingalsoafluorescencesignal.Notethattherelativeheight ofthefourfluorescencepeaksdependsonthepositionofthesefeaturesacrosstheDopplerwell.

spectra.However,therearetwoadditionalpeaksvisibleonlyin thefluorescencespectrum.Therearegroupsofatomsforwhich theirvelocitycomponentalongthedirectionofpropagationof thelasersissuchthattheDopplerred-shiftedfrequencyofthe 780nmlaserbeambecomesresonantwiththe5S1/2,F=3→5 P3/2,F=3oreventhe5S1/2,F=3→5P3/2,F=2transitions.

Thesegroupsofatomssee thefrequencyof the776nmlaser beamshiftedtotheblueandcanthenbeexcitedtotheF=2and F=1sublevelsofthe5D3/2state.Consequently,thetwomain peaksinthefluorescencespectrumandtheonlytwofeaturesdis- cernibleinthepolarizationandabsorptionspectracorrespondto thegroupofatomswhosevelocitycomponentalongthedirec- tionofpropagationofthelaserbeamsiszeroandforwhomthe excitationgoesthroughthe5P3/2,F=4;thefeaturetotheright iscausedbyatomsreachingthe5D3/2,F=4sublevel,while thelowerfrequencypeaksanddispersionsignalcorrespondto atomsexcited tothe 5 D3/2,F=3 state. The two remaining peaksappearinginthelowfrequencyendof thefluorescence signalarerespectivelygeneratedbyatomsmovinginthesame directionasthe780nmlaserbeamwithavelocitythatisenough forproducingaDopplershiftequaltotheseparationbetweenthe F=4andF=3,andtheF=4andF=2hyperfinesublevelsof the5P3/2state.Duetotheclosenessofthewavelengthsofthe twocomponents ofexcitationlight, practicallythesameshift butin the oppositedirection isproduced inthe frequencyof thepumplightinthereferenceframeofthesemovingatoms.

Hence,thefrequencyseparationofthefourpeaksobservedin thefluorescencespectracorrespondstothehyperfinestructure ofthe5D3/2state.Thelinearsectionsinthemiddleofthepolar- ization spectra dispersion-likecurvesare ideal for stabilizing thefrequencyofthesecondlaserofthistwo-photonexcitation scheme(Carretal.,2012;Pearmanetal.,2002).Thesesignals havebeenusedinourlaboratoryastheerrorsignalsthatarefed backtothefrequency-controllingelementofthe776nmECDL (eitherthelaserdiodecurrentorthevoltagesuppliedtothepiezo actuator)tokeepitlockedtotheatomicresonances.Thesetof spectrainFigure6demonstratesanalternativemodeofopera- tionofthesystemdescribedinthispaperfortherealizationof two-photonspectroscopyexperimentswithatomicrubidium.In thesemeasurementsthe780nmlaserwasscanningacrossthe DopplerbroadenedwellcorrespondingtotheD2lineof⁸⁵Rb.

Thefrequencyofthe776nmlaserbeamispassivelystabilized withoutlocking.Bymeansofthevoltagesuppliedtothepiezo actuatorcontrollingtheangleoftheECDLdiffractiongrating,it ispossibletocontrolthelocationofthetwo-photonresonances across theDopplerbroadened well,clearlydemonstratingthe selectionofvelocitiesnaturallyoccurringinthisphysicalsys- tem.Afluorescencesignalisobservedwheneverthesumofthe Dopplershiftedfrequenciesofthetwolasercomponentsinthe referenceframeofthemovingatomsissuchthatitcorresponds tothefrequencydifferencebetweenthe5S1/2upperhyperfine sublevelandthe5D3/2manifold.Inordertoestablisharelative

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frequencyreferenceinthesemeasurements, thegraphsinthe middleofFigure6showthesignalobtainedsimultaneouslyby means of the single-photon polarization spectroscopy system depictedinblock(A)ofFigure2.Thevoltagesignalinthese plotsisthereforeproportionaltotherotationofthepolarization inducedintheprobebeam(dottedbeampathinFigure2(A))as aresultoftheopticalpumpingeffectscausedbytheintense,cir- cularlypolarizedandcounterpropagatinglaserbeam(Pearman etal.,2002).Thisispreciselythedispersion-likesignalutilized forlockingthefrequencyofthislasertoanatomicreferencein themeasurementsshownbefore.Thetotalabsorptioninduced inthesecondarybeamofthe780nmprobescanninglaserwhen crossingthroughthesecondRbcellinthepresenceofthecoun- terpropagatingandcircularlypolarized776nmpumpbeamis presentedinthebottomplotsofFigure6.Thisabsorptionofthe probebeaminthetwo-photonpolarizationspectroscopysetupis givenbythesumofthesignalsregisteredbythetwophotodiodes thatconstitutethebalanceddetectionsystem.Thissignalshows thatasmallamountofprobebeamlightisretro-reflectedbythe windowsofthespectroscopycellproducingsaturatedabsorp- tionfeaturesintheDopplerbroadenedwell. Thesepeakscan thereforebeidentifiedwiththepolarizationspectroscopyfea- turesoftheD2linecyclingtransitionanddominatingcrossovers providingarelativefrequencyscaleforthetwo-photonspectra.

In addition,theabsorption profilesshow thereduction of the absorptionofthefirstphotonoftheladdercausedbytheexcita- tionofdifferentgroupsofvelocitiestothe5D3/2state,features that are accompaniedby fluorescence peaksin the topplots.

Theseplots thereforeshowtheeffectofthe two-photonexci- tationprocesses in the absorptionof the 780nm probe beam togetherwiththe fluorescencegeneratedasthe excitedatoms decaybacktothegroundstate.Bytuningthefrequencyofthe pumplaserit ispossibletoselectthevelocitygroupof atoms interactingwithbothlaserbeamsandthereforebeingpumped intothe5D3/2state.Ifthefrequencyofthe776nmpumpbeam isprepared above the 5 P3/2→5 D3/2 transitions, atomsthat areresonant withthetwo-photon transition mustbelong toa velocitygroupsuchthattheDopplershiftmakestheminteract withthe780nm light beamat afrequencythat isdetuned to theredofthe5 S1/2→5P3/2zero-velocityresonance.In this case,thetwo-photontransitionsignaturesappearonthelowfre- quency(left)sideoftheDopplerwell.Ontheotherhand,the two-photonresonancefeaturesappearatthehighfrequencyend oftheDopplerbroadenedwellwhenthefrequencyofthepump beamislowerthanthefrequencyofthe5P3/2→5D3/2tran- sitions.Hence,theDopplershiftcompensates thedetuningof thepumpbeambyselectingavelocitygroupthatseesthefre- quencyoftheprobebeamdetunedbythesameamountbutin theoppositedirectionandthensetsbothlasercomponents in resonancewiththerespectivetransitions.Aninterestingeffect thatcanbeclearlyobservedthankstoourfluorescencedetection systemisrelatedtotherelativeheightoftherecordedpeaks.The relativeheightofthepeakscorrespondingtoresonancesthatdo notgothroughthe5S1/2,F=3→5P3/2,F=4cyclingtransi- tiondependsonthefrequencyofthepumpbeamandtherefore onthepositionalongtheDopplerbroadenedD2linewell.The lowerthefrequencyofthe780nmbeam,thecloseritgetstothe

F=3→F=3,2transitionsandthegreaterthepopulationofthe velocitygroupofatomsbeingexitedviathesetransitions.Con- sequently,thereisalargerpopulationinthevelocitygroupsthat canbepumpedintothe5D3/2stateviatheseexcitationpathsand thereforecontributingtotheheightofthecorrespondingpeaks.

Finally,itisimportanttoemphasizethat notallthe processes thatareclearlyvisibleinthefluorescencespectradoshowupin theabsorptionorintherotationofthepolarizationoftheprobe beam,hencedemonstratingtheutilityofsimultaneouslyregis- teringinformationofthedifferentprocessesthatconstitutethe two-photonladderexcitationphenomena.

5. Conclusions

Basedontwohomemadediodelasersandaphotomultiplier tube,wehavebuiltasystemtoperformtwo-photonlaserspec- troscopyexperimentswithroomtemperaturerubidiumatoms.

Thesystemisdesignedtomeasuretheabsorptionandthepolar- izationrotationoftheprobelaserthatareinducedbyinteraction between the atoms andthe laser beams. It can also measure the 420nm fluorescence that results from the decay of the 6 Pj excited state in rubidium. The system was tested with electromagneticallyinducedtransparencyandvelocity-selective spectroscopy in the 5 S1/2→5P3/2→5 Dj ladder configura- tionoflevels,whereoneofthedecaypathsofthe5Dj states isthroughtheintermediate6Pjstates.Thesamefluorescence detectioncanbeusedforotherexcitationprocessesifthe6Pj

stateispartofthedecaycascade.Aone-colorpolarizationspec- troscopycellisincorporatedinthesetup,andthepolarization spectraallowadirectfrequencydeterminationoftheabsorption or fluorescence spectra. Theresults show significative differ- ences betweenabsorption andfluorescencespectra,andthese differencesprovidecomplementaryinformationaboutthepro- cesses that take placein the interaction between two optical fields andaDopplerbroadened atomicvapor.The setuppre- sentedinthispaperisalsoaccessibletoadvancedundergraduate laboratories.

Conﬂictofinterest

Theauthorshavenoconflictsofinteresttodeclare.

Acknowledgements

WewanttothankJ.Rangelforhishelpintheconstructionof ourdiodelasers.ThisworkwassupportedbyDGAPA-UNAM, México,underprojectsPAPIITNos.IN116309,IN110812,and IA101012, and by CONACyT, México, under projects Nos.

168451and168498.

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