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1、Crossphasemodulationinafive–levelatomicmedium:SemiclassicaltheoryCarloOttaviani,∗StojanRebi´c,DavidVitali,andPaoloTombesiDipartimentodiFisicaUniversit`adiCamerino,I-62032Camerino,Italy(Dated:February2,2008)Theinteractionofafive-levelatomicsysteminvolvingelectromagneticallyinducedt
2、ransparencywithfourlightfieldsisinvestigated.Twodifferentlight-atomconfigurationsareconsidered,andtheirefficiencyingeneratinglargenonlinearcross-phaseshiftscompared.Thedispersivepropertiesofthoseschemesareanalyzedindetail,andtheconditionsleadingtogroupvelocitymatchingfortwoofthelight
3、fieldsareidentified.Ananalyticaltreatmentbasedonamplitudeequationsisusedinordertoobtainapproximatesolutionsforthesusceptibilities,whichareshowntofitwellwiththenumericalsolutionofthefullBlochequationsinalargeparameterregion.PACSnumbers:42.50.Gy,42.65.-k,03.67.HkSfragrepla
ements(b)
4、I.INTRODUCTION(a)j2ij3iÆ2Anefficientcross-phasemodulation(XPM)inquan-Æ1tumandsemiclassicalregimesisbothinterestingand2usefulinmanypossibleapplications,suchasthosein2j2iÆ1opticalcommunications[1],opticalKerrshutters[2],1quantumnon-demolitionmeasurements[3]andquantumphasegates[4].In
5、allofthese,butthelasttwoespecially,1j3ialargeXPMisdesirableforlowpumppowersandhighj1isensitivities.j1iInastandardthree-levelcascadescheme,showninFIG.1:(a)Three-levelΛ–schemeforEIT.TransitionsareFig.1b,nonlineareffectsareobtainedalongsideabsorp-drivenbytheprobeandcouplingfields,wit
6、hRabifrequencytion,whichincreaseasthefieldsaretunedclosertotheΩ1andΩ2respectively.Whentheprobedetuningδ1matchesatomictransition[5].Toreducetheabsorptiontoanac-thetwophotonRaman-resonanceconditionwiththecouplingceptablelevel,lightfieldsneedtobestronglydetunedfield,theatomicmediumbec
7、omestransparentfortheprobefromtheintermediateatomiclevel
8、2i,simultaneouslyfield.(b)Three-levelcascadeconfiguration.Toobtainsignif-reducinghoweverthesizeofthenonlinearity,sincebothicantnonlineareffectsfortheprobefieldwithRabifrequencyareinverselyproportionaltothesquareofthedetuning.ω
9、1,alargedetuningδ1fromtheintermediatelevel
10、2iis
