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1、RAPIDCOMMUNICATIONSPHYSICALREVIEWA81,051606(R)(2010)TheoryofmagicopticaltrapsforZeeman-insensitiveclocktransitionsinalkali-metalatomsAndreiDerevianko*DepartmentofPhysics,UniversityofNevada,Reno,Nevada89557,USA(Received16December2009;published20May2010)Precisionmeasurementsandquantum-informat
2、ionprocessingwithcoldatomsmaybenefitfromtrappingatomswithspeciallyengineered,“magic”opticalfields.Atthemagictrappingconditions,therelevantatomicpropertiesremainimmunetostrongperturbationsbythetrappingfields.HerewedevelopatheoreticalanalysisofmagictrappingforespeciallyvaluableZeeman-insensitivec
3、locktransitionsinalkali-metalatoms.TheinvolvedmechanismreliesonapplyingamagicbiasBfieldalongacircularlypolarizedtrappinglaserfield.WemapouttheseBfieldsasafunctionoftrappinglaserwavelengthforallcommonlyusedalkalis.WealsohighlightacommonerrorinevaluatingStarkshiftsofhyperfinemanifolds.DOI:10.1103/
4、PhysRevA.81.051606PACSnumber(s):67.85.−d,37.10.Jk,06.30.FtArecurringthemeinmodernprecisionmeasurementsInitialstepsinidentifyingmagicconditionsforhyper-andquantum-informationprocessingwithcoldatomsandfinetransitionsinalkali-metalatomshavebeenmadeinmoleculesaretheso-calledmagictraps[1].Atthemag
5、icRefs.[6–8].Theproposals[7,8]identifiedmagic-wavelengthtrappingconditions,therelevantatomicpropertiesremainconditionsforMF=0states.Duetononvanishingmag-immunetostrongperturbationsbyopticaltrappingfields.neticmoments,thesestates,however,aresensitivetostrayForexample,inopticallatticeclocks,the
6、atomsareheldmagneticfieldswhichwouldleadtoclockinaccuraciesandusinglaserfieldsoperatingatmagicwavelengths[2].Thedecoherences(exceptforspecialcasesofrelativelylargeclocklevelsareshiftedduetothedynamicStarkeffectthatbiasfields,seebelow).Recently,ithasbeenrealizedbydependsonthetrappinglaserwavelen
7、gth.AtthespeciallyLundbladetal.[9]thatmagicconditionsmaybeattainedchosen,magicwavelength,bothclocklevelsareperturbedfortheZeeman-insensitiveMF=0statesaswell.Heretheidentically;thereforethedifferentialeffectoftrappingfieldsbiasmagneticfieldistunedtoma