exploring the van der waals atom-surface attraction in the - hal：探索范德瓦尔斯的原子的表面吸引力的哈尔

EXPLORINGTHEVANDERWAALSATOMSURFACEATTRACTIONINTHENANOMETRICRANGEMFICHET,GDUTIER,AYAROVITSKY,PTODOROV,IHAMDI,IMAURIN,SSALTIEL,DSARKISYAN,MPGORZA,DBLOCHANDMDUCLOYLABORATOIREDEPHYSIQUEDESLASERS,UMR7538DUCNRSETDELUNIVERSITPARIS1399,AVJBCLMENT,F93430VILLETANEUSE,FRANCEPERMANENTADDRESSLEBEDEVPHYSICSINSTITUTE,MOSCOWALSOATPHYSICSDEPARTMENT,SOFIAUNIVERSITY,BULGARIAINSTITUTEFORPHYSICALRESEARCH,NATIONALACADEMYOFSCIENCES,ASHTARAK2,ARMENIACORRESPONDENCETOBEADDRESSEDTOBLOCHLPLUNIVPARIS13FRPACS4250XAOPTICALTESTSOFQUANTUMTHEORY3450DYINTERACTIONSOFATOMSANDMOLECULESWITHSURFACESPHOTONANDELECTRONEMISSIONNEUTRALIZATIONOFIONS3270JZLINESHAPES,WIDTHS,ANDSHIFTSTHEVANDERWAALSATOMSURFACEATTRACTION,SCALINGASC3Z3FORZTHEATOMSURFACEDISTANCE,ISEXPECTEDTOBEVALIDINTHEDISTANCERANGE11000NM,COVERING810ORDERSOFMAGNITUDESINTHEINTERACTIONENERGYACSVAPOURNANOCELLALLOWSUSTOANALYZETHESPECTROSCOPICMODIFICATIONSINDUCEDBYTHEATOMSURFACEATTRACTIONONTHE6P3/26D5/2TRANSITIONTHEMEASUREDC3VALUEISFOUNDTOBEINDEPENDENTOFTHETHICKNESSINTHEEXPLOREDRANGE40130NM,ANDISINAGREEMENTWITHANELEMENTARYTHEORETICALPREDICTIONWEALSODISCUSSTHESPECIFICINTERESTOFEXPLORINGSHORTDISTANCESANDLARGEINTERACTIONENERGYTHEDIPOLEINDUCEDDIPOLEATTRACTIONBETWEENNEUTRALBODIESISAKEYPHENOMENONINTHEULTIMATECOHESIONOFMATTERANDISATTHEORIGINOFCOVALENTCRYSTALSANDVANDERWAALSMOLECULESTHISVANDERWAALSVWTYPEOFATTRACTIONBETWEENFLUCTUATINGATOMICDIPOLESISAPRECURSOROFTHEGENERALCASIMIRINTERACTION1,WHOSEPARAMOUNTIMPORTANCEINTHEQUANTUMTHEORYOFVACUUMHASBEENRECOGNIZEDRECENTLY,ENCOMPASSINGEFFECTSRELATEDTOTHENEEDOFA“COSMOLOGICALCONSTANT“INGENERALRELATIVITYTHEORY,ANDSPECULATIONSABOUTTHEDETECTIONOFAPOSSIBLEFIFTHFORCE2THEINTERESTFORTHEMEASUREMENTOFTHECASIMIREFFECTHASBEENLARGELYRENEWEDWITHTHERECENTUPSURGEOFPRECISIONEXPERIMENTS1,3,WHOSEINTERPRETATIONNOWREQUIRESTOTAKEINTOACCOUNTVARIOUSCORRECTIONSSUCHASTHENONIDEALITYOFTHEMATERIALS,SURFACEROUGHNESS,ANDNONZEROTEMPERATURECORRECTIONSSIMULTANEOUSLY,THEKNOWLEDGEOFTHEVWATTRACTIONBETWEENATOMICPARTICLES,WITHITSC6R6POTENTIALWITHRTHEINTERATOMICDISTANCE,NOWAPPEARSASAFUNDAMENTALNEEDTOPREDICTTHECOLLISIONALBEHAVIOROFACOLLECTIONOFATOMS4,ULTIMATELYCONNECTEDTOTHEPOSSIBILITYFORCOLDATOMSTOCONDENSEACCORDINGTOABOSEEINSTEINSTATISTICSBETWEENTHESETWORELATEDFUNDAMENTALPROBLEMS,ANINTERMEDIATESITUATIONISPROVIDEDBYTHEATOMSURFACEVWINTERACTION,DESCRIBEDBYAC3Z3POTENTIALZTHEATOMSURFACEDISTANCETOTHEORETICALLYESTIMATETHEC3VALUEFROMTHEKNOWLEDGEOFATOMICSTRUCTURES,ANELECTROSTATICMIRRORIMAGEAPPROACHISUSUALLYSATISFACTORYINMANYCASESTHEZ3DEPENDENCEISEXPECTEDTOBEVALIDFORDISTANCESALLOWINGTOIGNORETHESTRUCTURALDETAILSOFTHESURFACETYPICALLY1NM,UPTOTHEMICROMETRICRANGE,WHENRETARDATIONEFFECTSIMPOSETHEMORECOMPLETECASIMIRPOLDERDESCRIPTION2,5ITREMAINSFASCINATINGTONOTETHAT,ALTHOUGHTHEVWZ3ATTRACTIONLAWSHOULDCOVERABOUT810ORDERSOFMAGNITUDEOFENERGY,LITTLEHASBEENDONETOTESTTHISPREDICTEDDEPENDENCEINANEFFECTIVESITUATIONTHEVARIOUSDEVELOPMENTSINNANOTECHNOLOGIESANDNANOSCIENCESSHOULDMAKEITMOREIMPORTANTTOMEASUREEFFECTIVELYTHESEREMOTEFORCES,ASFORTHECASIMIRFORCEALREADYKNOWNTOBEAPOSSIBLELIMITINGFACTORINMEMSTECHNOLOGY6INTHESHORTERDISTANCELIMIT,THEVWATTRACTIONISONLYANASYMPTOTIC“LONGRANGE“TAILOFTHEATOMSURFACEPOTENTIAL,TOTHEEXACTSHAPEOFWHICHSURFACEPHYSICSEXPERIMENTSAREINSENSITIVE7FORLONGERDISTANCES,ANDAFTERPIONEERINGPRINCIPLEEXPERIMENTSUSINGDEFLECTIONOFANATOMICBEAM8,PRECISIONEXPERIMENTSTESTEDTHESPATIALDEPENDENCEONABEAMOFRYDBERGATOMS9CHANNELLEDBETWEENTWOPLATESSEPARATEDBYATLEAST500NMFOLLOWINGTHEBLOSSOMOFEXPERIMENTALMEASUREMENTSOFVWINTERACTIONEXERTEDONALONGLIVEDLEVEL10,11,THESPATIALDEPENDENCEOFVWINTERACTIONBETWEENAGROUNDSTATERBATOMANDAMETALSURFACEWASRECENTLYINVESTIGATEDINTHE20100NMRANGE12SELECTIVEREFLECTIONSRSPECTROSCOPYOFAVAPOURATANINTERFACE,INWHICHWEHAVEBEENINVOLVEDFORALONGTIME13,HASOFFEREDAUNIQUECAPABILITYTOPROBETHEVWINTERACTIONFORSHORTLIVEDEXCITEDSTATESITISALSOAPPROPRIATEFORANALYZINGTHEATOMINTERACTIONWITHATRANSPARENTDIELECTRICSURFACEALTHOUGHADIELECTRICSURFACECOMMONLYEXERTSAWEAKERINTERACTIONTHANAMETAL,OWINGTOANIMPERFECTREFLECTION,ASPECIFICREGIMEOFRESONANTCOUPLINGOFTHEATOMICEXCITATIONWITHTHEELECTROMAGNETICMODESOFTHEDIELECTRICSURFACE,COULDBEDEMONSTRATEDWITHTHISSRTECHNIQUE,LEADINGTOANEXOTICVWREPULSION14HOWEVER,THEDEPTHOFTHEREGIONPROBEDINTHESRTECHNIQUEREMAINSFIXED,ASGOVERNEDBYTHEREDUCEDWAVELENGTHOFTHEOPTICALPROBE13HERE,WEUSEANALTERNATETECHNIQUEOFSPECTROSCOPYINAVAPOUR“NANOCELL“15,WHOSETHICKNESSDISVARIEDINARANGED40130NMTHISALLOWSTOEXPLORETHESPATIALDEPENDENCEOFTHEVWINTERACTIONFORABEAMOFATOMSFLYINGPARALLELTOTHETWOWINDOWSANDATMIDDISTANCESEEEG9ACONSTANTVWSHIFTOFTHEATOMICRESONANCE,SCALINGAS1/D3,ISEXPECTED,EVENIFMULTIPLEDIELECTRICIMAGESARECONSIDEREDTHEVWSHIFTISHEREASPECTROSCOPICSHIFT,CORRESPONDINGTOTHEDIFFERENCEBETWEENTHEVWINTERACTIONEXERTEDONTOTHEFINALLEVELOFTHETRANSITION,ANDTHEONEEXERTEDONTOTHEINITIALONEHOWEVER,FORATOMSINAVAPOURPHASE,THEVWSHIFTISSPATIALLYINHOMOGENEOUS,ZD/2ISONLYTHELOCATIONOFTHEMINIMALVWSHIFT,ANDTHELINESHAPESUNDERGOASPATIALINHOMOGENEOUSBROADENINGLEADINGTODISTORTIONSANDASYMMETRIESINTHISSENSE,THEPRELIMINARYOBSERVATIONOFANELEMENTARY1/D3DEPENDENCEOFTHEFREQUENCYOFTHEMINIMALTRANSMISSION17WASNOTASUFFICIENTEVIDENCEOFTHEVWDEPENDENCETHEPRINCIPLEOFOURESTIMATEOFTHEVWINTERACTIONFORAGIVENNANOCELLTHICKNESSDRELIESONANUMERICALCOMPARISONBETWEENTHEEXPERIMENTALSPECTRAANDAFAMILYOFRELEVANTTHEORETICALLINESHAPESOUREXPERIMENTWASCONDUCTEDONTHE6P3/26D5/2TRANSITIONOFCS917NMINANANOCELLWITHYAGWINDOWSTHECHOICEOFATRANSITIONBETWEENEXCITEDSTATESISTOALLOWASTRONGVWSHIFT,MAINLYORIGINATINGINTHEVWINTERACTIONEXERTEDONTOTHEHIGHLYING6DLEVELFIG114ONEPREDICTSINDEEDC3METAL6D5/224KHZM3C3METAL6P3/24KHZM3,ANDINFRONTOFAYAGWINDOWC3YAG6D5/217KHZM3,C3YAG6P3/22KHZM3,YIELDINGASPECTROSCOPICC3VALUEOF15KHZM3FORYAGWINDOWSTOREACHTHETRANSITIONOFINTEREST,APRIORPUMPINGSTEPTOCS6P3/2ISNEEDED,WHICHISPERFORMEDWITHA852NMFREQUENCYSTABILIZEDLASERSEEFIG1YAGWINDOWSWEREPREFERREDTOSAPPHIREINTHEDESIGNOFTHENANOCELLBECAUSEINTHEATOMDIELECTRICSURFACE,THEREARENOSTRONGCOUPLINGSBETWEENYAGSURFACERESONANCESANDVIRTUALTRANSITIONSRELEVANTFORCS6D5/214THENANOCELL,ONCEEVACUATED,ISFILLEDWITHANALKALIMETALVAPOUR,ANDCONSISTSOFASYSTEMOFTWOTHICKWINDOWS,THATAREGLUEDANDMAINTAINEDSEPARATEDBYANANOMETRICSPACER15THEEXTERNALATMOSPHERICPRESSUREISRESPONSIBLEFORLOCALVARIATIONSOFTHENANOCELLTHICKNESS15,SOTHATTRANSLATINGTHECELLTHROUGHAFOCUSEDLASERALLOWSTOMONITORTHEINFLUENCEOFTHETHICKNESSUNDERUNCHANGEDEXPERIMENTALCONDITIONSASALREADYREPORTED,THEFABRYPEROTNATUREOFTHENANOCELLALLOWSACONVENIENTDETERMINATIONOFTHELOCALTHICKNESSD15HERE,FORTHEVERYSMALLTHICKNESSESWEAREINTERESTEDIN,ADUALWAVELENGTHMEASUREMENT633NMAND852NMISSUFFICIENTTHEACCURACYIS1TO5NM,DEPENDINGUPONTHEPARALLELISMOFTHEWINDOWSATTHECONSIDEREDSPOT,WHOSEDIAMETERIS100MALSO,THEFABRYPEROTNATUREOFTHENANOCELLALLOWSTHEDETECTIONOFBOTHTRANSMISSIONANDREFLECTIONSIGNALSRESPECTIVELYST,ANDSR15,16THESPECTRAWERESIMULTANEOUSLYRECORDED,FORTHICKNESSESD40NM,50NM,65NM,80NM,100NMAND130NMTHEDETECTIONSENSITIVITYISENHANCEDBYAPPLYINGAMODULATIONTOTHE852NMPUMPINGBEAM,WITHASUBSEQUENTSYNCHRONOUSDETECTIONONTHE917NMPROBETHETRANSITIONINFREESPACEISMONITOREDBYANAUXILIARYSATURATEDABSORPTIONSAEXPERIMENTONTHE917NMLINEINAMACROSCOPICCELLANDPROVIDESTHEFREQUENCYREFERENCEREQUIREDFORINTERPRETINGTHENANOCELLSPECTRAINANAPPROACHANALOGOUSTOTHEONEDEVELOPEDPREVIOUSLYEGIN14,EXPERIMENTSWEREPERFORMEDATSEVERALCSDENSITIESIETEMPERATUREFOREACHINVESTIGATEDSPOTOFTHENANOCELLTHISISTOMINIMIZETHEINFLUENCEOFCSPRESSUREONTHEEXTRACTEDC3VALUEALSO,AVARIETYOFPUMPINGCONDITIONSWASEXPLOREDTOASSESSTHESPATIALHOMOGENEITYOFTHE6P3/2POPULATIONINTHETHEORETICALMODELLING,THETRANSMISSIONANDREFLECTIONSIGNALSSTANDSRAREDERIVEDFROMLINEARLYINDEPENDENTINTEGRATIONS16OFTHELOCALVAPOURRESPONSEPZASGOVERNEDBYTHERESONANTLYINDUCEDATOMICDIPOLEOSCILLATIONTHISATOMICOSCILLATIONISMODELLEDONTHEBASISOFANINSTANTANEOUSRESONANTLORENTZIANRESPONSE/2I0Z1,THATDEPENDSUPONTHEDETUNINGBETWEENTHEEXCITATIONFREQUENCYANDTHELOCALVWSHIFTEDATOMICRESONANCE0ZISTHEOPTICALWIDTHITEXHIBITSANONLOCALDEPENDENCEUPONTHEIRRADIATINGFIELD,OWINGTOTHETRANSIENTREGIMEGOVERNINGTHEVELOCITYDEPENDENTATOMICRESPONSEOVERTHEWALLTOWALLTRAJECTORIESINTHEMODELLING,THEUNSHIFTEDTRANSITION,CANPOSSIBLYACCOMODATEPRESSUREBROADENINGANDSHIFTHENCE,STANDSRINTEGRATEACOMPLEXINTERPLAYOFNATURALWIDTH,DOPPLERBROADENINGANDVELOCITYDISTRIBUTION,PRESSUREEFFECTS,ANDSPATIALDEPENDENCEOFTHEVWPOTENTIALOURCOMPLETECALCULATIONEVENCONSIDERSMULTIPLEELECTROSTATICIMAGESFORTHEVWPOTENTIALALTHOUGHATWOWALLPOTENTIALVZC3Z3DZ3AGREESWITHIN5ASLONGASTHEDISPERSIONOFTHEDIELECTRICWINDOW14ISNEGLIGIBLESTRONGVARIATIONSOFTHELINESHAPESAREHENCEPREDICTEDWHENCHANGINGD,ORC318HOWEVER,WHENTHEVWINTERACTIONDOMINATESOVEROTHERCAUSESOFBROADENING,THESPECTRALSHIFTFOLLOWSA1/D3DEPENDENCERATHERWELLFORPARAMETERSRELEVANTTOOURPROBLEM,THEMODELLINGSHOWSTHATTHE40130NMRANGEISSUFFICIENTTOEXPLOREAFACTOR30INTHEENERGYOFSURFACEINTERACTIONSEEFIG2TECHNICALLY,THEANALYSISRELIESONAFITTINGOFTHEEXPERIMENTALSPECTRASTANDSRWITHTHEFAMILYOFC3CURVESCALCULATEDFORAGIVENTHICKNESSDTHESTRONGCONSTRAINTSONTHEVWSHIFTANDLINESHAPERESTRICTTHEC3VALUESPROVIDINGASATISFACTORYLEASTSQUAREFITTINGTOANARROWRANGE,TYPICALLY1020AROUNDTHECENTRALVALUEWHENTHEVWSHIFTISDOMINANT,THEVWSPATIALBROADENINGMAKESFITTINGSNEARLYINSENSITIVETOTHEADJUSTMENTOFTHEWIDTHOFTHEOPTICALTRANSITIONTHEMAINRESULTSOFOURSYSTEMATICANALYSISARETWOFOLDIFORAGIVENEXPERIMENT,AVERYGOODCONSISTENCYBETWEENTHESHAPESOFSTANDSRSIGNALSISDEMONSTRATED18THEIRRELATIVEAMPLITUDESAREALSOINAGREEMENTONCECONSIDEREDTHESCATTERINGLOSSES19THISCONSISTENCYISREMARKABLEBECAUSEITAPPEARSFORLINESHAPESTHATAREUNRELATED,ANDWITHFITTINGPARAMETERSTHATAREINDEPENDENTLYCHOSENIITHEOPTIMALFITTINGC3VALUESAREFOUNDTOBEINDEPENDENTOFTHETHICKNESSFIGURE3ILLUSTRATESSYNTHETICALLYTHISCONSISTENCYALLSPECTRARECORDEDINIDENTICALCONDITIONS,BUTFORVARIOUSTHICKNESSES,AREFITTEDWITHASINGLESETOFPARAMETERSTHERESIDUALDISCREPANCIESINTHEFITTINGDISAPPEARWITHMOREINDIVIDUALADJUSTMENTS,ANDTHEINDIVIDUALC3FITTINGVALUESAREMODIFIEDONLYMARGINALLYFIG4ISAPLOTOFTHEINDIVIDUALLYOPTIMIZEDFITTINGVALUEFORC3FORDIFFERINGTHICKNESES,ANDPRESSURECONDITIONSWHENRETAININGONLYTHEEXPERIMENTSATRELATIVELYLOWPRESSURE,ONEGETSANACCURATEVALUEC3143KHZM3FORTHESMALLESTTHICKNESSIEDOMINANTVWCONTRIBUTION,THEOBTAINEDC3VALUESAREINDEPENDENTONTHECSPRESSURE,INSPITEOFAPRESSUREBROADENINGVISIBLEINTHELINESHAPESFORLARGERTHICKNESSD80NM,THEVWSHIFTANDBROADENINGBECOMEPARTLYHINDEREDBYPRESSUREEFFECTS,ANDDECREASINGC3VALUESAREFOUNDWHENINCREASINGTHECSDENSITYANDINDEED,FORTHELARGETHICKNESSES,WHENTHEVWINTERACTIONTURNSTOBERELATIVELYSMALL,THEACCURACYOFTHEC3DETERMINATIONSTARTSTOBEAFFECTEDBYUNCERTAINTIESONTHE917NMSAREFERENCEFREQUENCYITSELFANUNCONTROLLEDPREFERENTIALPUMPINGTOASPECIFIC6P3/2HYPERFINESUBLEVELISSUSCEPTIBLETOOCCUR,OWINGTONONLINEARITIESINTHED2PUMPINGNOTWITHSTANDINGTHEEXCELLENTAGREEMENTBETWEENTHEEXPERIMENTALDATAANDTHETHEORETICALLYMODELLEDCURVES,THEREPRODUCIBILITYISSUESAREWORTHBEINGDISCUSSED,ASWELLASTHEEFFECTIVENATUREOFTHEINTERACTINGSURFACEREPRODUCIBILITYINTHEVICINITYOFADIELECTRICINTERFACEISSHOWNTOBEANISSUEIN2,WITHNUMEROUSERRATICPOINTSOBTAINED,EVENWITHWELLCHOSENSURFACESINOUREXPERIMENT,THEMEASUREDTHICKNESSISANAVERAGE,OVERTHELASERSPOTDIAMETER100MOFLOCALWALLTOWALLDISTANCEDBECAUSEOFTHELOCALSURFACEROUGHNESSESTIMATEDTO12NM,ANDOFTHEDEFECTSINPLANARITYORPARALLELISMTHEMINIMALOBSERVEDSLOPEOFTHENANOCELLCANBEASSMALLAS10NMFOR1MM15,THEOBSERVEDVWEFFECTCANVARYFORCOMPARABLESPOTSAS3THESURFACEOFOURNANOCELLLARGELYEXCEEDINGTHESPOTSIZE,SEVERALEXPERIMENTSWITHASIMILARNOMINALAVERAGETHICKNESSCANBECOMPAREDAPERFECTLINESHAPEREPRODUCIBILITYHASBEENFOUNDFORALLTHEVARIOUSINVESTIGATEDSPOTS,ASLONGASD65NMATD50NM,SEVERALSPOTSBUTNOTALLOFTHEMPRODUCERIGOROUSLYIDENTICALSPECTRATHEYARETHOSEHEREANALYZED,ASAPPARENTLYIMMUNETORANDOMDEFECTSOFTHESURFACETHATWOULDNOTBECOMPATIBLEWITHTHEOBSERVATIONOFSIMILARSPECTRAONADIFFERINGSPOTFORD40NM,SENSITIVEVARIATIONSAREOBSERVEDFROMSPOTTOSPOTHOWEVER,EXCEPTFORAFEWERRATICBEHAVIOURSCLEARLYOUTOFTHECONSIDEREDFAMILYOFLINESHAPES,MINORIRREPRODUCIBILITIESDONOTPROHIBITAFITTINGASEXEMPLIFIEDINFIG3REMARKABLY,INTHISREGIMEOFVERYSTRONGVWINTERACTION,MINORCHANGESINTHEFITTINGPARAMETERSSUFFICETOINTERPRETVISIBLEVARIATIONSINTHELINESHAPESTHEEXACTNATUREOFTHEINTERACTINGSURFACECANALSOBEANISSUE,ESPECIALLYBECAUSETHESURFACEISINCONTACTWITHAVAPOUR,ANDBECAUSEFORADIELECTRICSURFACE,RELATIVELYHIGHSTATICELECTRICFIELDSCANINDUCESTARKSHIFTSINAVAPOUR,CSATOMSARESUSCEPTIBLETODEPOSITON,ORPENETRATETHEYAGSURFACEHOWEVER,THEDIELECTRICFUNCTIONCHARACTERIZINGTHEVWSURFACERESPONSESHOULDREMAINNEARLYUNAFFECTEDBYTHESEKINDSOFNONRESONANTDOPANTS20THECOMPETITIONBETWEENTHEVWSHIFT,ANDTHESTARKSHIFTINDUCEDBYARESIDUALSTATICFIELDCANPOSEAMORESERIOUSPROBLEM,ASRECOGNIZEDIN9MOREOVER,STRONGERRESIDUALFIELDSCANBEEXPECTEDFORADIELECTRICWINDOW21THANFORAMETALCOATINGINPARTICULAR,FORSOMERANDOMDISTRIBUTIONSOFCRYSTALLINEDOMAINS,THEOVERALLSTARKSHIFTMAYEXHIBITAZ2DEPENDENCE9,THATCOULDBEHARDTODISTINGUISHFROMAVWSHIFTINTHESPECTROSCOPICRESPONSECONVERSELY,ACONSTANTSTARKSHIFTWOULDBEEASILYDETECTEDINANANALYSISOFOURFITTINGSTHISISASEVEREPROBLEMFOREXPERIMENTSONRYDBERGLEVELS,BECAUSEWHENINCREASINGTHEATOMICEXCITATION,THESTARKSHIFTGROWSFASTERTHANTHEVWSHIFTRESPECTIVELYLIKEN7,ANDN4INCOMMONAPPROXIMATIONS,FORNTHEEFFECTIVEQUANTUMNUMBERFROMOUROWNEXPERIENCEWITHCSCLOSETOAYAGWINDOW,WECANCONCLUDETHATTHEINFLUENCEOFRESIDUALFIELDSSHOULDREMAINMINORASREXPERIMENTONTHECS7P10DLINEAT13M22ATACOMPARABLEYAGINTERFACEHADINDEEDSHOWNTHESTARKSHIFTTOBENEGLIGIBLEIE100MHZEXTRAPOLATIONFROMCS10DN75TOCS6DWITHN35HENCEIMPLIESAMAXIMALSTARKSHIFTONTHEORDEROFMHZINSIMILARCONDITIONSEVENIFAPOSSIBLEZ2DEPENDENCEISCONSIDERED,THEINFLUENCEOFTHESTARKSHIFTSHOULDREMAINBELOWSEVERAL100MHZFORTHESMALLERNANOCELLTHICKNESSES,ANDBEEVENLESSFORLARGERTHICKNESSESTHISISWHYWEESTIMATETHATTHEMAJORCAUSESOFIRREPRODUCIBILITYARECONNECTEDTOUNCERTAINTIES,ATTHELEVELOFAFEWNM,INTHELOCALGEOMETRYOFTHETWOPLANARWINDOWS,RATHERTHANTOTHEEFFECTOFSTRAYFIELDSOURESTIMATEDVALUEC314KHZM3ISINVERYGOODAGREEMENTWITHTHE15KHZM3THEORETICALPREDICTIONTHISAGREEMENTMAYBECONSIDEREDASREMARKABLEINVIEWOFVARIOUSPITFALLS,EITHEREXPERIMENTAL,ORTHEORETICALAPRECISEEVALUATIONOFTHEDIELECTRICIMAGEFACTORAPPLICABLETOCS6D5/2ISDELICATE23BECAUSETHESITUATIONISNOTPURELYNONRESONANTTHEVIRTUALEMISSIONCOUPLINGCS6D5/2TO7DINTHE15MREGIONREQUIRESTHEACCURATEKNOWLEDGEOFTHEYAGSPECTRUMANDOFITSSURFACEMODESMOREOVER,INANANOCELL24,THEATOMCOUPLESTOAGUIDEDMODESTRUCTURE,ANDTHETWOWALLMODEL,ORITSSTRAIGHTFORWARDEXTENSIONTOMULTIPLEELECTROSTATICIMAGESMODEL,MAYREVEALTOOELEMENTARYALSO,THEORIENTATIONOFTHEATOMHASBEENASSUMEDTOBEISOTROPIC,IMPLYINGEQUALCONTRIBUTIONSFORTHEDIPOLEFLUCTUATINGALONGTHENORMAL,ANDPARALLELTOTHEINTERFACEHOWEVER,THEATOMCOULDUNDERGOAZEEMANPOLARIZATIONUNDERTHEINFLUENCEOFTHED2LINEPUMPINGTHEIRRADIATION,BEINGUNDERNEARNORMALINCIDENCE,ISPOLARIZEDPARALLELTOTHESURFACES,ORTHROUGHTHEPOLARIZEDEXCITATIONOFTHE917NMLASERTHISWOULDRESTRICTTHESUMMATIONOVERTHEVIRTUALDIPOLETRANSITIONSCONNECTINGTHE6D5/2LEVELTOONLYSOMEDIRECTIONS,REDUCINGTHEPREDICTEDC3VALUE24MOREGENERALLY,ARECENTWORK25SHOWSTHATC3ITSELFSHOULDEXHIBITASPATIALDEPENDENCEC3Z,BECAUSEATTHESMALLERDISTANCES,THENONRETARDEDCONTRIBUTIONOFTHEHIGHLYENERGETICTRANSITIONSINVOLVINGTHEELECTRONICCOREBECOMESSTRONGER4THISDEPENDENCE,ACTUALLYUNOBSERVED10,12,ISHOWEVEREXPECTEDTOBESMALLERINOURSITUATIONOFAHIGHLYINGSTATE13,THANFORAGROUNDSTATETOSUMMARIZE,WEHAVEINVESTIGATEDTHEZ3DEPENDENCEOFTHEVWPOTENTIALFORA40130NMTHICKNESSRANGE,ANDANENERGYSHIFTSPANNINGOVERAFACTOR30OURTECHNIQUECOULDBEEXTENDEDTOTESTTHERICHPHYSICSOFANATOMRESONANTLYINTERACTINGWITHCOUPLEDSURFACEMODESTHEDISTANCESINVESTIGATEDHEREAREANORDEROFMAGNITUDEBELOWTHOSEEXPLOREDYEARSAGOFOREXCITEDATOMSINRYDBERGLEVELS9,ANDCOMPARESFAVOURABLYWITHTHOSECURRENTLYINVESTIGATEDINPRECISIONCASIMIRMEASUREMENTS3,ORWITHTHEONEADDRESSEDINTHERECENTVWINTERACTIONEXPERIMENTSWITHGROUNDSTATEATOMS12NOTETHATINOURSITUATION,THEVWSHIFT,WHOSEMINIMALVALUEISTWICETHEONEUNDERGONEBYANATOMATADISTANCED/2,ISEQUIVALENTTHEONEOFANATOMLOCATEDAT04DFROMASINGLEWALLALSO,THECOMBINEDEFFECTSOFTHETRANSIENTREGIME,ANDTHESTEEPNESSOFTHEVWPOTENTIAL,MAKETHECENTRALREGIONOFTHENANOCELLSPECTRALLYDOMINANT,ASCANBEINFERREDFROMFIG2HENCE,THEINDIVIDUALEVALUATIONSC3DTURNOUTTOBENEARLYFREEOFSPATIALAVERAGINGLOWERINGTHEEFFECTIVEATOMSURFACEDISTANCEBELOW10NMAPPEARSAREALISTICOBJECTIVEFEASIBILITYOFD2030NMISREPORTEDIN17THISISINCONTRASTWITHTHEVWMEASUREMENTSBASEDUPONTHEREFLECTIONOFSLOWATOMS10,12THEMINIMALDISTANCEOFAPPROACHOFTHEOBSERVEDATOMICTRAJECTORIESISLIMITEDBYTHECONSIDERABLEFORCETHATSHOULDBEAPPLIEDTOEQUILIBRATETHEVWATTRACTIONSIMILARLY,THETECHNIQUESOFATOMICFORCEMICROSCOPYPRESENTLYUSEDFORTHEEVALUATIONOFCASIMIRINTERACTION,AREHARDLYCOMPATIBLEWITHTOOHIGHAPRESSURETHESTANDARDCALCULATIONPREDICTSINDEEDACASIMIRINTERACTIONEXCEEDINGTHEATMOSPHERICPRESSUREFORD10NMNOTETHATFORTHESESMALLDISTANCES,THEASYMPTOTICREGIMEOFVANDERWAALSCASIMIRRELATEDINTERACTIONREMAINSUNDERDEBATE26FINALLY,ITISWORTHMENTIONINGTHATINTHESMALLDISTANCEREGIMETHATWEEXPLOREHERE,WEDEMONSTRATEANINTERACTIONENERGYUPTO5GHZ,OR025KMUCHLARGERTHANOBTAINEDINALLPREVIOUSINVESTIGATIONSTHISCORRESPONDSTOACONSIDERABLEACCELERATION8107GFORACS6DATOM20NMAWAYFROMONEOFTHEWALL,EXCEEDINGBYORDERSOFMAGNITUDETHEONEOBTAINEDINLASERCOOLINGTECHNIQUESTHISMAYOPENAREALMOFEXOTICPOSSIBILITIES,SUCHASAGRADIENTOFDENSITYFORANATOMICGASINTHEEXTREMEVICINITYWITHTHESURFACEWORKPARTIALLYSUPPORTEDBYFASTNETEUROPEANCONTRACTHPRNCT200200304ANDBYFRENCHBULGARIANCOOPERATIONRILA09813UKREFERENCES1HBGCASIMIR,PROCKONNEDAKADWETENSHAP60,7931948FORREVIEWS,SEEEGMBORDAG,UMOHIDEENANDVMOSTEPANENKO,PHYSREP353,12001ALAMBRECHTANDSREYNAUD,INPOINCARSEMINAR2002,VACUUMENERGY,BVRIVASSEAUED,BIRKHAUSER,P1092003KAMILTON,JPHYSA,37,R20920042DMHARBERETAL,PHYSREVA72,03361020053UMOHIDEENANDAROY,PHYSREVLETT81,45491998TEDERTH,PHYSREVA620621042000,FCHENETAL,PHYSREVA69,02211720044ADEREVIANKOETAL,PHYSREVLETT82,358919995HBGCASIMIRANDDPOLDER,PHYSREV73,36019486HBCHANETAL,PHYSREVLETT87,2118012001EBUKSANDMLROUKES,EUROPHYSLETT5422020017FOGOODMANANDHYWACHMAN,“DYNAMICSOFGASSURFACESCATTERING“,ACADEMICPRESS,19768DRASKINANDPKUSCH,PHYSREV179,71219699VSANDOGHDARETAL,PHYSREVLETT6834321992PHYSREVA53,1919199610ALANDRAGINETAL,PHYSREVLETT77,1464199611REGRISENTIETAL,PHYSREVLETT83,17551999MBOUSTIMIETAL,PHYSREVLETT86,27662001FSHIMIZU,PHYSREVLETT,86,987990200112AKMOHAPATRAANDCSUNNIKRISHNAN,EUROPHYSLETT73,839200613FORAREVIEW,SEEDB