玻色-爱因斯坦凝聚课件

专题三：玻色－爱因斯坦凝聚经典统计分布函数量子统计分布函数玻色－爱因斯坦凝聚经典统计分布函数一绝热系统处在势场中：如粒子动力学只容许分立能量：普朗克能量均分定理利用它可推导出黑体辐射公式2.量子统计分布函数两个全同粒子，推广到n个全同粒子（玻色子），n个玻色子处于相同状态的几率n！倍于其经典几率。问题：将一个玻色子放在一个状态上去的几率和状态原有的玻色子数目有何关系？再放一个的几率是相应经典几率的(n+1)倍，增强因子（1+n）费米子：为得量子统计分布，还需精细平衡原理。费米子：1－n取代1+n玻色－爱因斯坦分布函数费米－狄拉克分布函数QuantumStatisticsPredicted1924…

…Created19953.玻色－爱因斯坦凝聚AgainstOurIntuition?!

Inmosteverydaymatter,thedeBrogliewavelengthismuchshorterthanthedistanceseparatingtheatoms.Inthiscase,thewavenatureofatomscannotbenoticed,andtheybehaveasparticles.ThewavenatureofatomsbecomenoticeablewhenthedeBrogliewavelengthisroughlythesameastheatomicdistance.Thishappenswhenthetemperatureislowenough,sothattheyhavelowvelocities.Inthiscase,thewavenatureofatomswillbedescribedbyquantumphysics,e.g.theycanonlystayatdiscreteenergystates(energyquantization).BoseandEinsteinIn1924anIndianphysicistnamedBosestudiedthequantumbehaviourofacollectionofphotons.BosesenthisworktoEinstein,whorealizedthatitwasimportant.Einsteingeneralizedtheideatoatoms,consideringthemasquantumparticleswithmass.Einsteinfoundthatwhenthetemperatureishigh,theybehavelikeordinarygases.However,whenthetemperatureisverylow,theywillgathertogetheratthelowestquantumstate.ThisiscalledBose-Einsteincondensation.Fermions(費米子)andBosons(玻色子)NotallparticlescanhaveBEC.Thisisrelatedtothespinoftheparticles.Thespinquantumnumberofaparticlecanbeanintegerorahalf-integer.Singleprotons,neutronsandelectronshaveaspinof½.Theyarecalledfermions.Theycannotappearinthesamequantumstate.BECcannottakeplace.Someatomscontainanevennumberoffermions.Theyhaveatotalspinofwholenumber.Theyarecalledbosons.Bosonsshowstrong“social”behaviour,andcanhaveBEC.Example:A23Naatomhas11protons,12neutronsand11electrons.TheMaterialForBEC

BECwasfoundinalkalimetalse.g.87Rb(铷),23Na(钠),7Li(锂)because:Theyarebosons.Eachatomisasmallmagneticcompass,sothatacoolingtechniquecalledmagneticcoolingcanwork.Theatomshaveasmallrepulsion,sothattheydonotliquefyorsolidifydowntoaverylowtemperature.CoolingDowntheAtomsSeetheanimation:Whenthetemperatureishigh,theatomshavehighenergiesonaverage.Theenergylevelsarealmostcontinuous.Itissufficienttodescribethesystembyclassicalphysics.Whenthetemperatureislow,theatomshavelowenergiesonaverage.Itisnecessarytodescribethesystembyquantumphysics.Whenthetemperatureisverylow,alargefractionofatomssuddenlycrashintothelowestenergystate.ThisiscalledBose-Einsteincondensation.Q2:HowIsBECMade?LaserbeamOtherequipment:laserequipment,computer,electronicsCostlessthanUS$100,000LaserCooling(激光冷卻)Thetechniqueoflasercoolingwasdevelopedbythewinnersofthe1997NobelPrizewinners.Inthephysicalworld,thelowesttemperaturesapproachalimitof–273oC.Thisiscalledtheabsolutezero.Nothingcanbeascoldastheabsolutezerobecauseallatomicandsubatomicmotionsstop.Lasercoolingcangettothelowtemperatureof0.18K(1K微開=10-6K).Chu朱棣文Cohen-TannoundjiPhillipsUsingtheDopplerEffectProblem:Thelasercanslowtheapproachingatoms,butitcanalsoblastofftherecedingones.Solution:UseDopplershift.Whentheatomisrecedingfromthelasersource,thewavelengthislengthenedandthereisaredshift.Whentheatomisapproachingthelasersource,thewavelengthisshortenedandthereisablueshift.Seetheanimation:LaserTrapping(激光陷阱)Supposethelaserhastherightcolourforthephotonstobeabsorbedbyanapproachingatom,thentheatomwillbesloweddown.However,thelaserwillnothavetherightcolourforthephotonstobeabsorbedbytherecedingatombecauseofDopplereffect.Hencetheatomwillnotchangeinthiscase.Whenlasersaresentinfromallthedifferentdirections,theatomscangetcoldveryquickly.Thisiscalledlasertrapping,andthetrappedatomsformanopticalmolass

(光學粘膠).Seetheanimation:MagneticTrapping(磁性陷阱)Problem:Lasercoolingcancooltheatomsdownto10K,becauseatomscanspontaneouslyemittheabsorbedphoton.ThisisstilltoohotforBEC.Solution:EvaporativecoolingTheatomsbehaveastinycompasses.Theycanbepulledbymagneticfields.Amagneticfieldcanbedesignedtopushtheatomsinwardsfrombothsides,formingamagnetictrap.Seetheanimation:EvaporativeCooling(挥发冷却)Principle:Evaporationtakesheat.Acupofteagetscoolaftersteamescapes,becausefasteratomsescapefromthecup,leavingbehindtheslowerones.Technique:Lowertheheightofthetrapquickly,sothattherearestillenoughatomsleftinthetraptogetinvolvedinBEC.TrytotrapthelargestnumberofatomsinBECintheanimation:CanYouBreakThisRecord?Q3:WhatDoesaBose-EinsteinCondensateLookLike?Thereisadropofcondensateatthecentre.Thecondensateissurroundedbyuncondensedgasatoms.Thecombinationlookslikeacherrywithapit.Seethemoviewhenitcoolsfrom400nKto50nK

(1nK=10-9K).:

TheNobelPrizeinPhysics2001

USA(EricA.Cornell,1961)Germany(WolfgangKettlerle,1957)USA(CarlE.Wieman,1951)“fortheachievementofBose-Einsteincondensationindilutegasesofalkaliatoms,andforearlyfundamentalstudiesofthepropertiesofthecondensates"Whatisanatomlaser?Anatomlaserisanalogoustoanopticallaser,butitemitsmatterwavesinsteadofelectromagneticwaves.Itsoutputisacoherentmatterwave,abeamofatomswhichcanbefocusedtoapinpointorcanbecollimatedtotravellargedistanceswithoutspreading.Thebeamiscoherent,whichmeans,forinstance,thatatomlaserbeamscaninterferewitheachother.Comparedtoanordinarybeamofatoms,thebeamofanatomlaserisextremelybright.Onecandescribelaser-likeatomsasatoms"marchinginlockstep".Althoughthereisnorigorousdefinitionfortheatomlaser(or,forthatmatter,anopticallaser),allpeopleagreethatbrightnessandcoherencearetheessentialfeatures.Ketterle‘shomepageAtomictrap ATOMICTRAPcoolsbymeansoftwodifferentmechanisms.First,sixlaserbeams(red)coolatoms,initiallyatroomtemperature,whilecorrallingthemtowardthecen-terofanevacuatedglassbox.Next,thelaserbeamsareturnedoff,andthemagneticcoils(copper)areener-gized.Currentflowingthroughthecoilsgeneratesamagneticfieldthatfurtherconfinesmostoftheatomswhileallowingtheenergeticonestoescape.Thus,theaverageenergyoftheremainingatomsdecreases,mak-ingthesamplecolderandevenmorecloselyconfinedtothecenterofthetrap.Ultimately,manyoftheatomsattainthelowestpossibleenergystateallowedbyquan-tummechanicsandbecomeasingleentityknownasaBose-Einsteincondensate.Sci.Am.,March1998,p.27.ThepartsofanatomlaserAlaserrequiresacavity(resonator),anactivemedium,andanoutputcoupler.IntheMITatomlaser,the"resonator"isamagnetictrapinwhichtheatomsareconfinedby"magneticmirrors".Theactivemediumisathermalcloudofultracoldatoms,andtheoutputcouplerisanrfpulsewhichcontrolsthe"reflectivity"ofthemagneticmirrors.Ketterle‘shomepageThegainprocessinanatomlaserTheanalogytospontaneousemissionintheopticallaseriselasticscatteringofatoms(collisionssimilartothosebetweenbilliardballs).Inalaser,stimulatedemissionofphotonscausestheradiationfieldtobuildupinasinglemode.Inanatomlaser,thepresenceofaBose-Einsteincondensate(atomsthatoccupya"singlemode"ofthesystem,thelowestenergystate)causesstimulatedscatteringbyatomsintothatmode.Moreprecisely,thepresenceofacondensatewithNatomsenhancestheprobabilitythatanatomwillbescatteredintothecondensatebyN+1.Ketterle‘shomepageThegainprocessinanatomlaserInanormalgas,atomsscatteramongthemanymodesofthesystem.ButwhenthecriticaltemperatureforBose-Einsteincondensationisreached,theyscatterpredominantlyintothelowestenergystateofthesystem,asingleoneofthemyriadofpossiblequantumstates.Thisabruptprocessiscloselyanalogoustothethresholdforoperatingalaser,whenthelasersuddenlyswitchesonasthesupplyofradiatingatomsisincreased.Inanatomlaser,the"excitation"ofthe"activemedium"isdonebyevaporativecooling-theevaporationprocesscreatesacloudwhichisnotinthermalequilibriumandrelaxestowardscoldertemperatures.Thisresultsingrowthofthecondensate.Afterequilibration,thenet"gain"oftheatomlaseriszero,i.e.,thecondensatefractionremainsconstantuntilfurthercoolingisapplied.Ketterle‘shomepageThegainprocessinanatomlaser Unlikeopticallasers,whichsometimesradiateinseveralmodes(i.e.atseveralnearbyfrequencies)thematterwavelaseralwaysoperatesinasinglemode.TheformationoftheBosecondensateactuallyinvolves"modecompetition":thefirstexcitedstatecannotbemacroscopicallypopulatedbecausethegroundstate"eatsupallthepie".Ketterle‘shomepageTheoutputofanatomlaserTheoutputofanopticallaserisacollimatedbeamoflight.Foranatomlaser,itisabeamofatoms.Eitherlasercanbecontinuousorpulsed-butsofar,theatomlaserhasonlybeenrealizedinthepulsedmode.Bothlightandatomspropagateaccordingtoawaveequation.LightisgovernedbyMaxwell'sequations,andmatterisdescribedbytheSchroedingerequation.ThediffractionlimitinopticscorrespondstotheHeisenberguncertaintylimitforatoms.Inanidealcase,theatomlaseremitsaHeisenberguncertaintylimitedbeam.Ketterle‘shomepageOpticalversusatomlaser:differencesPhotonscanbecreated,butnotatoms.Thenumberofatomsinanatomlaserisnotamplified.Whatisamplifiedisthenumberofatomsinthegroundstate,whilethenumberofatomsinotherstatesdecreases.Atomsinteractwitheachother-thatcreatesadditionalspreadingoftheoutputbeam.Unlikelight,amatterwavecannottravelfarthroughair.Atomsaremassiveparticles.Theyarethereforeacceleratedbygravity.Amatterwavebeamwillfalllikeabeamofordinaryatoms.ABosecondensatesoccupiesthelowestmode(groundstate)ofthesystem,whereaslasersusuallyoperateonveryhighmodesofthelaserresonator.ABosecondensedsystemisinthermalequilibriumandcharacterizedbyextremelylowtemperature.Incontrast,theopticallaseroperatesinanon-equilibriumsituationwhichcanbecharacterizedbyanegativetemperature.ThereisneveranypopulationinversioninevaporativecoolingorBosecondensation.Ketterle‘shomepageOscillationsSee