玻色-爱因斯坦凝聚.ppt

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 一个服从经典统计的系统处于温度T的热平衡中 其能量的每一独立的平方项都有平均值1 2kT 与b无关 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 在处于平衡的体系中考虑两个能级i与j 上面分别有ni及nj个粒子 令Ri j代表从i到j的跃迁几率 精细平衡 经典统计 有 对玻色子 有增强因子1 n 对所有能级成立 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 QuantumStatistics Predicted1924 Created1995 3 玻色 爱因斯坦凝聚 Q1 WhatIsBose EinsteinCondensation DeBroglie德布罗意 1929NobelPrizewinner proposedthatallmatteriscomposedofwaves Theirwavelengthsaregivenby deBrogliewavelengthh Planck sconstant普朗克常数m massv velocity AgainstOurIntuition Inmosteverydaymatter thedeBrogliewavelengthismuchshorterthanthedistanceseparatingtheatoms Inthiscase thewavenatureofatomscannotbenoticed andtheybehaveasparticles ThewavenatureofatomsbecomenoticeablewhenthedeBrogliewavelengthisroughlythesameastheatomicdistance Thishappenswhenthetemperatureislowenough sothattheyhavelowvelocities Inthiscase thewavenatureofatomswillbedescribedbyquantumphysics e g theycanonlystayatdiscreteenergystates energyquantization BoseandEinstein In1924anIndianphysicistnamedBosestudiedthequantumbehaviourofacollectionofphotons BosesenthisworktoEinstein whorealizedthatitwasimportant Einsteingeneralizedtheideatoatoms consideringthemasquantumparticleswithmass Einsteinfoundthatwhenthetemperatureishigh theybehavelikeordinarygases However whenthetemperatureisverylow theywillgathertogetheratthelowestquantumstate ThisiscalledBose Einsteincondensation Fermions 費米子 andBosons 玻色子 NotallparticlescanhaveBEC Thisisrelatedtothespinoftheparticles Thespinquantumnumberofaparticlecanbeanintegerorahalf integer Singleprotons neutronsandelectronshaveaspinof 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 CoolingDowntheAtoms Seetheanimation http www colorado edu physics 2000 bec what is it htmlWhenthetemperatureishigh theatomshavehighenergiesonaverage Theenergylevelsarealmostcontinuous Itissufficienttodescribethesystembyclassicalphysics Whenthetemperatureislow theatomshavelowenergiesonaverage Itisnecessarytodescribethesystembyquantumphysics Whenthetemperatureisverylow alargefractionofatomssuddenlycrashintothelowestenergystate ThisiscalledBose Einsteincondensation TheStrangeStateofBEC Whenalltheatomsstayinthecondensate alltheatomsareabsolutelyidentical Thereisnopossiblemeasurementthatcantellthemapart Beforecondensation theatomslooklikefuzzyballs Afterconsdensation theatomslieexactlyontopofeachother asuperatom Q2 HowIsBECMade Laserbeam Otherequipment laserequipment computer electronicsCostlessthanUS 100 000 LaserCooling 激光冷卻 Thetechniqueoflasercoolingwasdevelopedbythewinnersofthe1997NobelPrizewinners Inthephysicalworld thelowesttemperaturesapproachalimitof 273oC Thisiscalledtheabsolutezero Nothingcanbeascoldastheabsolutezerobecauseallatomicandsubatomicmotionsstop Lasercoolingcangettothelowtemperatureof0 18 K 1 K微開 10 6K Chu朱棣文 Cohen Tannoundji Phillips Ping pongBalls Photonsareparticles Theycarrymomentalikeping pongballs Youcanslowthemotionofanatombybouncinglaserlightofftheatoms Seetheanimationhttp www colorado edu physics 2000 bec lascool1 html TuningtheLaser Onlylaserlightwiththecorrectcolour frequency canbeabsorbedbytheatoms Ifthecolouriswrong theatomscannotabsorbthephotons Seetheanimationhttp www colorado edu physics 2000 bec lascool2 html UsingtheDopplerEffect Problem Thelasercanslowtheapproachingatoms butitcanalsoblastofftherecedingones Solution UseDopplershift Whentheatomisrecedingfromthelasersource thewavelengthislengthenedandthereisaredshift Whentheatomisapproachingthelasersource thewavelengthisshortenedandthereisablueshift Seetheanimation http www astro ubc ca scharein a311 Sim html LaserTrapping 激光陷阱 Supposethelaserhastherightcolourforthephotonstobeabsorbedbyanapproachingatom thentheatomwillbesloweddown However thelaserwillnothavetherightcolourforthephotonstobeabsorbedbytherecedingatombecauseofDopplereffect Hencetheatomwillnotchangeinthiscase Whenlasersaresentinfromallthedifferentdirections theatomscangetcoldveryquickly Thisiscalledlasertrapping andthetrappedatomsformanopticalmolass 光學粘膠 Seetheanimation http www colorado edu physics 2000 bec lascool4 html MagneticTrapping 磁性陷阱 Problem Lasercoolingcancooltheatomsdownto10 K becauseatomscanspontaneouslyemittheabsorbedphoton ThisisstilltoohotforBEC Solution EvaporativecoolingTheatomsbehaveastinycompasses Theycanbepulledbymagneticfields Amagneticfieldcanbedesignedtopushtheatomsinwardsfrombothsides formingamagnetictrap Seetheanimation http www colorado edu physics 2000 bec mag trap html EvaporativeCooling 挥发冷却 Principle Evaporationtakesheat Acupofteagetscoolaftersteamescapes becausefasteratomsescapefromthecup leavingbehindtheslowerones Technique Lowertheheightofthetrapquickly sothattherearestillenoughatomsleftinthetraptogetinvolvedinBEC TrytotrapthelargestnumberofatomsinBECintheanimation http www colorado edu physics 2000 bec evap cool html CanYouBreakThisRecord Q3 WhatDoesaBose EinsteinCondensateLookLike Thereisadropofcondensateatthecentre Thecondensateissurroundedbyuncondensedgasatoms Thecombinationlookslikeacherrywithapit Seethemoviewhenitcoolsfrom400nKto50nK 1nK 10 9K http www colorado edu physics 2000 bec what it looks like html 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 shomepage Atomictrap 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 Thepartsofanatomlaser Alaserrequiresacavity resonator anactivemedium andanoutputcoupler IntheMITatomlaser the resonator isamagnetictrapinwhichtheatomsareconfinedby magneticmirrors Theactivemediumisathermalcloudofultracoldatoms andtheoutputcouplerisanrfpulsewhichcontrolsthe reflectivity ofthemagneticmirrors Ketterle shomepage Thegainprocessinanatomlaser Theanalogytospontaneousemissionintheopticallaseriselasticscatteringofatoms collisionssimilartothosebetweenbilliardballs Inalaser stimulatedemissionofphotonscausestheradiationfieldtobuildupinasinglemode Inanatomlaser thepresenceofaBose Einsteincondensate atomsthatoccupya singlemode ofthesystem thelowestenergystate causesstimulatedscatteringbyatomsintothatmode Moreprecisely thepresenceofacondensatewithNatomsenhancestheprobabilitythatanatomwillbescatteredintothecondensatebyN 1 Ketterle shomepage Thegainprocessinanatomlaser Inanormalgas atomsscatteramongthemanymodesofthesystem ButwhenthecriticaltemperatureforBose Einsteincondensationisreached theyscatterpredominantlyintothelowestenergystateofthesystem asingleoneofthemyriadofpossiblequantumstates Thisabruptprocessiscloselyanalogoustothethresholdforoperatingalaser whenthelasersuddenlyswitchesonasthesupplyofradiatingatomsisincreased Inanatomlaser the excitation ofthe activemedium isdonebyevaporativecooling theevaporationprocesscreatesacloudwhichisnotinthermalequilibriumandrelaxestowardscoldertemperatures Thisresultsingrowthofthecondensate Afterequilibration thenet gain oftheatomlaseriszero i e thecondensatefractionremainsconstantuntilfurthercoolingisapplied Ketterle shomepage Thegainprocessinanatomlaser Unlikeopticallasers whichsometimesradiateinseveralmodes i e atseveralnearbyfrequencies thematterwavelaseralwaysoperatesinasinglemode TheformationoftheBosecondensateactuallyinvolves modecompetition thefirstexcitedstatecannotbemacroscopicallypopulatedbecausethegroundstate eatsupallthepie Ketterle shomepage Theoutputofanatomlaser Theoutputofanopticallaserisacollimatedbeamoflight Foranatomlaser itisabeamofatoms Eitherlasercanbecontinuousorpulsed butsofar theatomlaserhasonlybeenrealizedinthepulsedmode Bothlightandatomspropagateaccordingtoawaveequation LightisgovernedbyMaxwell sequations andmatterisdescribedbytheSchroedingerequation ThediffractionlimitinopticscorrespondstotheHeisenberguncertaintylimitforatoms Inanidealcase theatomlaseremitsaHeisenberguncertaintylimitedbeam Ketterle shomepage Opticalversusatomlaser differences Photonscanbecreated butnotatoms Thenumberofatomsinanatomlaserisnotamplified Whatisamplifiedisthenumberofatomsinthegroundstate whilethenumberofatomsinotherstatesdecreases Atomsinteractwitheachother thatcreatesadditionalspreadingoftheoutputbeam Unlikelight amatterwavecannottravelfarthroughair Atomsaremassiveparticles Theyarethereforeacceleratedbygravity Amatterwavebeamwillfalllikeabeamofordinaryatoms ABosecondensatesoccupiesthelowestmode groundstate ofthesystem whereaslasersusuallyoperateonveryhighmodesofthelaserresonator ABosecondensedsystemisinthermalequilibriumandcharacterizedbyextremelylowtemperature Incontrast theopticallaseroperatesinanon equilibriumsituationwhichcanbecharacterizedbyanegativetemperature ThereisneveranypopulationinversioninevaporativecoolingorBosecondensation Ketterle shomepage Oscillations Seetheanimation http