玻色爱因斯坦凝聚和激光冷却汇总课件

AtomsinUnisonintheCoolestGasintheUniverse超冷世界的原子大合唱

LaserCooling激光冷却Whatisthesignificanceofthe2001and1997NobelPrizeinPhysics?

1AtomsinUnisonintheCoolestTheNobelPrize(2001)“fortheachievementofBose-Einsteincondensation(玻色-愛因斯坦凝聚態)

indilutegasesofalkaliatoms(碱原子),andforearlyfundamentalstudiesofthepropertiesofthecondensates"2TheNobelPrize(2001)“fortheTheWinnersEricA.Cornell康奈爾JILA&NIST,Boulder,Colorado.1961-WolfgangKetterle克特勒MIT1957-CarlE.Wieman維曼JILA&UniversityofColorado,Boulder.1951-3TheWinnersEricA.CornellWolfTheGodfatherRamsey(1989)Kleppner(1H)Phillips(1997)PritchardWieman(87Rb)Hulet(7Li)Chu(1997)Ketterle(23Na)Cornell(87Rb)TheSonsTheGrandsons4TheGodfatherRamsey(1989)KlepQ1:WhatIsBose-EinsteinCondensation?DeBroglie德布羅意(1929NobelPrizewinner)proposedthatallmatteriscomposedofwaves.Theirwavelengthsaregivenby=deBrogliewavelengthh=Planck’sconstant普朗克常數m=massv=velocity5Q1:WhatIsBose-EinsteinCondAgainstOurIntuition?!

Inmosteverydaymatter,thedeBrogliewavelengthismuchshorterthanthedistanceseparatingtheatoms.Inthiscase,thewavenatureofatomscannotbenoticed,andtheybehaveasparticles.ThewavenatureofatomsbecomenoticeablewhenthedeBrogliewavelengthisroughlythesameastheatomicdistance.Thishappenswhenthetemperatureislowenough,sothattheyhavelowvelocities.Inthiscase,thewavenatureofatomswillbedescribedbyquantumphysics,e.g.theycanonlystayatdiscreteenergystates(energyquantization).6AgainstOurIntuition?!InmosBoseandEinsteinIn1924anIndianphysicistnamedBosestudiedthequantumbehaviourofacollectionofphotons.BosesenthisworktoEinstein,whorealizedthatitwasimportant.Einsteingeneralizedtheideatoatoms,consideringthemasquantumparticleswithmass.Einsteinfoundthatwhenthetemperatureishigh,theybehavelikeordinarygases.However,whenthetemperatureisverylow,theywillgathertogetheratthelowestquantumstate.ThisiscalledBose-Einsteincondensation.7BoseandEinsteinIn1924anInFermions(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.8Fermions(費米子)andBosons(玻色子TheMaterialForBEC

BECwasfoundinalkalimetalse.g.87Rb(金如),23Na(鈉),7Li(鋰)because:Theyarebosons.Eachatomisasmallmagneticcompass,sothatacoolingtechniquecalledmagneticcoolingcanwork.Theatomshaveasmallrepulsion,sothattheydonotliquefyorsolidifydowntoaverylowtemperature.9TheMaterialForBECBECwasfCoolingDowntheAtomsSeetheanimation:/physics/2000/bec/what_is_it.htmlWhenthetemperatureishigh,theatomshavehighenergiesonaverage.Theenergylevelsarealmostcontinuous.Itissufficienttodescribethesystembyclassicalphysics.Whenthetemperatureislow,theatomshavelowenergiesonaverage.Itisnecessarytodescribethesystembyquantumphysics.Whenthetemperatureisverylow,alargefractionofatomssuddenlycrashintothelowestenergystate.ThisiscalledBose-Einsteincondensation.10CoolingDowntheAtomsSeetheTheStrangeStateofBECWhenalltheatomsstayinthecondensate,alltheatomsareabsolutelyidentical.Thereisnopossiblemeasurementthatcantellthemapart.Beforecondensation,theatomslooklikefuzzyballs.Aftercondensation,theatomslieexactlyontopofeachother(asuperatom).11TheStrangeStateofBECWhenaQ2:HowIsBECMade?LaserbeamOtherequipment:laserequipment,computer,electronicsCostlessthanUS$100,00012Q2:HowIsBECMade?LaserbeamLaserCooling(激光冷卻)Thetechniqueoflasercoolingwasdevelopedbythewinnersofthe1997NobelPrizewinners.Inthephysicalworld,thelowesttemperaturesapproachalimitof–273oC.Thisiscalledtheabsolutezero.Nothingcanbeascoldastheabsolutezerobecauseallatomicandsubatomicmotionsstop.Lasercoolingcangettothelowtemperatureof0.18K(1K微開=10-6K).Chu朱棣文Cohen-TannoundjiPhillips13LaserCooling(激光冷卻)ThetechniSteven

Chu(朱棣文)

StanfordUniversity

USATheRoyalSwedishAcademyofSciences

hasawardedthe1997NobelPrizeinPhysicsjointlyto:

“fordevelopmentofmethodstocoolandtrapatomswithlaserlight”NobelPrizeinPhysics1997C.Cohen-Tannoudji

EcoleNormaleSuperieure&CollegedeFranceFranceWilliamsPhillips

NationalInstituteofStandards&TechnologyUSA14StevenChu(朱棣文)

StanfordUn工作经历：1976-1978在加州大学伯克利分校做博士后研究。1978-1983任电磁现象研究贝尔实验室研究人员。1983-1987美国电话、电报公司贝尔实验室量子电子学研究部主任。1987至今斯坦福大学物理和应用物理教授。2008年12月被任命为美国能源部长朱棣文朱棣文是继李政道、杨振宁、丁肇中、李远哲之后的第5位华裔诺贝尔奖获得者。生于1948年2月28日江苏省太仓县人现职：美国斯坦福大学物理学和应用物理教授教育背景：1970年毕业于罗彻斯特大学，获数学学士和物理学学士。1976年获加州大学伯克利分校物理学博士。15工作经历：朱棣文朱棣文是继李政道、杨振宁、丁肇中、李远哲之Ping-pongBallsPhotonsareparticles.Theycarrymomentalikeping-pongballs.Youcanslowthemotionofanatombybouncinglaserlightofftheatoms.Seetheanimation/physics/2000/bec/lascool1.html.16Ping-pongBallsPhotonsareparTuningtheLaserOnlylaserlightwiththecorrectcolour(frequency)canbeabsorbedbytheatoms.Ifthecolouriswrong,theatomscannotabsorbthephotons.Seetheanimation/physics/2000/bec/lascool2.html17TuningtheLaserOnlylaserligMechanicaleffectsoflightAsaconsequenceoftheconservationofenergyandmomentum,atomscanexperiencelight-inducedforcesduringtheirinteractionwitharadiationfield.Next,wediscusstheapplicationoftheseforcesincausingthedeflection,coolingoftheatomicbeams.18MechanicaleffectsoflightAs1.AtomicdeflectionWhenanatomabsorbsoremitsaphotonoffrequencyνfromalightbeam,atransferofrecoilmomentum

takesplacebetweentheatomandthefield.191.AtomicdeflectionWhenanatIfabsorptionisfollowedbystimulatedemission,nonetmomentumistransferredtotheatomasthemomentumtransferredintheprocessofabsorptioniscanceledbyequalbutoppositetransferofmomentumintheprocessofstimulatedemission.20IfabsorptionisfollowedbysIf,however,absorptionisfollowedbyspontaneousemission,thereisanetmomentumtransfertotheatomasthespontaneousemissioninarbitrarydirectionsgivesnoaveragecontributiontothemomentum.Ifthisprocesstakesplacealargenumberoftimes,asubstantialtransferofmomentumcanoccur,fromthelightbeamtotheatom,leadingtoatomicdeflection.21If,however,absorptionisfolAsdiscussedabove,anatomexperienceamomentumrecoilofuponeachradiativeevent.Hencetheabsorptiveforceoftheatomisgivenbywhereristherateofradiationdecayorthenetfluorescencerate.Foratwo-levelatom

atrest,withatransitionfrequencyω,therateγisproportionaltotheupperleveloccupancyρaaoftheatom,i.e.,whereΓisthespontaneousemissionratefromtheexcitedstate|a>tothegroundstate|b>.22Asdiscussedabove,anatomexTheinteractionofatwo-levelatomwitharadiationfieldoffrequencyνisdescribedbythefollowingsetofequationsforthedensitymatrixelements:wherethedetuningisΔ=ω-ν,ΩRistheRabifrequencyassociatedwiththelightbeam.23Theinteractionofatwo-levelAsteady-statesolutionofthedensitymatrixelementsyieldsTheabsorptiveforceisthusgivenbyandisinthesamedirectionasthelightbeam.24Asteady-statesolutionofthe2.LasercoolingSofarwehaveconsideredtheforceofalightbeamonanatomatrest.Iftheatomismovingwithavelocityvalongthelightbeam,itseesaDopplershiftedfrequency,ν±kv,ofthelightbeam.Herethe+(or-)signcorrespondstoasituationwhentheatomismovingintheopposite(orsame)directiontothelightbeam.252.LasercoolingSofarwehaveTheexpressionfortheabsorptiveforceFathenbecomesInthelimitofnosaturation(ΩR=0inthedenominator)andasmallvelocity,wecanexpandthedenominator.TheresultingexpressionforFais26Theexpressionfortheabsorptwhereisaconstantdeflectingforce,Thesecondterm,proportionaltoatomicvelocity,actslikeafrictionterm.27whereisaconstantdeflectingIftheatomislocatedinastandingwave,itseestwooppositelymovinglightwaves,oneinthesamedirectionasthevelocityoftheatomandotherintheoppositedirection.Weassumethattheforcesduetothetwobeamscanbesuperimposed.Hencethetotalforceontheatominastandingwaveisi.e.,thedeflectionforcesFocancelandthefrictionforcesfromthetwobeamsremain.Thefrictionforceisresponsiblefortheslowingdownoftheatomleadingtolasercooling.28IftheatomislocatedinastPhysically,wecanunderstandtheprocessoflasercoolingasfollows.IfthefieldmovingintheoppositedirectiontotheatomwillbeDopplerup-shifted,thuscompensatingthedetuning.Theatomwillthereforebedecelerated.Bythismechanismtheatomscanbesloweddowntothepaceofextremelysluggishatomicmolasses.ωνkvatomlight29Physically,wecanunderstandUsingtheDopplerEffect(多普勒效应)Problem:Thelasercanslowtheapproachingatoms,butitcanalsoblastofftherecedingones.Solution:UseDopplershift.Whentheatomisrecedingfromthelasersource,thewavelengthislengthenedandthereisaredshift.Whentheatomisapproachingthelasersource,thewavelengthisshortenedandthereisablueshift.Seetheanimation:http://www.astro.ubc.ca/~scharein/a311/Sim.html30UsingtheDopplerEffect(多普勒效多普勒冷却原则上可以使原子的热速度从室温下的几百m/s降至很低，但是却不能无限低下去，存在着一个极限TD。多普勒冷却极限因为原子在每次吸收和自发发射光子而获得阻碍其运动的过程中，由于自发发射的随机性，每发射一个光子以后原子都获得一个在时间和方向上都随机的反冲动量，因而导致原子动量的起伏。这种起伏相应于激光对原子的一种加热过程，它是难于消除的。激光对原子的冷却速率与这种加热过程达到平衡的温度，也就是激光冷却的多普勒极限温度TD。31多普勒冷却原则上可以使原子的热速度从室温下的几百m/s降至很需要其他的冷却机制将原子冷却至比TD更低的温度，它们基本上都是在“光学粘胶”中依靠其它机制来实现。32需要其他的冷却机制将原子冷却至比TD更低的温度，它们基本上都LaserTrapping(激光陷阱)Supposethelaserhastherightcolourforthephotonstobeabsorbedbyanapproachingatom,thentheatomwillbesloweddown.However,thelaserwillnothavetherightcolourforthephotonstobeabsorbedbytherecedingatombecauseofDopplereffect.Hencetheatomwillnotchangeinthiscase.Whenlasersaresentinfromallthedifferentdirections,theatomscangetcoldveryquickly.Thisiscalledlasertrapping,andthetrappedatomsformanopticalmolass(光学黏胶).Seetheanimation:/physics/2000/bec/lascool4.html33LaserTrapping(激光陷阱)Supposet真空中的一束钠原子被迎面而来的激光束阻止了下来，然后把钠原子引进两两相对，沿三个正交方向的六束激光的交汇处。其效果就是不管钠原子企图向何方运动，都会遇上具有恰当能量的光子，被推回到六束激光交汇的区域。于是，在这个小区域里，聚集了大量冷却下来的原子，组成了肉眼看去像是豌豆大小的发光气团。由六束激光组成的阻尼机制就像某种粘稠的流体，原子陷入其中会不断降低速度。这种机制就叫做“光学粘胶”。光学粘胶34真空中的一束钠原子被迎面而来的激光束阻止了下来，然后把钠原子3535MagneticTrapping(磁性陷阱)Problem:Lasercoolingcancooltheatomsdownto10K,becauseatomscanspontaneouslyemittheabsorbedphoton.ThisisstilltoohotforBEC.Solution:EvaporativecoolingTheatomsbehaveastinycompasses.Theycanbepulledbymagneticfields.Amagneticfieldcanbedesignedtopushtheatomsinwardsfrombothsides,formingamagnetictrap.Seetheanimation:/physics/2000/bec/mag_trap.html36MagneticTrapping(磁性陷阱)Proble在光学粘胶装置的基础上再加上两个磁性线圈，设计了一种很有效的陷阱，叫做磁光陷阱。磁光陷阱会产生一个比重力大的力，从而把原子拉回到陷阱中心。磁光阱37在光学粘胶装置的基础上再加上两个磁性线圈，设计了一种很有效的EvaporativeCooling(揮發冷卻)Principle:Evaporationtakesheat.Acupofteagetscoolaftersteamescapes,becausefasteratomsescapefromthecup,leavingbehindtheslowerones.Technique:Lowertheheightofthetrapquickly,sothattherearestillenoughatomsleftinthetraptogetinvolvedinBEC.TrytotrapthelargestnumberofatomsinBECintheanimation:/physics/2000/bec/evap_cool.html38EvaporativeCooling(揮發冷卻)Prin39394040CanYouBreakThisRecord?41CanYouBreakThisRecord?41Q3:WhatDoesaBose-EinsteinCondensateLookLike?Thereisadropofcondensateatthecentre.Thecondensateissurroundedbyuncondensedgasatoms.Thecombinationlookslikeacherrywithapit.Seethemoviewhenitcoolsfrom400nKto50nK(1nK納開=10-9K).: /physics/2000/bec/what_it_looks_like.html42Q3:WhatDoesaBose-EinsteinAtomLaser(原子激射)Laseroflight:allthephotonsareexactlythesameincolour,directionandphase(positionsofpeaksandvalleys).Laserofatoms:alltheatomsinthecondensateareexactlythesame.Seetheanimation:/ketterle_group/Animation_folder/Atom_laser.htm43AtomLaser(原子激射)LaseroflighOscillationsSeetheanimation:/ketterle_group/Animation_folder/Oscillations.htmNotethe“shape”motionand“sloshing”motion.44OscillationsSeetheanimation:InterferencePattern(干涉图像)WhentwoBose-Einsteincondensatesspreadout,theinterferencepatternrevealstheirwavenature.Seetheanimation:/ketterle_group/Animation_folder/TOFsplit.htm45InterferencePattern(干涉图像)WheVortices(旋涡)Whenthecondensateisrotated,vorticesappear.Theangularmomentumofeachofthemhasadiscretevalue.46Vortices(旋涡)WhenthecondensaQ4:WhatIsBose-EinsteinCondensationGoodFor?Thisisacompletelynewarea.Applicationsaretooearlytopredict.Theatomlasercanbeusedin:atomoptics(studyingtheopticalpropertiesofatoms)atomlithography光刻(fabricatingextremelysmallcircuits)precisionatomicclocksothermeasurementsoffundamentalstandardshologram全息图communicationsandcomputation.Fundamentalunderstandingofquantummechanics.Modelofsupernovaexplosion

超新星爆炸.Modelofblackholes

黑洞.47Q4:WhatIsBose-EinsteinCondReferencesHomepageoftheNobele-Museum(http://www.nobel.se/).BECHomepageattheUniversityofColorado(/physics/2000/bec/).KetterleGroupHomepage(http://www.cua.mit/ketterle_group/).TheCoolestGasintheUniverse(ScientificAmerican,December2000,92-99).AtomLasers(PhysicsWorld,August1999,31-35).48ReferencesHomepageoftheNobeAtomsinUnisonintheCoolestGasintheUniverse超冷世界的原子大合唱

LaserCooling激光冷却Whatisthesignificanceofthe2001and1997NobelPrizeinPhysics?

49AtomsinUnisonintheCoolestTheNobelPrize(2001)“fortheachievementofBose-Einsteincondensation(玻色-愛因斯坦凝聚態)

indilutegasesofalkaliatoms(碱原子),andforearlyfundamentalstudiesofthepropertiesofthecondensates"50TheNobelPrize(2001)“fortheTheWinnersEricA.Cornell康奈爾JILA&NIST,Boulder,Colorado.1961-WolfgangKetterle克特勒MIT1957-CarlE.Wieman維曼JILA&UniversityofColorado,Boulder.1951-51TheWinnersEricA.CornellWolfTheGodfatherRamsey(1989)Kleppner(1H)Phillips(1997)PritchardWieman(87Rb)Hulet(7Li)Chu(1997)Ketterle(23Na)Cornell(87Rb)TheSonsTheGrandsons52TheGodfatherRamsey(1989)KlepQ1:WhatIsBose-EinsteinCondensation?DeBroglie德布羅意(1929NobelPrizewinner)proposedthatallmatteriscomposedofwaves.Theirwavelengthsaregivenby=deBrogliewavelengthh=Planck’sconstant普朗克常數m=massv=velocity53Q1:WhatIsBose-EinsteinCondAgainstOurIntuition?!

Inmosteverydaymatter,thedeBrogliewavelengthismuchshorterthanthedistanceseparatingtheatoms.Inthiscase,thewavenatureofatomscannotbenoticed,andtheybehaveasparticles.ThewavenatureofatomsbecomenoticeablewhenthedeBrogliewavelengthisroughlythesameastheatomicdistance.Thishappenswhenthetemperatureislowenough,sothattheyhavelowvelocities.Inthiscase,thewavenatureofatomswillbedescribedbyquantumphysics,e.g.theycanonlystayatdiscreteenergystates(energyquantization).54AgainstOurIntuition?!InmosBoseandEinsteinIn1924anIndianphysicistnamedBosestudiedthequantumbehaviourofacollectionofphotons.BosesenthisworktoEinstein,whorealizedthatitwasimportant.Einsteingeneralizedtheideatoatoms,consideringthemasquantumparticleswithmass.Einsteinfoundthatwhenthetemperatureishigh,theybehavelikeordinarygases.However,whenthetemperatureisverylow,theywillgathertogetheratthelowestquantumstate.ThisiscalledBose-Einsteincondensation.55BoseandEinsteinIn1924anInFermions(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.56Fermions(費米子)andBosons(玻色子TheMaterialForBEC

BECwasfoundinalkalimetalse.g.87Rb(金如),23Na(鈉),7Li(鋰)because:Theyarebosons.Eachatomisasmallmagneticcompass,sothatacoolingtechniquecalledmagneticcoolingcanwork.Theatomshaveasmallrepulsion,sothattheydonotliquefyorsolidifydowntoaverylowtemperature.57TheMaterialForBECBECwasfCoolingDowntheAtomsSeetheanimation:/physics/2000/bec/what_is_it.htmlWhenthetemperatureishigh,theatomshavehighenergiesonaverage.Theenergylevelsarealmostcontinuous.Itissufficienttodescribethesystembyclassicalphysics.Whenthetemperatureislow,theatomshavelowenergiesonaverage.Itisnecessarytodescribethesystembyquantumphysics.Whenthetemperatureisverylow,alargefractionofatomssuddenlycrashintothelowestenergystate.ThisiscalledBose-Einsteincondensation.58CoolingDowntheAtomsSeetheTheStrangeStateofBECWhenalltheatomsstayinthecondensate,alltheatomsareabsolutelyidentical.Thereisnopossiblemeasurementthatcantellthemapart.Beforecondensation,theatomslooklikefuzzyballs.Aftercondensation,theatomslieexactlyontopofeachother(asuperatom).59TheStrangeStateofBECWhenaQ2:HowIsBECMade?LaserbeamOtherequipment:laserequipment,computer,electronicsCostlessthanUS$100,00060Q2:HowIsBECMade?LaserbeamLaserCooling(激光冷卻)Thetechniqueoflasercoolingwasdevelopedbythewinnersofthe1997NobelPrizewinners.Inthephysicalworld,thelowesttemperaturesapproachalimitof–273oC.Thisiscalledtheabsolutezero.Nothingcanbeascoldastheabsolutezerobecauseallatomicandsubatomicmotionsstop.Lasercoolingcangettothelowtemperatureof0.18K(1K微開=10-6K).Chu朱棣文Cohen-TannoundjiPhillips61LaserCooling(激光冷卻)ThetechniSteven

Chu(朱棣文)

StanfordUniversity

USATheRoyalSwedishAcademyofSciences

hasawardedthe1997NobelPrizeinPhysicsjointlyto:

“fordevelopmentofmethodstocoolandtrapatomswithlaserlight”NobelPrizeinPhysics1997C.Cohen-Tannoudji

EcoleNormaleSuperieure&CollegedeFranceFranceWilliamsPhillips

NationalInstituteofStandards&TechnologyUSA62StevenChu(朱棣文)

StanfordUn工作经历：1976-1978在加州大学伯克利分校做博士后研究。1978-1983任电磁现象研究贝尔实验室研究人员。1983-1987美国电话、电报公司贝尔实验室量子电子学研究部主任。1987至今斯坦福大学物理和应用物理教授。2008年12月被任命为美国能源部长朱棣文朱棣文是继李政道、杨振宁、丁肇中、李远哲之后的第5位华裔诺贝尔奖获得者。生于1948年2月28日江苏省太仓县人现职：美国斯坦福大学物理学和应用物理教授教育背景：1970年毕业于罗彻斯特大学，获数学学士和物理学学士。1976年获加州大学伯克利分校物理学博士。63工作经历：朱棣文朱棣文是继李政道、杨振宁、丁肇中、李远哲之Ping-pongBallsPhotonsareparticles.Theycarrymomentalikeping-pongballs.Youcanslowthemotionofanatombybouncinglaserlightofftheatoms.Seetheanimation/physics/2000/bec/lascool1.html.64Ping-pongBallsPhotonsareparTuningtheLaserOnlylaserlightwiththecorrectcolour(frequency)canbeabsorbedbytheatoms.Ifthecolouriswrong,theatomscannotabsorbthephotons.Seetheanimation/physics/2000/bec/lascool2.html65TuningtheLaserOnlylaserligMechanicaleffectsoflightAsaconsequenceoftheconservationofenergyandmomentum,atomscanexperiencelight-inducedforcesduringtheirinteractionwitharadiationfield.Next,wediscusstheapplicationoftheseforcesincausingthedeflection,coolingoftheatomicbeams.66MechanicaleffectsoflightAs1.AtomicdeflectionWhenanatomabsorbsoremitsaphotonoffrequencyνfromalightbeam,atransferofrecoilmomentum

takesplacebetweentheatomandthefield.671.AtomicdeflectionWhenanatIfabsorptionisfollowedbystimulatedemission,nonetmomentumistransferredtotheatomasthemomentumtransferredintheprocessofabsorptioniscanceledbyequalbutoppositetransferofmomentumintheprocessofstimulatedemission.68IfabsorptionisfollowedbysIf,however,absorptionisfollowedbyspontaneousemission,thereisanetmomentumtransfertotheatomasthespontaneousemissioninarbitrarydirectionsgivesnoaveragecontributiontothemomentum.Ifthisprocesstakesplacealargenumberoftimes,asubstantialtransferofmomentumcanoccur,fromthelightbeamtotheatom,leadingtoatomicdeflection.69If,however,absorptionisfolAsdiscussedabove,anatomexperienceamomentumrecoilofuponeachradiativeevent.Hencetheabsorptiveforceoftheatomisgivenbywhereristherateofradiationdecayorthenetfluorescencerate.Foratwo-levelatom

atrest,withatransitionfrequencyω,therateγisproportionaltotheupperleveloccupancyρaaoftheatom,i.e.,whereΓisthespontaneousemissionratefromtheexcitedstate|a>tothegroundstate|b>.70Asdiscussedabove,anatomexTheinteractionofatwo-levelatomwitharadiationfieldoffrequencyνisdescribedbythefollowingsetofequationsforthedensitymatrixelements:wherethedetuningisΔ=ω-ν,ΩRistheRabifrequencyassociatedwiththelightbeam.71Theinteractionofatwo-levelAsteady-statesolutionofthedensitymatrixelementsyieldsTheabsorptiveforceisthusgivenbyandisinthesamedirectionasthelightbeam.72Asteady-statesolutionofthe2.LasercoolingSofarwehaveconsideredtheforceofalightbeamonanatomatrest.Iftheatomismovingwithavelocityvalongthelightbeam,itseesaDopplershiftedfrequency,ν±kv,ofthelightbeam.Herethe+(or-)signcorrespondstoasituationwhentheatomismovingintheopposite(orsame)directiontothelightbeam.732.LasercoolingSofarwehaveTheexpressionfortheabsorptiveforceFathenbecomesInthelimitofnosaturation(ΩR=0inthedenominator)andasmallvelocity,wecanexpandthedenominator.TheresultingexpressionforFais74Theexpressionfortheabsorptwhereisaconstantdeflectingforce,Thesecondterm,proportionaltoatomicvelocity,actslikeafrictionterm.75whereisaconstantdeflectingIftheatomislocatedinastandingwave,itseestwooppositelymovinglightwaves,oneinthesamedirectionasthevelocityoftheatomandotherintheoppositedirection.Weassumethattheforcesduetothetwobeamscanbesuperimposed.Hencethetotalforceontheatominastandingwaveisi.e.,thedeflectionforcesFocancelandthefrictionforcesfromthetwobeamsremain.Thefrictionforceisresponsiblefortheslowingdownoftheatomleadingtolasercooling.76IftheatomislocatedinastPhysically,wecanunderstandtheprocessoflasercoolingasfollows.IfthefieldmovingintheoppositedirectiontotheatomwillbeDopplerup-shifted,thuscompensatingthedetuning.Theatomwillthereforebedecelerated.Bythismechanismtheatomscanbesloweddowntothepaceofextremelysluggishatomicmolasses.ωνkvatomlight77Physically,wecanunderstandUsingtheDopplerEffect(多普勒效应)Problem:Thelasercanslowtheapproachingatoms,butitcanalsoblastofftherecedingones.Solution:UseDopplershift.Whentheatomisrecedingfromthelasersource,thewavelengthislengthenedandthereisaredshift.Whentheatomisapproachingthelasersource,thewavelengthisshortenedandthereisablueshift.Seetheanimation:http://www.astro.ubc.ca/~scharein/a311/Sim.html78UsingtheDopplerEffect(多普勒效多普勒冷却原则上可以使原子的热速度从室温下的几百m/s降至很低，但是却不能无限低下去，存在着一个极限TD。多普勒冷却极限因为原子在每次吸收和自发发射光子而获得阻碍其运动的过程中，由于自发发射的随机性，每发射一个光子以后原子都获得一个在时间和方向上都随机的反冲动量，因而导致原子动量的起伏。这种起伏相应于激光对原子的一种加热过程，它是难于消除的。激光对原子的冷却速率与这种加热过程达到平衡的温度，也就是激光冷却的多普勒极限温度TD。79多普勒冷却原则上可以使原子的热速度从室温下的几百m/s降至很需要其他的冷却机制将原子冷却至比TD更低的温度，它们基本上都是在“光学粘胶”中依靠其它机制来实现。80需要其他的冷却机制将原子冷却至比TD更低的温度，它们基本上都LaserTrapping(激光陷阱)Supposethelaserhastherightcolourforthephotonstobeabsorbedbyanapproachingatom,thentheatomwillbesloweddown.However,thelaserwillnothavetherightcolourforthephotonstobeabsorbedbytherecedingatombecauseofDopplereffect.Hencetheatomwillnotchangeinthiscase.Whenlasersaresentinfromallthedifferentdirections,theatomscangetcoldveryquickly.Thisiscalledlasertrapping,andthetrappedatomsformanopticalmolass(光学黏胶).Seetheanimation:/physics/2000/bec/lascool4.html81LaserTrapping(激光陷阱)Supposet真空中的一束钠原子被迎面而来的激光束阻止了下来，然后把钠原子引进两两相对，沿三个正交方向的六束激光的交汇处。其效果就是不管钠原子企图向何方运动，都会遇上具有恰当能量的光子，被推回到六束激光交汇的区域。于是，在这个小区域里，聚集了大量冷却下来的原子，组成了肉眼看去像是豌豆大小的发光气团。由六束激光组成的阻尼机制就像某种粘稠的流体，原子陷入其中会不断降低速度。这种机制就叫做“光学粘胶”。光学粘胶82真空中的一束钠原子被迎面而来的激光束阻止了下来，然后把钠原子8335MagneticTrapping(磁性陷阱)Problem:Lasercoolingcancooltheatomsdownto10K,becauseatomscanspontaneouslyemittheabsorbedphoton.ThisisstilltoohotforBEC.Solution:EvaporativecoolingTheatomsbehaveasti