玻色—愛(ài)因斯坦凝結(jié)created1995Predicted1924…Long-timestory!統(tǒng)計(jì)熱力學(xué)電教課之一

In1924theIndianphysicistSatyendraNathBosesentAlbertEinstein

apaperinwhichheusedastatisticalargumenttoderivetheblack-bodyphotonSpectrum.

AndthenEinstein

extendedtheideatothecaseofnon-interactingatoms

Bose'stheorytoanidealgasofidenticalatomsormoleculesforwhichthenumberofparticlesisconserved.1995．．．．．．AlbertEinsteintranslateditintoGermanandgotitpublished．Inthesameyear,predictedthatatsufficientlylowtemperaturestheparticleswouldbecomelockedtogetherinthelowestquantumstateofthesystem

——Bose-Einsteincondensation(BEC).統(tǒng)計(jì)熱力學(xué)電教課之一§7.6玻色—愛(ài)因斯坦凝結(jié)Bose-Einsteincondensation討論非相對(duì)論性自由玻色系在低溫下的性質(zhì)

自由玻色系的特征

CharacteristicoffreeBosonsystems

玻色—愛(ài)因斯坦凝結(jié)

Bose_EinstainCondensationλ相變

λ-PhaseTrnsation

玻色—愛(ài)因斯坦凝結(jié)的新進(jìn)展

NewProgressesinBEC統(tǒng)計(jì)熱力學(xué)電教課之一1.自由玻色系的特征CharacteristicoffreeBosonsystems單粒子能級(jí)

統(tǒng)計(jì)熱力學(xué)電教課之一考慮自由玻色子組成的體系粒子按能級(jí)分布粒子數(shù)守恒確定α因而μ(=–α/β)求和變積分統(tǒng)計(jì)熱力學(xué)電教課之一基態(tài)(ε0=0)粒子數(shù)非負(fù)

α

0,μ

＜0假定無(wú)簡(jiǎn)并ωl=1（如He原子）統(tǒng)計(jì)熱力學(xué)電教課之一求和變積分正確性??l=0即

ε=0(p=0)項(xiàng)(點(diǎn))??計(jì)入l=0開(kāi)區(qū),未計(jì)入

加上挖去的能量零點(diǎn)統(tǒng)計(jì)熱力學(xué)電教課之一非零能級(jí)項(xiàng)x=βε統(tǒng)計(jì)熱力學(xué)電教課之一２．玻色—愛(ài)因斯坦凝結(jié)(BEC)Bose_EinstainCondensation定性分析定N.

降T（增β），μ必然增，至0則停T

TC,

α0α>0時(shí)不突出統(tǒng)計(jì)熱力學(xué)電教課之一T<TCα=0

突出統(tǒng)計(jì)熱力學(xué)電教課之一基態(tài)粒子比份T＞TC

彌散態(tài)T＜

TC

凝結(jié)態(tài)T＝

TC

相變點(diǎn)T

0

全部凝結(jié)1

01統(tǒng)計(jì)熱力學(xué)電教課之一

●

●

●

●●●●●●●P=0級(jí)

●

●

●●●●●●●●彌散態(tài)(動(dòng)量空間)凝聚態(tài)

玻色凝結(jié)：μ=0,<n0>與N可比動(dòng)量空間的凝聚現(xiàn)象體系的化學(xué)勢(shì)隨溫度變化（如光子μ=0而不隨溫變）降溫可以使μ=0，否則沒(méi)有玻色凝結(jié)。維數(shù)的影響：一、二維系統(tǒng)無(wú)玻色凝結(jié)

不會(huì)趨0

統(tǒng)計(jì)熱力學(xué)電教課之一3.λ

相變?chǔ)?PhaseTrnsationCV/Nk

相I

相II3/2

CV

T3/2

TC~3.14

TSpecificHeatofBoseGasesBEC??ExperimentalCurveofλ–SpecificHeatCV

TC~2.19

T統(tǒng)計(jì)熱力學(xué)電教課之一4He(Boson)

的λ

–

比熱反映Bose-Condensation?λ

–

比熱反映的相變?yōu)槎?jí)相變！內(nèi)能E的一階導(dǎo)數(shù)連續(xù)，二階導(dǎo)數(shù)不連續(xù)歷史上解釋?zhuān)?！后人?He相變還不是玻色凝結(jié)態(tài)的證明！？（二流體模型）HeI正常態(tài)HeII超流態(tài)（凝結(jié)態(tài)）尋找玻色子在實(shí)空間的凝結(jié)—新形態(tài)??統(tǒng)計(jì)熱力學(xué)電教課之一4．玻色凝結(jié)的新進(jìn)展

NewProgressesinBEC

ConditionsforBoseCondensationNobelPrizeinPhysics1997NobelPrizeinPhysics2001

BECinChina統(tǒng)計(jì)熱力學(xué)電教課之一ConditionsforAchievementofBEC(1)Lowtemperature

T~10–9(e.g.Rb)

Coolingandtrappingatoms

(2)Higherdensity

n~1011-12

Trappingatomsbyusinglaser(3)Systemkeepsinthegasphase

(Non-interaction)nλ3～

2.612λT–1/2n=N/VSpinpolarizationHatoms

Alkalimetalatoms

1995統(tǒng)計(jì)熱力學(xué)電教課之一

TheNobelPrizeinPhysics1997"fordevelopmentofmethodstocoolandtrapatomswithlaserlight"StanfordUniv.

Stanford,CA,USA

b.1948CollègedeFranceandécoleNornaleSupérieureParis,Franceb.1933NationalInstituteofStandardsandtechnology,MD,USAb.1948Theirresearchishelpingustostudyfundamentalphenomenaandmeasureimportantphysicalquantitieswithunprecedentedprecision.ClaudeCohen-Tannoudji

StevenChu

WilliamD.Phillips統(tǒng)計(jì)熱力學(xué)電教課之一1980swhenWilliamPhillipsdevelopednewmethodsofdeceleratingafastatombeam.In1985thefirstreportscamefromexperimentswherethemeanvelocityhadbeenreducedfrom1000m/stozero.DecelerationofAtoms

MOTThemostoftenusedforatomtrapistheMagneto-OpticalTrap(MOT).

StevenChu

usedDopplercoolingwiththreepairsofcounter-propagatinglaserbeams.Atom,regardlessofwhatdirectionitismoving,willencounterafrictionforceandthevelocityspread(andthetemperature)willbereducedopticalMolasses.Acollectionofsodiumatoms(yellowdotinmiddleofpicture)trappedinaMOT.Lightactsmechanicallyonmaterialobjects,tochangetheirpositionsandvelocities.Laserreducesthevelocityspread(cooling),orconfinetheatoms(trapping).統(tǒng)計(jì)熱力學(xué)電教課之一NewcoolingmechanismsExplanationsofthelowtemperatureswerefoundbyClaudeCohen-TannoudjiandbyStevenChu.GreekmythologyhasitthatSisyphusmustendlesslyrollastoneupahillintheUnderworld.Assoonashereachesthetopthestonerollsdownagain.Oneexampleofthenewcoolingmechanismsis

Sisyphuscooling,wheretheconceptsoflightshiftandopticalpumpingplayanimportantrole.

統(tǒng)計(jì)熱力學(xué)電教課之一SisyphuscoolingCohen-Tannoudji

developedthefollowingphysicalpicture:10-6KTheatomsmoveonasinusoi-dallymodulatedpotentialsurface,

whentheyinteractwithlight(lightshift).Whentheytravel'uphill'theylosespeed.Astheyreachthetopofthe'hill'theyareopticallypumpedtothebottomofa'valley'.Inthiswaytheatomswillalwaystravel'uphill',andthustheirvelocitywillgraduallybereduced.繼續(xù)降溫玻色凝結(jié)統(tǒng)計(jì)熱力學(xué)電教課之一TheNobelPrizeinPhysics2001"fortheachievementofBose-Einsteincondensationindilutegasesofalkaliatoms,andforearlyfundamentalstudiesofthepropertiesofthecondensates"EricA.CornellUSAUniversityofColorado,JILA

Boulder,CO,USAb.1961WolfgangKetterleFRG

MIT,

Cambridge,MA,USAb.1957

CarlE.WiemanUSAUniversityofColorado,JILA

Boulder,CO,USAb.1951統(tǒng)計(jì)熱力學(xué)電教課之一

Program

GetfirstlyagreatdealofBoseatoms

withhighdensityandcooledtemperature(Lasercoolingandtrappingtechnology)Putthesampleinastaticmagneticwell(Magnetictrapping)Chillingevaporativelytheatomgas(Evaporativelychillingtechnology)Observingcondensation(Resonantabsorption)統(tǒng)計(jì)熱力學(xué)電教課之一Rubidium(Rb)1995EricA.CornellCarlE.Wieman統(tǒng)計(jì)熱力學(xué)電教課之一

Threedensitydistributionsoftheexpandedcloudsofrubidiumatomsatthreedifferenttemperatures.Theoriginalexperimentaldataisatwo-dimensionalblackandwhiteshadowimage,buttheseimageshavebeenconvertedtothreedimensionsandgivenfalsecolordensitycontours.0.2mm400nK200nK50nK統(tǒng)計(jì)熱力學(xué)電教課之一統(tǒng)計(jì)熱力學(xué)電教課之一Sodium(Na)1995WolfgangKetterle統(tǒng)計(jì)熱力學(xué)電教課之一ObservationofBose-Einsteincondensationbyabsorptionimaging.Shownisabsorptionvs.twospatialdimensions.Theleftpictureshowsanexpandingcloudcooledtojustabovethetransitionpoint;middle:justafterthecondensateappeared;right:afterfurtherevaporativecoolinghasleftanalmostpurecondensate.Thewidthoftheimagesis1.0mm.Thetotalnumberofatomsatthephasetransitionisabout7x105,thetemperatureatthetransitionpointis2

mK.統(tǒng)計(jì)熱力學(xué)電教課之一Fig.4.DirectobservationoftheformationofaBose-Einste