多分量玻色爱因斯坦凝聚低能动力学的研究

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1、万方数据论了在有效势作用下两种玻色子集体白旋的振动，这一效应有可能在实验上加以观测。关键词：玻色爱因斯坦凝聚元激发低能有效理论万方数据AbstractlIIIItlllllJllttllltlllllllllllllllllllllllllllllY2706019Bose-Einsteincondensationisamacroscopicquantumphenomena．In1924，EinsteingeneralizedBose’Sstatisticaltheoryofelectromagneticradiationtomassiveatoms，andDre

2、dictedthatifthetemperatureofaBosongasWasloweredtoacriticalvalue，thelowestenergystateshouldbemacroscopicallyoccupied，whichgavethenameofBEC．ThiswaSthefirstexampleinhistorythataphasetransitionOccurspurelyduetoquantumeffect，withoutthehelpofinteraction．Duetothetechnicallimitations，BEChasn

3、otbeenobservedforalongtime．In1995．threegroupsinJILA，RiceUniversityandMITcooledacloudofrubidiumatomsto20billionsofakelvinthroughlasercoolingandevaporativecooling，and￡orthefirsttimerealizedBECinexperiment，TillnOW，BEChasbeenrealizedexDerimentallyindilutegasesofhydrogen，lithium，sodium，po

4、tassium，rubidiumetc．Therichinternalstructuresofvariousatomsprovidewithpeoplepowerfultoolsforquantumsimulation．Inearlvexperimentstheatomswereconfinedbymagnetictraps，andusuallyonlyatomsoccupyingacertaininternalstatecanbeconfined．Sincetheintroductionofopticaltrap，theinternaldegreesoffre

5、edomarereleasedandthetrappedatomscanoccupydifferentinternalstatessimultaneously,whichcouldbecalledmulticomponentBEC．Sincetheinternalstatesareconventionallydenotedasspincomponents，itcanalsobecalledspinorBEC．ThepurposeofthisthesisistostudythepropertyofamixtureoftwospeciesofspinorBEC，in

6、cludingtwoparts：oneisthemixtureoftwospeciesofpseudospin一1／2atoms，anotheristhemixtureoftwospeciesofspin—latores．Thepaperisorganizedasfollows：^’InChapter1，wefirstgiveabriefintroductionoftheearlyhistoryofBECstudy—ingandtheexperimentaltechniqueoflasercoolingandmagnetic—opticaltrap，thenⅥ，

7、euseGross-Pitaevskiiequationandeffectivefieldtheorytosolvetheelementaryexcitations，finallywediscusstherelationbetweenBECandsuperfluidity．Chapter2describesspinorBEC，mainlythegroundstateandelementaryexcl—tationsoftwocomponentBECandspin-1BEC．Thenwepresentthewayofcon-structinginteraction

8、Hamiltonianf