玻色-愛因斯坦凝聚體的集體激發(fā)及非線性動(dòng)力學(xué)研究.pdf

1、Y11318a9舟類密緞話喜皂泰彳弛失巷碩士學(xué)位論文玻色一愛因斯坦凝聚體的集體激發(fā)及非線性動(dòng)力學(xué)研究導(dǎo)師姓名職稱專業(yè)名稱李冠強(qiáng)薛具奎教授理論物理研究方向：玻色一愛困斯坦凝聚中的非線譬苧!墮為論文答辯日期2007年5月學(xué)位授予時(shí)間答辯委員會(huì)主席i平聞人2007年月oo七年五月AbstractInrecentyears，BoseEinsteincondensation(BEC)indiluteatomicgaseshasbecomeanin

2、terestingstudysubjectofphysicsNotonlycanitprovideamacrosystem，bywhichquantummechanicscanbestudiedinanotherwaybutalsoitwillopena麗deperspectiveofapplication，such勰atomiclaser，quantuminformationprocessing，andprecisionmeasure

3、mentsNonlinearityandexternalpotentialmakethesystemdisintegrableandcomplex，SOtheexplorationaboutthismacroquantumobjecthasalsobecomeoneofmaintasksinthefieldofnonlineardynamicsInthisthesis，bymeanfieldframeoftheGrossPitaevsk

4、iiequation，thecollectivebehaviorsoftheBECareinvestigatedanalyticallyandnumericallyInthefirstpartthecollectiveexcitationsofaquasionedimensionalBECinaamharmonictrapy(x)=(妒婦4)areinvestigatedTwolowenergycollectivemodesaxeder

5、ivedanalyticallybyusingstandardvariationalmethod，andtheeffectsofanilarmonicityofthetraponexcitationsofaBECarestudiedItisfoundthatthelowenergycollectivefrequenciesareblueorredshifteddependingonA0orA0Meanwhilethevariationo

6、fwidthandthemotionofthecenterofmassarediscussedTheresultshowthatthebeatingscorrespondingtovariationofwidthwhichindicatecouplingbetweenthemodes，OccuratdifferentdrivingamplitudesFinallythecollapseandrevivalofcollectiveexci

7、tationinducedbymodecouplingisalsodemonstratedSecondlytheparametricexcitationsintwocomponentBECsdescribedbytwoconpiedGressPitaevskiiequations(GPEs)areinvestigatedanalyticallyandnumericallyByusingthevariationalapproximatio

8、n，wederivethecoupledequationsofmotionforthecenterofmasscoordinatesofthetwocendensatesandtheirwidthsTheharmonicgenerationandnonlinearcouplingofoscillationmodesassociatedwiththenonlineardynamicsofbinarymixturesaxerevealedb

9、yexcitingtheinternalparameterofthesystemMeanwhile，weobtainanalyticallytheresonanceconditionandresonanceboundariesintermsofthemodulationfrequencyandthestrengthofintercomponentinteractionInparticular，wedemonstrateanovelmet

10、hodofformationofmultisolitonconfigurations(includingsolitontrains，solitonpairsanddomainwalls)throughparametricresonanceintwocomponentBECsbydirectnumericalsimulationfortheonedimeusionalcoupledGPEsFinauytheevolutionofBEC8l

11、oarledintoaperiodicringopticallattices(OL)trapisstudiedByme眥softhevariationalmethodanddirectnumericalsimulationsoftheGrossPitaevskii(GP)equation，thegroundstatepropertiesandthevortexstabilitiesoftheeondensatesforbothrepul