非線性混沌景象及其在激光原子相互作用和玻色愛因斯坦凝聚中的表現(xiàn)

劉杰北京運(yùn)用物理與計(jì)算數(shù)學(xué)研討所非線性研討中心/zhaoshengjj/boshizy/lilunwl/lilunwl.htmliu_jie@iapcm.ac揚(yáng)州大學(xué)物理系2005年三月概要1、非線性動(dòng)力學(xué)混沌景象簡(jiǎn)介保守系統(tǒng)的混沌耗散系統(tǒng)的混沌量子混沌2、運(yùn)用于強(qiáng)激光的原子電離3、運(yùn)用于波色---愛因斯坦凝聚體4、運(yùn)用于納米資料〔如有時(shí)間〕一、非線性系統(tǒng)的混沌景象保守系統(tǒng)與耗散系統(tǒng)區(qū)別點(diǎn)相體積收縮與否一樣點(diǎn)混沌軌道有李雅譜諾夫指數(shù)描畫保守系統(tǒng)的規(guī)范映象耗散系統(tǒng)的洛侖茲系統(tǒng)保守哈密頓系統(tǒng)的混沌根源及KAM定理1、正那么變換與作用量角變量pqArea=2\piIItheta2、可積系統(tǒng)與不可積系統(tǒng)Integrability:ifKisindependenceofangularvariable,i.e.allmotionsareeitherperiodicorquasiperiodic不可積的解析根源---小分母共振景象幾何根源---分界限的復(fù)雜化〔穩(wěn)定和不穩(wěn)定流形的橫截相交〕badnewsgoodnews不可積系統(tǒng)的普遍性KAM定理3、統(tǒng)計(jì)物理的根本假設(shè)---各態(tài)歷經(jīng)KAM定理：思索條件：1〕排除共振

2〕非兌化結(jié)論：存在不變環(huán)面〔積分〕Arnold分散4、經(jīng)典混沌的量子表象能譜統(tǒng)計(jì)波函數(shù)統(tǒng)計(jì)可信度〔Fidelity)量子運(yùn)動(dòng)是周期的或準(zhǔn)周期的無混沌不可積性的表現(xiàn)能譜間距統(tǒng)計(jì)Fidelityofquantumevolution二、強(qiáng)激光場(chǎng)中的原子——非微擾景象及實(shí)際

強(qiáng)場(chǎng)物理概略超短超強(qiáng)激光技術(shù)曾經(jīng)提供激光功率密度到達(dá)10**21W·cm**2時(shí)，相應(yīng)的局域電場(chǎng)將高達(dá)10**12V/cm，已是氫原子中束縛基態(tài)電子的庫侖場(chǎng)強(qiáng)的170倍。激光與原子、分子、離子、電子、團(tuán)簇以及等離子體等各種形狀物質(zhì)之間的相互作用研討，將進(jìn)入到了一個(gè)前所未有的高度非線性和相對(duì)論性的強(qiáng)場(chǎng)范圍。由此而開創(chuàng)出了超強(qiáng)激光場(chǎng)物理這樣一個(gè)全新的現(xiàn)代科學(xué)技術(shù)的前沿學(xué)科領(lǐng)域。強(qiáng)場(chǎng)物理概略超短、超強(qiáng)激光與物質(zhì)相互作用產(chǎn)生的主要物理景象研討。1〕激光與原子、分子、離子、電子、團(tuán)簇各種形狀物質(zhì)之間的相互作用研討。2〕與等離子體相互作用。反常吸收和加熱效率，相對(duì)論效應(yīng)和有質(zhì)動(dòng)力引起的臨界面景象，強(qiáng)激光在等離子體中傳播和對(duì)光傳播的影響，帶電粒子加速，自生磁場(chǎng)產(chǎn)生和對(duì)光束傳播的影響等。強(qiáng)場(chǎng)物理概略相關(guān)高技術(shù)及根底學(xué)科中潛在運(yùn)用的研討。1〕快點(diǎn)火研討的突破能夠降低激光聚變點(diǎn)火能量約一個(gè)量級(jí)，使激光聚變能源研討產(chǎn)生革命性影響。2〕超快、高相關(guān)性、高亮度的X光源的運(yùn)用在推進(jìn)深層次物質(zhì)構(gòu)造的認(rèn)識(shí)、開展生命科學(xué)和21世紀(jì)資料科學(xué)以及信息科學(xué)等都有重要意義。3)強(qiáng)場(chǎng)超強(qiáng)梯度加速器的研制導(dǎo)致加速器超小型化，并導(dǎo)致加速器技術(shù)革命性變化。激光技術(shù)的開展Intensity(wattspersquarecentimeter)Q_switchingModelockingChirpedpulseamplificationNonlinearQEDNonlinearrelativisticopticsatoms,plasmas,ICF強(qiáng)激光場(chǎng)中的原子----引言近些年來，強(qiáng)場(chǎng)與原子相互作用問題引起人們的廣泛關(guān)注。這主要由于在過去幾十年里激光技術(shù)和實(shí)驗(yàn)技術(shù)的飛速開展使得①電磁場(chǎng)強(qiáng)度與庫侖場(chǎng)(原子玻爾半徑處)在同．一量級(jí)(甚至超越)；②可以非常準(zhǔn)確地丈量光電子的能量及角分布等物理量。由于場(chǎng)強(qiáng)很強(qiáng)，傳統(tǒng)的微擾實(shí)際失效，因此需求開展新的非微擾實(shí)際。這在實(shí)際上是具有挑戰(zhàn)性的。

主要的非微擾景象A.多光子電離、閾上電離原子可以吸收超越閾值數(shù)的光子。1999年Agostini首先在實(shí)驗(yàn)上察看到這種景象，引起了人們的廣泛興趣與研討熱潮。B．原子穩(wěn)定化景象原子穩(wěn)定化景象就是指在一定的參數(shù)條件下，電離率隨著場(chǎng)強(qiáng)的增大而減小。主要物理機(jī)制是：在超強(qiáng)場(chǎng)中快速抖動(dòng)〔QUIVER〕的電子有較少的時(shí)機(jī)與核交換動(dòng)量。Dynamic穩(wěn)定化景象Adiabatic穩(wěn)定化景象

C.高次諧波原子和激光相互作用時(shí)可發(fā)射光子。當(dāng)場(chǎng)很強(qiáng)時(shí)有高次諧波。由于高次諧波發(fā)射能夠成為有效的全相關(guān)短波光源，因此引起人們的注重。一、單電子電離實(shí)驗(yàn)G.G.PaulusetalPRL72(1994)2851B.Yang,etalexperiment,PRL71(1993)3770HatomsintheintenselaserfieldsPhys.LetterA,236,533-542(1997)HatomsintheintenselaserfieldsHatomsintheintenselaserfieldsHeatominintenselaserfieldsHeatominintenselaserfieldsExplainthe“knee〞structureandtheratiobetweentheHe1+andHe2+ionsobservedinexperimentsExplainthemomentumdistributionoftheHeionsrecordedinexperiments.Phys.Rev.A,Vol.63,011404(R)(2001)Phys.Rev.A,Vol65(2):art.no.021406FEB(2002)Phys.Rev.A,Vol.63,043416(2001)HeatominintenselaserfieldsHeatominintenselaserfieldsHeatominintenselaserfieldsTheMomentumdistributionofHe2+ion原子在激光場(chǎng)中的穩(wěn)定化景象穩(wěn)定化景象對(duì)應(yīng)于在超強(qiáng)超高頻的激光場(chǎng)作用下，原子的電離隨場(chǎng)強(qiáng)和頻率的添加反而下降的景象。這種下降可區(qū)分為以下兩類：動(dòng)力學(xué)穩(wěn)定化和漸進(jìn)穩(wěn)定化。這里主要引見漸進(jìn)穩(wěn)定化。在這方面比較勝利的實(shí)際是由Gavrila等人開展起來的基于對(duì)激光場(chǎng)頻率倒數(shù)進(jìn)展展開高頻Floquet(HFFT)實(shí)際。三、Bose-EinsteinCondensates(BECs)andBogoliubovExcitation1.BasicconceptofBECsJILAgroup,Rubidiumatoms,Science269,198(1995)MITgroup,Sodium;Ricegroup,Lithium(1995)CornellandWiemancooledasmallsampleofatomsdowntoonlyafewbillionths(0.000,000,001)ofadegreeaboveAbsoluteZero!ThatwaswhattheyneededtodotoseeBose-Einsteincondensation.HowcoldofBECWhatitisTypicalparametersofBEC,DensityTemperaturenkSizeThenumberofatom10^2-10^8Atomsareidenticalandbehavesinthesameway,actcollectivelydemonstratingmacroscopicquantumfluidphenomenaWhatisBECsgoodforToonewandweknowtoolittlePotentialapplication:Sensitivemeasurement,tinyinstrument,atomlaser,quantuminformation,etc.WeshouldunderstandBECsdynamicsfirstUltracoldatomsinapulsedlaserbeam:PeriodicallykickedrotatormodelBECLaserbeamWhathappensifwereplacetheultra-coldatomwiththeBEC?1.KickedBose-EinsteincondensateonaringQuasi-onedimensionalringtrapisthehealinglengthGross-PitaveskiiequationisinteractionstrengthLengthunit:Energyunit:Timeunit:NormalizationconditionPeriodicBoundarycondition:EvolutionofthemeanenergyofeachparticleAnti-ResonanceQuantumbeatingInstabilityKickstrengthKickperiodInitialstateTwo-modeapproximationQuantumbeatingforweakinteractionTotalenergyisverysmallTotalparityisconservedSpinHamiltonianPopulationdifferenceRelativePhaseNormalizationconditionTheHamiltonianissimilartoakickedtopmodelJ.Liu,B.Wu,andQ.Niu,Phys.Rev.Lett.90,170404(2003);SpinDynamicsNoninteraction:Anewexplanationofanti-resonanceFreeevolution:ananglerotationaboutthezaxisKick:ananglerotationabout-xaxisWeakinteraction:QuantumbeatingFreeevolution:ananglerotationaboutthezaxisKick:ananglerotationabout-xaxisRedarrows:quantumbeatingBluearrows:anti-resonanceEvolutionofrelativephaseandpopulationdifferencePopulationdifferenceoscillateswithtime,similarastheenergyRelativephaseincreasesalmostlinearlyandreaches2inonebeatperiodBeatFrequencyTheslope:TothefirstorderingInonebeatperiod,itreachesAnalyticexpressionsforbeatandoscillationfrequenciesScatters:NumericalsimulationLines:AnalyticexpressionsPhasespaceportraitsintwo-modeapproximationQuantumAnti-ResonanceQuantumBeatingReddotsandline:thetrajectorieswithinitialconditionsBlackdotsandlines:thetrajectorieswithotherinitialconditionsInstabilityforstronginteractionDynamicsintwo-modeapproximationAsinstabilityoccursforstronginteraction,two-modeisnotagoodapproximationRandomevolutioninthetemporaldomain:---IrregularpatternofenergyevolutionEvidencesforinstabilityinaBECBogoliubovTheoryThemeannumberofnoncondensedatomsatzerotemperatureistheprojectionoperatoriscondensatewavefunctionisthechemicalpotentialdescribethedeviationofthewavefunctionfromthecondensatewavefunctionExponentialsensitivitytoinitialcondition:---ExponentialgrowthofnoncondensedatomsinunstableregimeSimilartotheexponentialdivergenceofnearbytrajectoriesGrowthrateissimilartoLyapounovexponentNoncondensedatomsnumber:GrowthrateCriticalphenomena--scalinglawg=0.1g=1.5g=2.0ChangeofdensitydistributionsacrosscriticalpointUnstableregime:Stableregime:1.Condensatedensityoscillatesregularly2.Noncondensatedensityincreasesslowlyandshowsmainpeaksaroundand0()mode1.Condensatedensityoscillatesirregularly2.Noncondensatedensityincreasesexponentiallyandshowsmainpeaksaround()modeCanbeusedtoidentifythetransitiontoinstability58Thebeatingphenomenoncanbeusedtomeasureatominteractionstrength.ApplicationsandfuturedirectionsDynamicallocalizationandquantumresonanceinakickedBEC?---theeffectsofnonlinearityThedensitydistributioncanbeusedtoobservethetransitiontoinstabilityinexperimentThearticlepublishedinPhysicalReviewLetters,Vol.92,054101(2004)4.BECinbilliards

Phys.Rev.Lett.93,074101(2004)

Ultra-coldatomsinopticaltrapofstadiumbilliardsIntergrable:PossiondistributionofthelevelspacingsLocalizedeigenfunctionsNonintergrable:WignerdistributionofthelevelspacingsExtendedeigenfunctions(chaoticstate)scars,Question:Whathappensifwereplacetheultra-coldatomswiththeBECThedistributionoflevelspacingsofBogoliubovexcitation?EigenstateofBogoliubovexcitation?ThepropertiesoftheBogoliubovwave?GeometricopticsapproximationssupposeConsiderslowly-varyingmediaissmallThebogoliubovequationcanbetransformedintotheEikonalequationInthenoninteraction