Modern Atomic and Optical Physics_Lukin

Modern Atomic and Optical Physics_Lukin

ID:39786395

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頁數(shù):285頁

時間:2019-07-11

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1、Chapter1Preface:Quantummechanicsandatomicphysicsreview1.1IntroductionInthiscourse,wewillapproachthe?eldofatomicphysicsbypresentingauni?edpictureofcoherentevolutionandenvironmentaldecoherenceanddissipation.Thecoursewilldeveloparoundthreethemes:?rstly,wewillelucidatetheoreticaltech

2、niquesforsimultaneouslytreatingbothcoherentanddissipativeprocesses.Wewillalsoconsiderexperimentalmethodsforstudyingatomicsystems,including,forexamplediscussionofhighresolutionspectroscopy,lasertrappingandcoolingandpreparationofquantumstatesofions.Finally,wewillincorporateexamples

3、whichillustratehowtheseexperimentalandtheoreticaltechniques?ndapplicationincurrentresearch.Thebasicphilosophyofthecourseistodevelopatheoreticalunder-standingof”simple”systems?rst,thatissystemswhereonlyafewstates,afewparticles,orafewquantaarerelevant.Thiswillleadustoexploresomenon

4、-trivialquantumdynamicsandstudythepossibilityofcontrollingrealisticquantumsystems,includingimperfectionsin”realworld”experi-ments.Oncethesebasicbuildingblocksaremastered,wewillconsidermorecomplexsystemsbycombiningelementswealreadyunderstandatabasicphysicallevel.Tounderstandthedyn

5、amicsofthesystemswewillstudyinthiscourse,wewillneedtotreatbothdissipationandcoherentquantumevolutiononanequalfooting.11.2Reviewofquantummechanics1.2.1StatesWebrie?yreviewbasicquantummechanicsandsomeelementaryresultsofatomicphysics.Themostcompleteknowledgeofthesystemiscontainedint

6、hestatevector

7、ψi,whichisanelementofaHilbertspaceH.Wecanexpandthestatevector

8、ψiinanyorthonormalbasis{

9、ni}oftheHilbertspace,X

10、ψi=

11、nihn

12、ψi.(1.1)nForconvenience,wewritecn=hn

13、ψifortheprojectionofthestate

14、ψionthebasisstate

15、ni,whichgivesustheexpansioncoe?cientsofthestate

16、ψiinthebasis{

17、n

18、i}.Theprobabilityof?ndingthesysteminthestate

19、niisthenPn=

20、cn

21、2.1.2.2Superpositions-InterferenceQuantummechanicsallowsforsuperpositionsofstates,inparticular,fortwostatesX

22、ψi=c(1)

23、niand(1.2)1nnX

24、ψi=c(2)

25、ni,(1.3)2nntheirsuperposition√1(

26、ψi+

27、ψi)hastheuniquepropertythattheproba-122bili

28、tyofbeinginstate

29、niisnotingeneralgivenby

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