Table Of ContentGraduate Texts in Physics
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Graduate Texts in Physics
Graduate Texts in Physics publishes core learning/teaching material for graduate- and ad-
vanced-levelundergraduatecoursesontopicsofcurrentandemergingfieldswithinphysics,
both pure and applied. These textbooks serve students at the MS- or PhD-level and their
instructorsascomprehensivesourcesofprinciples,definitions,derivations,experimentsand
applications(asrelevant)fortheirmasteryandteaching,respectively.Internationalinscope
and relevance, the textbooks correspond to course syllabi sufficiently to serve as required
reading.Theirdidacticstyle,comprehensivenessandcoverageoffundamentalmaterialalso
makethemsuitableasintroductionsorreferencesforscientistsentering,orrequiringtimely
knowledgeof,aresearchfield.
SeriesEditors
ProfessorRichardNeeds
CavendishLaboratory
JJThomsonAvenue
CambridgeCB30HE,UK
[email protected]
ProfessorWilliamT.Rhodes
DepartmentofComputerandElectricalEngineeringandComputerScience
ImagingScienceandTechnologyCenter
FloridaAtlanticUniversity
777GladesRoadSE,Room456
BocaRaton,FL33431,USA
[email protected]
ProfessorSusanScott
DepartmentofQuantumScience
AustralianNationalUniversity
ScienceRoad
Acton0200,Australia
[email protected]
ProfessorH.EugeneStanley
CenterforPolymerStudiesDepartmentofPhysics
BostonUniversity
590CommonwealthAvenue,Room204B
Boston,MA02215,USA
[email protected]
ProfessorMartinStutzmann
WalterSchottkyInstitut
TUMünchen
85748Garching,Germany
[email protected]
Frank Grossmann
Theoretical
Femtosecond
Physics
Atoms and Molecules in Strong Laser Fields
Second Edition
FrankGrossmann
InstitutfürTheoretischePhysik
TechnischeUniversitätDresden
Dresden,Sachsen,Germany
ISSN1868-4513 ISSN1868-4521(electronic)
GraduateTextsinPhysics
ISBN978-3-319-00605-5 ISBN978-3-319-00606-2(eBook)
DOI10.1007/978-3-319-00606-2
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013944233
©SpringerInternationalPublishingSwitzerland2008,2013
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To thememoryofmyfather
HansGrossmann
Preface to the Second Edition
Themainmotivationforthissecondeditionofthebookwastheinclusionofmore
exercisesand,mostimportantly,alsoacollectionofsolutionsoftheseexercisesat
theendofthebook.Sometypeerrorsandmoresevereflawsofthefirsteditionthat
havecometomyattentionhavebeencorrected.Thebookis,however,intendedas
a comprehensive introduction to a topic of current interest and not as a complete
review of the field. I have therefore not added more (advanced) material into the
maintext.Furthermore,Ihavereservedlyupdatedtheliteraturelistbyincludinga
fewmoreresearchpapers,althoughalotmoreworkhasbeendoneinthelastfive
years and a related new field, the field of attosecond physics, has emerged. Some
moretextbookreferencesandreviewshavealsobeenaddedwhereappropriate.
Again, I would like to express my thanks for enlightening discussions on the
topics touched herein to more generations of students that attended my related
lectures at TU Dresden and also to Larry Schulman, Jan Handt, Werner Koch,
Christoph-MarianGoletz,AlexanderKästner,MichaelFischer,CarlosZagoya,Se-
bastianKrause,NiklasRohling,MaxBuchholz,andTobiasFiedelschusterfor on-
goingexchangeofideasandtoAlexanderKästnerforprovidingnumericalresults.
Formakingthebookavailableaspartoftheseries“GraduateTextsinPhysics”,
and for support during the production stage I would like to thank Claus Ascheron
andhisteamfromSpringerVerlag.
Dresden,Germany FrankGrossmann
March2013
vii
Preface to the First Edition
The development of modern pulsed lasers with power densities larger than
1016 W/cm2 andwithveryshortpulsedurationinthefemtosecondregimeenables
experimentaliststostudyelementaryprocessessuchaschemicalreactionsandex-
citation mechanisms in different areas in physics in the time domain. In parallel
totheexperimentalinvestigations,analyticalandnumericalstudiesoflaserdriven
atomsandmoleculeswitha limitednumberofdegreesoffreedomareperformed.
Thesetheoreticalinvestigationshaveledtothepredictionand/ortheexplanationof
a large variety of partly counter-intuitive phenomena. Among those are the gener-
ation of high harmonics using laser excited atoms or molecules, the ionization of
atomsabovethecontinuumthreshold,thestabilizationofatomsagainstionization
inverystrongfields,counter-intuitivepulsesequencestoselectivelypopulatevibra-
tional states in molecules and, last but not least, the control of chemical reactions
byspeciallytailoredlaserpulses.
This book originated out of a course, that I have given on a regular basis since
2000 for advanced undergraduate and graduate students at Technische Universität
Dresden.Itoffersatheoreticallyorientedapproachtothefieldoflaserdrivenatomic
and molecular systems and requires some knowledge of basic classical and quan-
tum mechanics courses as well as of classical electrodynamics. The book has two
introductorychaptersinPartIthatpavethewayfortheapplicationsinPartII.PartI
andalsoChap.3ofPartIIcontainaselectionoftextbookmaterialthatisneededto
understand the rest of the book. The material presented in the last two chapters is
closetotherecentliterature.Ihavechosenonlysuchworks,however,thatdealwith
fundamentalconceptsandarebasedonsimplemodelcalculations.Abiasedandin-
completelistareferencesisgivenattheendofthechapters,precededbysomenotes
andhintsforfurtherreading.Forthosereaderswhoareinterestedinsomecomputa-
tionaldetails,thesearegivenintheappendicesattheendofthecorrespondingchap-
ters.Furthermore,atseveralplacesthroughoutthetext,exercisesareplaced,whose
independentsolutionallowsadeeperunderstandingofthematerialpresented.
InChap.1,westartwithashortintroductionintothefoundationsofthelaser.We
willespeciallyconcentrateonthoseaspectsofpulsedlasersthatwillbeimportant
forthetheoreticalinvestigationsinPartIIofthebook.
ix
x PrefacetotheFirstEdition
The next fundamental chapter is devoted to the non-relativistic time-dependent
Schrödinger equation. In the case of lasers of up to atomic field strengths, this
equation allows the theoretical description of the phenomena we want to investi-
gateinPartII.Analyticalaswellasnumericalmethodstosolvethetime-dependent
Schrödinger equation are thus in the focus of Chap.2. Throughout the whole pre-
sentation,inordertokeeptheapproachassimpleaspossible,wetouchthetopicof
correlatedmanyparticledynamicsonlywherenecessaryandconcentrateonthede-
scriptionofelectronicaswellasnucleardynamicswiththehelpofmodelswithas
fewdegreesoffreedomaspossible.ThecontentsandthepresentationofChap.2are
inspiredbytheexcellentnewtextbookbyDavidTannor,IntroductiontoQuantum
Mechanics: A Time-Dependent Perspective, which hopefully will start a “revolu-
tion”inthewayquantummechanicsistaughtinthefuture.
Thesecondpartofthebook,startingwithChap.3,containsacollectionofequiv-
alentwaystocouplea chargedparticletoaclassicalelectromagneticfield.As the
basic postulate we use the principle of minimal coupling. By using unitary trans-
formations,onecantheneitherderivethelengthformortheKramers-Henneberger
form of the coupling. As first examples of laser-matter interaction, we study the
dynamicsof(structure-less)two-levelsystemsinlaserfields.PhenomenalikeRabi
oscillations of the occupation probability, occurring there, will be encountered off
an on in the remainder of the book. Furthermore, also the fundamental so-called
rotatingwaveapproximationwillbediscussedforthefirsttimeinthiscontext.
Selectedexamplesoflaser-matterinteractioninatomicphysicsarereviewedin
Chap.4.Here,weconcentrateonthephenomenaofionizationandhighharmonic
generationofasingleelectroninaCoulombpotentialofpossiblyreduceddimen-
sionality.Itturnsoutthataperturbationtheoreticapproachwouldnotbesuitedto
understand most of the phenomena presented in this chapter. Thus the numerical
wavepacketmethodsthatwereinthefocusof Chap.2willfindtheirfirstapplica-
tion.
The next step in the direction of higher complexity of the dynamics will be
takeninChap.5.Herewedealwithlaser-drivensystemsinmolecularandchemical
+
physics. The simplest molecule, the hydrogen molecular ion, H , will serve as a
2
vehicletounderstandsomeofthebasicconceptsofmolecularphysicssuchaselec-
tronicpotentialsurfaces.Inthefollowing,thefullnumericalsolutionofthecoupled
+
electron nuclear problem of H in a monochromatic laser field will be reviewed.
2
AfterdiscussingthefundamentalBorn-Oppenheimerapproximation,fortherestof
thechapter,wethenassumethatthesolutionoftheelectronicmanybodyproblem
isatourdisposalintheformofanalyticallyornumericallygivenpotentialenergy
surfaces.Afterashortdigressiononnuclearmotiononasingleelectronicsurface,
andthediscussionofasimpletwocoupledsurfacesproblem,wethenreviewsome
modernapplicationsinthefieldsoffemtosecondspectroscopy,optimalcontrolthe-
ory,andquantuminformationprocessingundertheforegoingassumption.
AtthispointIthankthestudentsatTUDresdenwhohaveattendedmylectures.
Theyhaveinspiredmeenormously,throughtheirintensecollaboration,duringthe
lectures, as well as during the exercise classes. This has motivated me to rethink
PrefacetotheFirstEdition xi
thematerialpresentedagainandagainandthestudentshavethuscontributedsub-
stantially to the improvement of the manuscript. Also the hospitality of the Max-
Planck-InstituteforthePhysicsofComplexSystems,thatofferedmetheopportu-
nitytoattendandrunseveralconferencesinthefieldwasveryimportanttoshape
myunderstandingpresentedhere.Furthermore,IexpressmydeepgratitudetoJan-
MichaelRostandRüdigerSchmidtfortheircontinuousavailabilityfordiscussions
andforlong-termcollaboration.Moreover,IamgratefultoPeterHänggiforthein-
troductiontothefieldofdrivenquantumsystemsduringmyPh.D.workwithhim,
andtoEricHellerforopeningtheworldoftime-dependentsemiclassicstome.In
addition,I have benefittedfrom uncountablediscussions with and valuable advice
offormermembersoftheTheoreticalQuantumDynamicsGroupinFreiburg,espe-
ciallyGernotAlber,RichardDehnen,VolkerEngel,ChristophMeier,Gerdvande
Sand, and Gerhard Stock. Furthermore, former and present members of the Theo-
reticalAtomicandMolecularPhysicsGroupattheInstituteofTheoreticalPhysics
ofTUDresdenandtheFiniteSystemsDepartmentattheMPIPKSinDresdenhave
helped shape my understanding. Among many others these are Andreas Becker,
AgapiEmmanouilidou,CelalHarabati,AnatoleKenfack,ThomasKunert,UlfSaal-
mann, and Mathias Uhlmann. For helping me by answering specific questions or
supplyinginformationandvaluablegraphs,IwouldliketothankWolfgangSchle-
ich,JanWerschnik,MatthiasWollenhauptandShuheiYoshida.Foradviceandhelp
withrespecttographicsissues,IthankArndBäckerandWernerKoch.Finally,Iam
indebtedtoDavidTannor,whosuppliedmewithpreliminaryversionsofhisbook
ataveryearlystageandthushelpedshapethepresentationheretoasubstantialde-
gree.ThefocusofDavid’sbookonatime-dependentviewofquantumphenomena
isanabsolutenecessityifonewantstostudylaser-drivensystems.
Dresden,Germany FrankGrossmann
May2008
