Quantum Efficiency in Complex Systems, Part I: Biomolecular systems PDF
Preview Quantum Efficiency in Complex Systems, Part I: Biomolecular systems
Semiconductors and Semimetals SeriesEditors EickeR.Weber ChennupatiJagadish Director AustralianLaureateFellow Fraunhofer-Institut andDistinguishedProfessor fu¨rSolare DepartmentofElectronic EnergiesystemeISE MaterialsEngineering Sprecher,Allianz ResearchSchoolofPhysics Energieder andEngineering Fraunhofergesellschaft AustralianNationalUniversity, Heidenhofstr.2,79110 Canberra,ACT0200, Freiburg,Germany Australia Quantum Efficiency in Complex Systems, Part I: Biomolecular systems SEMICONDUCTORS AND SEMIMETALS Volume 83 EICKE R. WEBER Freiburg,Germany MICHAEL THORWART Hamburg,Germany ULI WU¨RFEL Freiburg,Germany AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEWYORK • OXFORD • PARIS • SANDIEGO SANFRANCISCO • SINGAPORE • SYDNEY • TOKYO AcademicPressisanimprintofElsevier AcademicPressisanimprintofElsevier 525BStreet,Suite1900,SanDiego,CA92101-4495,USA 30CorporateDrive,Suite400,Burlington,MA01803,USA 32JamestownRoad,LondonNW17BY,UK Firstedition2010 Copyright(cid:13)c 2010ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeanselectronic,mechanical,photocopying, recordingorotherwisewithoutthepriorwrittenpermissionofthepublisher. 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ISBN:978-0-12-375042-6 ISSN:0080-8784 ForinformationonallAcademicPresspublications visitourwebsiteatelsevierdirect.com PrintedandboundedinUSA 10 11 12 13 10 9 8 7 6 5 4 3 2 1 FOREWORD Condensed matter physics is rapidly developing, in recent years, to pro- vide the basis for a solid fundamental understanding of the behavior of electriccarriersinevermorecomplexstructures. This development is fueled, on the one side, by stunning progress in ourunderstandingofthefundamentalphysicalprocesses:nonequilibrium statistics,quantummechanicsofopensystems,quantumchaos,quantum information science, experimental quantum optics, surface physics, pho- tonics, and computational physics have matured to a level that, today, allows us to do the first steps toward a control of complex systems, in the classical as well as in the quantum realm. Condensed matter physics is no more restricted to the solid state but is, nowadays, discussed and realizedinprimafacieverydiversephysicalsettings,fromatomicmatter waves over interacting Rydberg atoms to clusters and photonic crystals. With an unprecedented control on the microscopic constituents of mat- ter,nowadays,weareabletoisolatesinglefeaturesofsolid-statetransport phenomena in dedicated experiments and to scrutinize their robustness when embedded in ever more complex environments. Powerful compu- tational methods together with a much deeper analytical understanding of the mathematical structure of many body quantum mechanics per- mit quantitative treatments at a level of complexity far beyond what was consideredtobeachievableonlyfewdecadesago. Ontheotherside,thetechnologicalneedsofmodern,highlydeveloped societiesonaglobalscaledefineunprecedentedchallenges,notablyinthe energysector.Thesewillonlybemetifwesucceedtocomeupwithnovel technologicalsolutions,whichqualitativelyenhanceourenergyefficiency. The novel devices that will emerge from such a technological revolu- tion ought to be available at lower cost, yet with qualitatively improved performance. They need to be robust and transportable. The fundamen- tal insights expected from the above research areas, therefore, need to be implemented with the help of affordable, hitherto unknown, novel (solid state) materials. The invention of such materials itself will require a detailed understanding of their microscopic structure, and thus hinges onceagainonourprogressesonthefundamentalscienceside. vii viii Foreword Although such challenge is enormous, it is also intellectually highly rewardingandattractiveasitfosterstheconfluenceofwidelydiversesci- entific disciplines, which would otherwise rarely make contact: quantum physicsmeetschemistry,engineering,andmaterialscience. A case in point is the field of organic electronics and of electronic and energy transfer processes in biological systems. New and suprising experimentaldataabound,whichsuggestthatquantummechanicsmight playamuchmoreprominentroleinsuchprocessesatroomtemperature. Already today we can expect that the insight we gain from the study of thesehighlystructured,multihierarchical,nonequilibriumsystemscanbe utilizied for new kinds of electronic switching and computing, or for the harvestingofenergyfromthesunintheformofphotovoltaics–toname justafewofpotentiallyhighlyrelevantapplications. Yet, we have, so far, little understanding to which degree quantum phenomenasuchasmany-bodycoherencesandentanglementplayarole in determining the electronic and optical properties of such complex structures. Neither do we understand under which conditions quantum coherencecanpersistinsuch,ingeneral,widelyopensystems,andwhat definestherelevanttimescales,nordowehaveageneralunderstandingof thedynamicalmanifestationsthereof.Thespecificresearchareaoforganic electronics and of biological charge and energy-transfer units provides, thus, a nucleus for the truly interdisciplinary research effort, which will beneededtofacetheabovechallengesahead. The two parts of this volume will present a unique collection of con- tributions from leading scientists daring to venture into this, rather, new field.Mostofthechapterauthorsparticipatedinaworkshoponthetopic, “QuantumEfficiency–FromBiologytoMaterilasScience”intheseriesof black-forest workshops, sponsored by the Freiburg Institute of Advanced StudiesFRIAS,andjointlyorganisedtogetherwiththeInstituteofPhysics oftheAlbert-LudwigsUniversityofFreiburg,intheFallof2009. Itisexpectedthatthisvolumewillstimulatefurtherworkinthisfield, with the objective to, ultimately, use the fundamental insights that will begainedtoguidethedevelopmentofmoreefficientopto-electronicand light-harvestingdevices,atthelowestpossiblecost. EickeR.Weber Freiburg,September2010 LIST OF CONTRIBUTORS EickeR.Weber,DirectorFraunhofer-Institutfu¨rSolareEnergiesysteme ISESprecher,AllianzEnergiederFraunhofergesellschaft Heidenhofstr.2,79110Freiburg,Germany.(Foreword) AndreasBuchleitner,DepartmentforQuantumOpticsandStatistics, InstituteofPhysics,AlbertLudwigsUniversityofFreiburg, Hermann-Herder-Str.3,D-79104Freiburg,email: [email protected].(Ch1) FlorianMintert,DepartmentforQuantumOpticsandStatistics,Institute ofPhysics,AlbertLudwigsUniversityofFreiburg, Hermann-Herder-Str.3,D-79104Freiburg,email: fl[email protected].(Ch1) Ju¨rgenKo¨hler,ExperimentalPhysicsIV,andBayreuthInstituteof MacromolecularResearch(BIMF),UniversityofBayreuth,95440 Bayreuth,Germany,email:[email protected].(Ch3) MichaelThorwart,I.Institutfu¨rTheoretischePhysik,Universita¨t Hamburg,Jungiusstraße9,20355Hamburg,Germany,email: [email protected].(Ch2) PeterNalbach,SchoolofSoftMatterResearch,FreiburgInstitutefor AdvancedStudies(FRIAS),Albert-Ludwigs-Universita¨tFreiburg, Albertstraße,19,79104Freiburg,Germany. I.Institutfu¨rTheoretischePhysik,Universita¨tHamburg, Jungiusstraße9,20355Hamburg,Germany,email: [email protected].(Ch2) RichardJ.Cogdell,ExperimentalPhysicsIV,andBayreuthInstituteof MacromolecularResearch(BIMF),UniversityofBayreuth,95440 Bayreuth,Germany.(Ch3) TorstenScholak,DepartmentforQuantumOpticsandStatistics,Institute ofPhysics,AlbertLudwigsUniversityofFreiburg, Hermann-Herder-Str.3,D-79104Freiburg,email: [email protected].(Ch1) ix x ListofContributors ThomasWellens,DepartmentforQuantumOpticsandStatistics, InstituteofPhysics,AlbertLudwigsUniversityofFreiburg, Hermann-Herder-Str.3,D-79104Freiburg,email: [email protected].(Ch1) 1 CHAPTER Transport and Entanglement T.Scholak,F.Mintert,T.Wellens,andA.Buchleitner Contents 1. CoherentTransportinDisorderedSystems 4 1.1. ModelHamiltonian 4 1.2. Pathamplitudes 6 1.3. Weaklocalization 7 1.4. Andersonlocalization 9 1.5. Fluctuations 11 2. Many-BodyCoherenceandEntanglement 13 2.1. Basicconcepts 13 2.2. Toolstocharacterizeentanglement 17 3. FastandEfficientTransportinMolecularNetworks 23 3.1. Modelanddefinitionofthetransferefficiency 23 3.2. Optimalconfigurations 26 3.3. Impactofdecoherence 28 3.4. Transportandentanglement 29 4. Conclusions 32 Appendix 34 A. Tangles 34 References 36 Transportphenomenaareallaroundus,frommicroscopictomacroscopic scales,andtheymediatefundamentaltransferprocessesofmatter,charge, or energy. Much of present day science and technology ultimately relies ontransportprocesses,fromradiationtransferintheatmosphere,withits very tangible impact on climatic conditions, over the long distance trans- fer of electrical energy, controlled chemical reactions in large molecules, signalprocessinginbiologicaltissue,tochargetransferinsemiconductor devices–beitdetectorsofhigh-energyorlow-energyparticlesorphotons, SemiconductorsandSemimetals,Volume83 (cid:13)c 2010ElsevierInc. ISSN0080-8784,DOI:10.1016/B978-0-12-375042-6.00001-8 Allrightsreserved. 1 2 T.Scholak,F.Mintert,T.Wellens,andA.Buchleitner efficientlightsourceslikeLEDs,orphotovoltaicsolarcells–randomlasers, and even quantum cryptography and computation. Irrespective of the actual scale, all practical applications here listed, and equally so all the underlying,paradigmaticmodelsystemsbearthecommonfeatureofsome sort of complexity, in the sense that transport is mediated by many more than just one degree of freedom, and that these different degrees of free- domareonlypartiallycontrolledandgarnishthedynamicswithdifferent characteristic length and timescales. The unavoidable lack of control is summarized as “disorder” or “noise” inflicted on the transport process ofinterest–whichoccursinthe“system’s”degreesoffreedom–bysome noisyenvironment. Complexityisambivalentinnature,becauseitcreatesnovelandunex- pected patterns that emerge, e.g., as, often very robust, collective modes, butcanalsoinduceinstabilitiesandsuddenphasetransitions.Hence,dis- order,noise,andothertypicaltraitsofcomplexsystemscanmanifestasa nuisance as well as a virtue, on macroscopic, as well as on microscopic scales (Anderson, 1958; Buchleitner and Hornberger, 2002; Gammaitoni et al., 1998; Gutzwiller, 1990; Haake, 1991; Wellens et al., 2004). When it comes to technological and engineering applications, however, disorder andnoisearewidelyconsideredaspurelydetrimental,andtheartofengi- neering,thus,largelyconsistsinscreeningthemout.Thisisevermoretrue onthemicroscopiclevelandinthecontextofquantumengineering–the quantum computer being a prime example: here, disorder and noise are conceivedasthecauseofdecoherence,i.e.,ofthefadingawayofquantum interference effects – which are the very source of its formidable poten- tialefficiencyascomparedwithclassicalsupercomputingdevices.Inturn, when disorder and noise cannot be screened away, the widespread opin- ionisthatquantumcoherenceeffectsareboundtofaintontheassociated length and timescales. Biological systems, large macromolecular struc- tures, and equally so multilayered semiconductor structures as used in detector,LED,andsolarcelltechnology–whichoftenoperateatambient temperatures–apparentlyfall,precisely,inthislattercategory. It must be noted, however, that much of this intuitive judgement on the sustainability of quantum coherence at high temperatures, and, possibly, on large scales, neglects the potential role of residual symme- tries and implicitly assumes thermodynamic equilibrium. Weak local- ization (Bergmann, 1958; van Albada and Lagendijk, 1985; Wellens and Gre´maud, 2009; Wolf and Maret, 1985) and maser and laser theory (Briegel et al., 1994; Cai et al., 1994; Haken, 1994) provide highly relevant examples for coherence effects that prevail in the presence of disorder and noise – because of time-reversal symmetry in the first case, and becauseofnonequilibriumstatisticaleffectsinthelatter.Becausebiologi- cal systems are off-equilibrium by their very definition, and so are any TransportandEntanglement 3 technological devices that exhibit time-dependent transport; it is there- fore much less clear-cut a case that quantum coherence cannot persist, at least on transient, yet exploitable timescales, even in such complex sys- tems. Under this perspective, the actual challenge rather is to identify the relevant degrees of freedom which potentially sustain coherence, the associatedtimescales,andthespecificorpotentialfunctionalroleofcoher- ence. Once again, this challenge is highly nontrivial as a result of the abundance and intricate coupling of a complex system’s many degrees offreedom. Incomparisontoengineers,biologicalevolutionhashadampletimeto testthepotentialofquantumcoherenceforitsspecificpurposetoimprove aspecies’adaptiontoitsenvironment.Indeed,recentexperimentalresults (Cheng and Fleming,2009; Collini et al., 2010; Engel et al., 2007; Lee et al., 2007;Panitchayangkoonetal.,2010)onthephotosyntheticlight-harvesting complexesused,e.g.,bybacteriaor higherplants(Blankenship,2001;van Amerongen et al., 2000), provide unambiguous evidence of a crucial role of quantum coherence for the stunning efficiency of excitation transfer on the underlying macromolecular level. These experiments raise novel andhighlyintriguingquestions,e.g.,onthephysicaloriginofthesurpris- ingly long coherence times and lengths, and on the mechanisms that, in the presence of that coherence, mediate the efficient transport. Convinc- ing answers to these questions have the potential to very fundamentally alterourunderstandingoftheroleofquantummechanicsforthephysical realityaroundus–asweperceiveit,andasweshapeit. In our present contribution, we provide the skeleton of a modern quantum mechanical transport theory for molecular samples such as the FMO light-harvesting complex (Blankenship, 2001) often investigated in theabove-mentionedexperiments.Wedonotstrivehereforthequantita- tively accurate modeling of a specific biological functional unit, though, but rather for identifying the fundamental features of coherent quan- tum transport on multiply connected, finite and disordered structures, together with the relevant timescales, which need to be compared with typical,environment-induceddecayrates.Giventhevariabilityofbiologi- calsamplesandtheremainingexperimentaluncertainties,e.g.,onrelevant coupling constants, as well as the astonishing ability of evolution to tune itsbasicconstituentsforbetterperformanceinvariableenvironmentalcon- ditions, our approach is statistical from the very outset. This allows us to identify rare molecular configurations that exploit quantum coherence for better excitation transfer, to assess their statistical weight as well as their robustness, and to statistically correlate multisite coherence proper- ties with transfer efficiencies. Indeed, we will show that strong multisite coherence and entanglement are an essential, necessary prerequisite for efficienttransport.
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