Quantum Efficiency in Complex Systems, Part I: Biomolecular systems

128 Pages·2010·4.202 MB·English

by  Eicke R. Weber, Michael Thorwart and Uli Würfel (Eds.)

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
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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:
[e-mail].(Ch1)
FlorianMintert,DepartmentforQuantumOpticsandStatistics,Institute
ofPhysics,AlbertLudwigsUniversityofFreiburg,
Hermann-Herder-Str.3,D-79104Freiburg,email:
fl[e-mail].(Ch1)
Ju¨rgenKo¨hler,ExperimentalPhysicsIV,andBayreuthInstituteof
MacromolecularResearch(BIMF),UniversityofBayreuth,95440
Bayreuth,Germany,email:[e-mail].(Ch3)
MichaelThorwart,I.Institutfu¨rTheoretischePhysik,Universita¨t
Hamburg,Jungiusstraße9,20355Hamburg,Germany,email:
[e-mail].(Ch2)
PeterNalbach,SchoolofSoftMatterResearch,FreiburgInstitutefor
AdvancedStudies(FRIAS),Albert-Ludwigs-Universita¨tFreiburg,
Albertstraße,19,79104Freiburg,Germany.
I.Institutfu¨rTheoretischePhysik,Universita¨tHamburg,
Jungiusstraße9,20355Hamburg,Germany,email:
[e-mail].(Ch2)
RichardJ.Cogdell,ExperimentalPhysicsIV,andBayreuthInstituteof
MacromolecularResearch(BIMF),UniversityofBayreuth,95440
Bayreuth,Germany.(Ch3)
TorstenScholak,DepartmentforQuantumOpticsandStatistics,Institute
ofPhysics,AlbertLudwigsUniversityofFreiburg,
Hermann-Herder-Str.3,D-79104Freiburg,email:
[e-mail].(Ch1)
ix
x ListofContributors
ThomasWellens,DepartmentforQuantumOpticsandStatistics,
InstituteofPhysics,AlbertLudwigsUniversityofFreiburg,
Hermann-Herder-Str.3,D-79104Freiburg,email:
[e-mail].(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.