Quantum Efficiency in Complex Systems, Part I (eBook)

Biomolecular Systems

Eicke R. Weber (Herausgeber)

eBook Download: PDF | EPUB

2010 | 1. Auflage
120 Seiten
Elsevier Science (Verlag)
978-0-08-096340-2 (ISBN)

Infos

Since its inception in 1966, the series of numbered volumes known as Semiconductors and Semimetals has distinguished itself through the careful selection of well-known authors, editors, and contributors. The 'Willardson and Beer' Series, as it is widely known, has succeeded in publishing numerous landmark volumes and chapters. Not only did many of these volumes make an impact at the time of their publication, but they continue to be well-cited years after their original release. Recently, Professor Eicke R. Weber of the University of California at Berkeley joined as a co-editor of the series. Professor Weber, a well-known expert in the field of semiconductor materials, will further contribute to continuing the series' tradition of publishing timely, highly relevant, and long-impacting volumes. Some of the recent volumes, such as Hydrogen in Semiconductors, Imperfections in III/V Materials, Epitaxial Microstructures, High-Speed Heterostructure Devices, Oxygen in Silicon, and others promise that this tradition will be maintained and even expanded. Reflecting the truly interdisciplinary nature of the field that the series covers, the volumes in Semiconductors and Semimetals have been and will continue to be of great interest to physicists, chemists, materials scientists, and device engineers in modern industry.

---

Since its inception in 1966, the series of numbered volumes known as Semiconductors and Semimetals has distinguished itself through the careful selection of well-known authors, editors, and contributors. The "e;Willardson and Beer"e; Series, as it is widely known, has succeeded in publishing numerous landmark volumes and chapters. Not only did many of these volumes make an impact at the time of their publication, but they continue to be well-cited years after their original release. Recently, Professor Eicke R. Weber of the University of California at Berkeley joined as a co-editor of the series. Professor Weber, a well-known expert in the field of semiconductor materials, will further contribute to continuing the series' tradition of publishing timely, highly relevant, and long-impacting volumes. Some of the recent volumes, such as Hydrogen in Semiconductors, Imperfections in III/V Materials, Epitaxial Microstructures, High-Speed Heterostructure Devices, Oxygen in Silicon, and others promise that this tradition will be maintained and even expanded. Reflecting the truly interdisciplinary nature of the field that the series covers, the volumes in Semiconductors and Semimetals have been and will continue to be of great interest to physicists, chemists, materials scientists, and device engineers in modern industry.

Inhalt

Front Cover 1
Quantum Efficiency in Complex Systems, Part I: Biomolecular systems 4
Copyright 5
Table of Contents 6
Foreword 8
List of Contributors 10
Chapter 1. Transport and Entanglement 12
1. Coherent Transport in Disordered Systems 15
2. Many-Body Coherence and Entanglement 24
3. Fast and Efficient Transport in Molecular Networks 34
4. Conclusions 43
Appendix 45
References 47
Chapter 2. Quantum Coherence and Entanglement in Photosynthetic Light-Harvesting Complexes 50
1. Excitonic Energy Transfer in Photosynthetic Light-Harvesting Complexes 51
2. Bath-Sustained Quantum Coherence in a Single Exciton Pair 56
3. Bath-Sustained Quantum Entanglement of Two Chromophore Pairs 61
4. Role of Spatial Correlations 67
5. Conclusions 78
Appendices 80
References 84
Chapter 3. Sunlight, Purple Bacteria, and Quantum Mechanics: How Purple Bacteria Harness Quantum Mechanics for Efficient Light Harvesting 88
1. Introduction 88
2. The Light-Harvesting Apparatus of Purple Bacteria 91
3. Frenkel Excitons 95
4. Linear versus Cyclic Aggregate: A Comparison 98
5. The B850 Assembly of LH2 as a Quantum Aggregate of Molecules 100
6. Can We Learn from Nature how to Synthesise Artificial Light-Harvesting Molecules? 103
Acknowledgments 104
References 104
Index 106
Contents of Volumes in this Series 110
Color Plates 136

Textauszug

Chapter 1

Transport and Entanglement

T. Scholak; F. Mintert; T. Wellens; A. Buchleitner

Publisher Summary

This chapter reviews the essential ingredients of quantum transport in disordered systems, and introduces measures of quantum coherence and entanglement in multisite systems. It explains excitation transport in Fenna–Matthews–Olsen (FMO)-like structures under strictly coherent conditions as well as in presence of a dephasing environment. The statistical treatment of excitation transport across a molecular network mimicking the FMO light-harvesting complex shows the potential of quantum coherence to enhance transport, on transient timescales. The transfer probability thus achieved can reach 100%—a value unachievable by classically diffusive, unbiased transport. Furthermore, because such quantum transfer is brought about by constructive multipath interference along intermediate sites of the molecular complex, coherent quantum transport is certainly faster than classically diffusive transport for comparable inter-site coupling strengths. Taking both transfer probability and transfer time together, coherence thus defines levels of quantum efficiency unreached by a classical transport process on the same network. The quantum coherence holds the potential to steer quantum transport efficiencies in engineered devices as abundant in semiconductor technology.

Transport phenomena are all around us, from microscopic to macroscopic scales, and they mediate fundamental transfer processes of matter, charge, or energy. Much of present day science and technology ultimately relies on transport processes, from radiation transfer in the atmosphere, with its very tangible impact on climatic conditions, over the long distance transfer of electrical energy, controlled chemical reactions in large molecules, signal processing in biological tissue, to charge transfer in semiconductor devices – be it detectors of high-energy or low-energy particles or photons, efficient light sources like LEDs, or photovoltaic solar cells – random lasers, and even quantum cryptography and computation. Irrespective of the actual scale, all practical applications here listed, and equally so all the underlying, paradigmatic model systems bear the common feature of some 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 freedom are only partially controlled and garnish the dynamics with different characteristic length and timescales. The unavoidable lack of control is summarized as “disorder” or “noise” inflicted on the transport process of interest – which occurs in the “system's” degrees of freedom – by some noisy environment.

Complexity is ambivalent in nature, because it creates novel and unexpected patterns that emerge, e.g., as, often very robust, collective modes, but can also induce instabilities and sudden phase transitions. Hence, disorder, noise, and other typical traits of complex systems can manifest as a 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 and noise are widely considered as purely detrimental, and the art of engineering, thus, largely consists in screening them out. This is ever more true on the microscopic level and in the context of quantum engineering – the quantum computer being a prime example: here, disorder and noise are conceived as the cause of decoherence, i.e., of the fading away of quantum interference effects – which are the very source of its formidable potential efficiency as compared with classical supercomputing devices. In turn, when disorder and noise cannot be screened away, the widespread opinion is that quantum coherence effects are bound to faint on the associated length and timescales. Biological systems, large macromolecular structures, and equally so multilayered semiconductor structures as used in detector, LED, and solar cell technology – which often operate at ambient temperatures – apparently fall, precisely, in this latter category.

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 symmetries and implicitly assumes thermodynamic equilibrium. Weak localization (Bergmann, 1958; van Albada and Lagendijk, 1985; Wellens and Grémaud, 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 because of nonequilibrium statistical effects in the latter. Because biological systems are off-equilibrium by their very definition, and so are any technological devices that exhibit time-dependent transport; it is therefore much less clear-cut a case that quantum coherence cannot persist, at least on transient, yet exploitable timescales, even in such complex systems. Under this perspective, the actual challenge rather is to identify the relevant degrees of freedom which potentially sustain coherence, the associated timescales, and the specific or potential functional role of coherence. Once again, this challenge is highly nontrivial as a result of the abundance and intricate coupling of a complex system's many degrees of freedom.

In comparison to engineers, biological evolution has had ample time to test the potential of quantum coherence for its specific purpose to improve a species' adaption to its environment. Indeed, recent experimental results (Cheng and Fleming, 2009; Collini et al., 2010; Engel et al., 2007; Lee et al., 2007; Panitchayangkoon et al., 2010) on the photosynthetic light-harvesting complexes used, e.g., by bacteria or higher plants (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 and highly intriguing questions, e.g., on the physical origin of the surprisingly long coherence times and lengths, and on the mechanisms that, in the presence of that coherence, mediate the efficient transport. Convincing answers to these questions have the potential to very fundamentally alter our understanding of the role of quantum mechanics for the physical reality around us – as we perceive it, and as we shape it.

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 the above-mentioned experiments. We do not strive here for the quantitatively accurate modeling of a specific biological functional unit, though, but rather for identifying the fundamental features of coherent quantum transport on multiply connected, finite and disordered structures, together with the relevant timescales, which need to be compared with typical, environment-induced decay rates. Given the variability of biological samples and the remaining experimental uncertainties, e.g., on relevant coupling constants, as well as the astonishing ability of evolution to tune its basic constituents for better performance in variable environmental conditions, 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 properties with transfer efficiencies. Indeed, we will show that strong multisite coherence and entanglement are an essential, necessary prerequisite for efficient transport.

We will start out, in Section 1, by a short recollection of the essential ingredients of quantum transport in disordered systems, before we introduce measures of quantum coherence and entanglement in multisite systems in Section 2. Section 3 will then specialize on excitation transport in FMO-like structures – under strictly coherent conditions as well as in presence of a dephasing environment. Section 4 concludes the article.

1 COHERENT TRANSPORT IN DISORDERED SYSTEMS

To set the stage, we will first introduce a general model Hamiltonian for quantum transport in disordered systems. Then, we will focus on the question whether quantum interference acts constructively or destructively on the transport efficiency. As we will see, partial – or even complete – suppression of transport is expected after averaging over the disorder. However, quantum coherence typically leads to large fluctuations, thus admitting more efficient transport for certain realizations of the disorder.

1.1 Model Hamiltonian

Although most systems in which energy transport occurs, such as solar cells or light-harvesting complexes, are typically composed of a large number of microscopic constituents, they can often be effectively described in terms of relatively few relevant degrees of...

Produkt-Details

• Erscheint lt. Verlag: 14.12.2010
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-096340-4 / 0080963404
• ISBN-13: 978-0-08-096340-2 / 9780080963402