DOI: 10.1063/1.3002335. Environment-assisted quantum walks in photosynthetic energy transfer

Environment-assisted quantum walks in photosynthetic energy transfer

10.1063/1.3002335

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Energy transfer within photosynthetic systems can display quantum effects such as delocalized excitonic transport. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna–Matthews–Olson (FMO) protein complex [Engel et al., Nature (London) 446, 782 (2007)]. However, the relevance of quantum dynamical processes to the exciton transfer efficiency is to a large extent unknown. Here, we develop a theoretical framework for studying the role of quantum interference effects in energy transfer dynamics of molecular arrays interacting with a thermal bath within the Lindblad formalism. To this end, we generalize continuous-time quantum walks to nonunitary and temperature-dependent dynamics in Liouville space derived from a microscopic Hamiltonian. Different physical effects of coherence and decoherence processes are explored via a universal measure for the energy transfer efficiency and its susceptibility. In particular, we demonstrate that for the FMO complex, an effective interplay between the free Hamiltonian evolution and the thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%.

Bibliography

Mohseni, M., Rebentrost, P., Lloyd, S., & Aspuru-Guzik, A. (2008). Environment-assisted quantum walks in photosynthetic energy transfer. The Journal of Chemical Physics, 129(17).

Authors 4

Masoud Mohseni (first)
Patrick Rebentrost (additional)
Seth Lloyd (additional)
Alán Aspuru-Guzik (additional)

References 60 Referenced 992

{'volume-title': 'Molecular Mechanism of Photosynthesis', 'year': '2002', 'key': '2023062604102363200_c1'} / Molecular Mechanism of Photosynthesis (2002)
10.1021/jp963777g / J. Phys. Chem. B (1997)
10.1021/jp011032r / J. Phys. Chem. B (2001)
10.1021/jp0496001 / J. Phys. Chem. B (2004)
10.1021/jp050788d / J. Phys. Chem. B (2005)
{'key': '2023062604102363200_c6', 'first-page': '93', 'volume-title': 'Modern Quantum Chemistry, Istanbul Lectures', 'author': 'Sinanoglu', 'year': '1965'} / Modern Quantum Chemistry, Istanbul Lectures by Sinanoglu (1965)
10.1146/annurev.physchem.54.011002.103746 / Annu. Rev. Phys. Chem. (2003)
{'volume-title': 'Charge and Energy Transfer Dynamics in Molecular Systems', 'year': '2004', 'key': '2023062604102363200_c8'} / Charge and Energy Transfer Dynamics in Molecular Systems (2004)
10.1016/B978-1-4832-3114-3.50007-6 / Adv. Magn. Reson. (1965)
10.1063/1.1674761 / J. Chem. Phys. (1971)
10.1080/00268977300100081 / Mol. Phys. (1973)
10.1007/BF01399723 / Z. Phys. (1973)
10.1103/PhysRevLett.33.803 / Phys. Rev. Lett. (1974)
{'volume-title': 'Exciton Dynamics in Molecular Crystals and Aggregates', 'year': '1982', 'key': '2023062604102363200_c14'} / Exciton Dynamics in Molecular Crystals and Aggregates (1982)
10.1063/1.476212 / J. Chem. Phys. (1998)
10.1016/S0301-0104(01)00540-7 / Chem. Phys. (2002)
10.1103/PhysRevLett.92.218301 / Phys. Rev. Lett. (2004)
10.1103/PhysRevLett.96.028103 / Phys. Rev. Lett. (2006)
10.1021/jp070111l / J. Phys. Chem. B (2007)
10.1063/1.1786922 / J. Chem. Phys. (2004)
10.1038/nature05678 / Nature (London) (2007)
10.1126/science.1142188 / Science (2007)
{'volume-title': 'The Feynman Lectures on Physics', 'year': '1964', 'key': '2023062604102363200_c23'} / The Feynman Lectures on Physics (1964)
{'volume-title': 'Quantum Mechanics and Path Integrals', 'year': '1965', 'key': '2023062604102363200_c24'} / Quantum Mechanics and Path Integrals (1965)
{'key': '2023062604102363200_c25', 'first-page': '143', 'volume': '76A', 'year': '1980', 'journal-title': 'Phys. Lett.'} / Phys. Lett. (1980)
10.1103/PhysRevA.48.1687 / Phys. Rev. A (1993)
{'key': '2023062604102363200_c27', 'first-page': '302', 'volume': '44', 'year': '2003', 'journal-title': 'Contemp. Phys.'} / Contemp. Phys. (2003)
{'key': '2023062604102363200_c28', 'first-page': '1169', 'volume': '17', 'year': '2006', 'journal-title': 'Math. Struct. Comp. Sci.'} / Math. Struct. Comp. Sci. (2006)
10.1103/PhysRevA.58.915 / Phys. Rev. A (1998)
10.1023/A:1019609420309 / Quantum Inf. Process. (2002)
{'year': '2001', 'key': '2023062604102363200_c31', 'first-page': '50'} (2001)
10.1007/BF02199356 / J. Stat. Phys. (1996)
10.1103/PhysRevA.67.042305 / Phys. Rev. A (2003)
10.1103/PhysRevA.66.052319 / Phys. Rev. A (2002)
10.1063/1.2179427 / J. Chem. Phys. (2006)
10.1103/PhysRev.109.1492 / Phys. Rev. (1958)
10.1103/PhysRevLett.79.325 / Phys. Rev. Lett. (1997)
10.1006/jmbi.1997.1189 / J. Mol. Biol. (1997)
{'volume-title': 'Principles of Nonlinear Optical Spectroscopy', 'year': '1995', 'key': '2023062604102363200_c38'} / Principles of Nonlinear Optical Spectroscopy (1995)
10.1529/biophysj.105.079483 / Biophys. J. (2006)
{'volume-title': 'The Theory of Open Quantum Systems', 'year': '2002', 'key': '2023062604102363200_c40'} / The Theory of Open Quantum Systems (2002)
10.1073/pnas.84.6.1532 / Proc. Natl. Acad. Sci. U.S.A. (1987)
10.1021/jp020708v / J. Phys. Chem. B (2002)
10.1063/1.1739400 / J. Chem. Phys. (2004)
{'volume-title': 'An Open Systems Approach to Quantum Optics', 'year': '1993', 'key': '2023062604102363200_c44'} / An Open Systems Approach to Quantum Optics (1993)
10.1103/PhysRevB.78.085115 / Phys. Rev. B (2008)
10.1103/PhysRevB.71.045334 / Phys. Rev. B (2005)
10.1073/pnas.0708222104 / Proc. Natl. Acad. Sci. U.S.A. (2007)
P. Rebentrost, M. Mohseni, and A. Aspuru-Guzik, e-print arXiv:0806.4725.
P. Rebentrost, M. Mohseni, S. Lloyd, I. Kassal, and A. Aspuru-Guzik, e-print arXiv:0807.0929.
M. B. Plenio and S. F. Huelga, e-print arXiv:0807.4902.
F. W. Strauch, e-print arXiv:0808.3403.
P. Rebentrost, I. Serban, T. Schulte-Herbrueggen, and F. K. Wilhelm, e-print arXiv:quant-ph/0612165.
C. A. Rodriguez-Rosario and E. C. G. Sudarshan, e-print arXiv:0803.1183.
M. Mohseni and A. T. Rezakhani, e-print arXiv:0805.3188.
10.1103/PhysRevLett.92.187902 / Phys. Rev. Lett. (2004)
D. I. Tsomokos, M. B. Plenio, I. de Vega, and S. F. Huelga, e-print arXiv:0808.2261v.
10.1103/PhysRevLett.68.580 / Phys. Rev. Lett. (1992)
10.1016/j.cplett.2005.11.052 / Chem. Phys. Lett. (2006)
10.1295/polymj.PJ2007006 / Polym. J. (Tokyo, Jpn.) (2007)

Dates

Type	When
Created	16 years, 9 months ago (Nov. 7, 2008, 2:01 p.m.)
Deposited	2 years, 2 months ago (June 26, 2023, 12:10 a.m.)
Indexed	2 days, 10 hours ago (Aug. 30, 2025, 1:06 p.m.)
Issued	16 years, 9 months ago (Nov. 6, 2008)
Published	16 years, 9 months ago (Nov. 6, 2008)
Published Online	16 years, 9 months ago (Nov. 6, 2008)
Published Print	16 years, 9 months ago (Nov. 7, 2008)

Funders 0

None

BibTeX

@article{Mohseni_2008, title={Environment-assisted quantum walks in photosynthetic energy transfer}, volume={129}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.3002335}, DOI={10.1063/1.3002335}, number={17}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Mohseni, Masoud and Rebentrost, Patrick and Lloyd, Seth and Aspuru-Guzik, Alán}, year={2008}, month=nov }

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