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Quantum entanglement in photosynthetic light-harvesting complexes

Nature Physics volume 6, pages 462–467 (2010)Cite this article

Abstract

Light-harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long timescales, despite the decohering effects of their environments. Here, we analyse entanglement in multichromophoric light-harvesting complexes, and establish methods for quantification of entanglement by describing necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna–Matthews–Olson protein to extract the initial state and temperature dependencies of entanglement. We show that, although the Fenna–Matthews–Olson protein in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement should exist even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical use of entanglement in densely packed molecular aggregates such as light-harvesting complexes.

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Figure 1: The light-harvesting apparatus of green sulphur bacteria and the FMO protein.
Figure 2: Global entanglement in the FMO protein.
Figure 3: Bipartite entanglement in the FMO protein when the initial state is an excitation localized on site 1.
Figure 4: Bipartite entanglement in the FMO protein when the initial state is an excitation localized on site 6.

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References

  1. Einstein, A., Podolsky, B. & Rosen, B. Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 47, 777–780 (1935).

    Article  ADS  Google Scholar 

  2. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812 (1935).

    Article  ADS  Google Scholar 

  3. Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  4. Horodecki, R., Horodecki, P., Horodecki, M. & Horodecki, K. Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  5. Vedral, V. Quantifying entanglement in macroscopic systems. Nature 453, 1004–1007 (2008).

    Article  ADS  Google Scholar 

  6. Vedral, V. Entanglement production in non-equilibrium thermodynamics. J. Phys. Conf. Ser. 143, 012010–012018 (2007).

    Article  Google Scholar 

  7. Quiroga, L., Rodriguez, F. J., Ramirez, M. E. & Paris, R. Nonequilibrium thermal entanglement. Phys. Rev. A 75, 032308 (2007).

    Article  ADS  Google Scholar 

  8. Cai, J., Popescu, S. & Briegel, H. J. Dynamic entanglement in oscillating molecules and potential biological implications. Preprint at http://arxiv.org/abs/0809.4906 (2008).

  9. Thorwart, M., Eckel, J., Reina, J. H., Nalbach, P. & Weiss, S. Enhanced quantum entanglement in the non-Markovian dynamics of biomolecular excitons. Chem. Phys. Lett. 478, 234–237 (2009).

    Article  ADS  Google Scholar 

  10. Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007).

    Article  ADS  Google Scholar 

  11. Lee, H., Cheng, Y-C. & Fleming, G. R. Coherence dynamics in photosynthesis: Protein protection of excitonic coherence. Science 316, 1462–1465 (2007).

    Article  ADS  Google Scholar 

  12. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644–648 (2010).

    Article  ADS  Google Scholar 

  13. Panitchayangkoon, G. et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Preprint at http://arxiv.org/abs/1001.5108 (2010).

  14. Blankenship, R. E. Molecular Mechanisms of Photosynthesis (Wiley-Blackwell, 2002).

    Book  Google Scholar 

  15. Pullerits, T., Chachisvilis, M. & Sundstrom, V. Exciton delocalization length in the B850 antenna of Rhodobacter sphaeroides. J. Phys. Chem. 100, 10787–10792 (1996).

    Article  Google Scholar 

  16. Monshouwer, R., Abrahamsson, M., van Mourik, F. & van Grondelle, R. Superradiance and exciton delocalization in bacterial photosynthetic light-harvesting systems. J. Phys. Chem. B 101, 7241–7248 (1997).

    Article  Google Scholar 

  17. van Amerongen, H., Valkunas, L. & van Grondelle, R. Photosynthetic Excitons (World Scientific, 2000).

    Book  Google Scholar 

  18. van Enk, S. J. Single-particle entanglement. Phys. Rev. A 72, 064306 (2005).

    Article  ADS  Google Scholar 

  19. Hill, S. & Wootters, W. K. Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997).

    Article  ADS  Google Scholar 

  20. Vedral, V., Plenio, M. B., Rippin, M. A. & Knight, P. L. Quantifying entanglement. Phys. Rev. Lett. 78, 2275–2279 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  21. Camara-Artigas, A., Blankenship, R. E. & Allen, J. P. The structure of the FMO protein from Chlorobium tepidum at 2.2 A resolution. Photosynth. Res. 75, 49–55 (2003).

    Article  Google Scholar 

  22. Adolphs, J. & Renger, T. How proteins trigger excitation energy transfer in the FMO complex of green sulphur bacteria. Biophysical J. 91, 2778–2797 (2006).

    Article  ADS  Google Scholar 

  23. Ishizaki, A. & Fleming, G. R. Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equations approach. J. Chem. Phys. 130, 234111 (2009).

    Article  ADS  Google Scholar 

  24. Wen, J., Zhang, H., Gross, M. L. & Blankenship, R. E. Membrane orientation of the FMO antenna protein from Chlorobaculum tepidum as determined by mass spectrometry-based footprinting. Proc. Natl Acad. Sci. USA 106, 6134–6139 (2009).

    Article  ADS  Google Scholar 

  25. Meier, T., Zhao, Y., Chernyak, V. & Mukamel, S. Polarons, localization, and excitonic coherence in superradiance of biological antenna complexes. J. Chem. Phys. 107, 3876–3893 (1997).

    Article  ADS  Google Scholar 

  26. Read, E. L. et al. Visualization of excitonic structure in the Fenna–Metthews–Olson photosynthetic complex by polarization-dependent two-dimensional electronic spectroscopy. Biophysical J. 95, 847–856 (2008).

    Article  ADS  Google Scholar 

  27. Mohseni, M., Rebentrost, P., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum walks in energy transfer of photosynthetic complexes. J. Chem. Phys. 129, 174106 (2008).

    Article  ADS  Google Scholar 

  28. Plenio, M. B. & Huelga, S. F. Dephasing-assisted transport: Quantum networks and biomolecules. New J. Phys. 10, 113019 (2008).

    Article  ADS  Google Scholar 

  29. Mukai, K., Abe, S. & Sumi, H. Theory of rapid excitation-energy transfer from B800 to optically-forbidden exciton states of B850 in the antenna system LH2 of photosynthetic purple bacteria. J. Phys. Chem. B 103, 6096–6102 (1999).

    Article  Google Scholar 

  30. Scholes, G. D. & Fleming, G. R. On the mechanism of light harvesting in photosynthetic purple bacteria: B800 to B850 energy transfer. J. Phys. Chem. B 104, 1854–1868 (2000).

    Article  Google Scholar 

  31. Jang, S., Newton, M. D. & Silbey, R. J. Multichromophoric Förster resonance energy transfer. Phys. Rev. Lett. 92, 218301 (2004).

    Article  ADS  Google Scholar 

  32. Sumi, H. Bacterial photosynthesis begins with quantum-mechanical coherence. Chem. Record 1, 480–493 (2001).

    Article  Google Scholar 

  33. Cheng, Y-C. & Silbey, R. J. Coherence in the B800 ring of purple bacteria LH2. Phys. Rev. Lett. 96, 028103 (2006).

    Article  ADS  Google Scholar 

  34. Ishizaki, A. & Fleming, G. R. Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature. Proc. Natl Acad. Sci. USA 106, 17255–17260 (2009).

    Article  ADS  Google Scholar 

  35. Lombardi, E., Sciarrino, F., Popescu, S. & De Martini, F. Teleportation of a vacuum-one-photon qubit. Phys. Rev. Lett. 88, 070402 (2002).

    Article  ADS  Google Scholar 

  36. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: Beating the standard quantum limit. Science 306, 1330–1336 (2004).

    Article  ADS  Google Scholar 

  37. Roos, C. F., Chwalla, M., Kim, K., Riebe, M. & Blatt, R. ‘Designer atoms’ for quantum metrology. Nature 443, 316–319 (2006).

    Article  ADS  Google Scholar 

  38. Nagata, T., Okamoto, R., O’Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).

    Article  ADS  Google Scholar 

  39. Lagoudakis, P. G. et al. Experimental evidence for exciton scaling effects in self-assembled molecular wires. Phys. Rev. Lett. 93, 257401 (2004).

    Article  ADS  Google Scholar 

  40. Tischler, J. R. et al. Solid state cavity QED: Strong coupling in organic thin films. Org. Electron. 8, 94–113 (2007).

    Article  Google Scholar 

  41. Burgarth, D. & Bose, S. Perfect quantum state transfer with randomly coupled quantum chains. New J. Phys. 7, 135–147 (2005).

    Article  ADS  Google Scholar 

  42. Schrödinger, E. Discussion of probability relations between separated systems. Proc. Cambridge Phil. Soc. 31, 555–563 (1935).

    Article  ADS  Google Scholar 

  43. Horodecki, M., Horodecki, P. & Horodecki, R. Separability of mixed states: Necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  44. Peres, A. Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1415 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  45. May, V. & Kühn, O. Charge and Energy Transfer Dynamics in Molecular Systems (Wiley-VCH, 2004).

    Google Scholar 

  46. Brixner, T. et al. Two-dimensional spectroscopy of electronic couplings in photosynthesis. Nature 434, 625–628 (2005).

    Article  ADS  Google Scholar 

  47. Cho, M., Vaswani, H. M., Brixner, T., Stegner, J. & Fleming, G. R. Exciton analysis in 2D electronic spectroscopy. J. Phys. Chem. B 109, 10542–10556 (2005).

    Article  Google Scholar 

  48. Ishizaki, A. & Fleming, G. R. On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer. J. Chem. Phys. 130, 234110 (2009).

    Article  ADS  Google Scholar 

  49. Tanimura, Y. Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems. J. Phys. Soc. Jpn 75, 082001 (2006).

    Article  ADS  Google Scholar 

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Acknowledgements

We are grateful to Y-C. Cheng, J. Dawlaty, V. Vedral and M. Plenio for conversations and comments. This material is based on work supported by DARPA under award No N66001-09-1-2026. This work was supported by the Director, Office of Science, Office of Basic Energy Sciences of the US Department of Energy under contract No DE-AC02-05CH11231 and by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, US Department of Energy under contract DE-AC03-76SF000098. A.I. appreciates the support of a Japan Society for the Promotion of Science (JSPS) Postdoctoral Fellowship for Research Abroad.

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Authors and Affiliations

  1. Berkeley Center for Quantum Information and Computation, Berkeley, California 94720, USA

    Mohan Sarovar & K. Birgitta Whaley

  2. Department of Chemistry, University of California, Berkeley, California 94720, USA

    Mohan Sarovar, Akihito Ishizaki, Graham R. Fleming & K. Birgitta Whaley

  3. Physical Bioscience Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    Akihito Ishizaki & Graham R. Fleming

Authors
  1. Mohan Sarovar
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Calculations were carried out by M.S. and A.I. All authors contributed extensively to the planning, discussion and writing up of this work.

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Correspondence to Mohan Sarovar.

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Sarovar, M., Ishizaki, A., Fleming, G. et al. Quantum entanglement in photosynthetic light-harvesting complexes. Nature Phys 6, 462–467 (2010). https://doi.org/10.1038/nphys1652

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