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Quantum coherences reveal excited-state dynamics in biophysical systems

Nature Reviews Chemistry volume 3, pages 477–490 (2019)Cite this article

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Abstract

Ultrafast, multi-dimensional spectroscopic measurements of photosynthetic light-harvesting complexes have revealed quantum coherences with timescales comparable to those of energy-transfer processes. These observations have led to a debate regarding the states that give rise to the coherences and whether the presence of the coherences has implications for photosynthetic light harvesting. In these experiments, laser pulses create a coherent superposition of quantum states with a defined phase relationship across an ensemble, which gives rise to the quantum coherence and associated quantum beating signal. Dephasing of these quantum coherences, seen as a decay of the beating signal, is among the most sensitive probes of the interactions between a system and its surrounding environment. In this Review, we discuss the proposed origin and assignment of the observed quantum coherences in photosynthetic systems as electronic, vibronic or vibrational. We describe the latest experimental efforts towards unravelling the nature of the coherences, in particular ultrafast, two-dimensional electronic spectroscopy, as well as the accompanying theoretical and computational results. We discuss how measuring coherences can inform us about the excited-state dynamics of biophysical and chemical systems relevant to natural light harvesting and how these measurements reveal electronic structure beyond that captured by simplistic models.

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Fig. 1: Overview of quantum beats resulting from quantum coherences observed with nonlinear spectroscopy.
Fig. 2: Data analysis to resolve the physical origin of quantum coherences.
Fig. 3: Understanding contributions of a Liouville-space pathway to a measured coherence.
Fig. 4: Observed quantum coherences in the Fenna–Matthews–Olson complex.
Fig. 5: Energy-transfer dynamics of the Fenna–Matthews–Olson complex governed by the interplay between interchromophoric coupling and system–bath coupling.

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References

  1. Srinivasarao, M. Nano-optics in the biological world: beetles, butterflies, birds, and moths. Chem. Rev. 99, 1935–1962 (1999).

    Article  CAS  PubMed  Google Scholar 

  2. Goodman, J. W. Some fundamental properties of speckle. J. Opt. Soc. Am. 66, 1145–1150 (1976).

    Article  Google Scholar 

  3. Bennett, C. H. & DiVincenzo, D. P. Quantum information and computation. Nature 404, 247–255 (2000).

    Article  CAS  PubMed  Google Scholar 

  4. Scholes, G. D. et al. Using coherence to enhance function in chemical and biophysical systems. Nature 543, 647–656 (2017). Review of coherent mechanisms shown throughout biology and chemistry details opportunities to engineer coherence for function.

    Article  CAS  PubMed  Google Scholar 

  5. Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007). Quantum beating is observed in a photosynthetic pigment–protein complex with two-dimensional electronic spectroscopy.

    Article  CAS  PubMed  Google Scholar 

  6. Savikhin, S., Buck, D. R. & Struve, W. S. Oscillating anisotropies in a bacteriochlorophyll protein: evidence for quantum beating between exciton levels. Chem. Phys. 223, 303–312 (1997).

    Article  CAS  Google Scholar 

  7. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644–647 (2010). Coherence observed in room–temperature marine algal light-harvesting antennae with two-dimensional electronic spectroscopy.

    Article  CAS  PubMed  Google Scholar 

  8. Panitchayangkoon, G. et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl Acad. Sci. USA 107, 12766–12770 (2010). Temperature dependence of the coherence signal is observed and shows persistence of the signal on the timescale of energy transfer, even at physiological temperature.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Panitchayangkoon, G. et al. Direct evidence of quantum transport in photosynthetic light-harvesting complexes. Proc. Natl Acad. Sci. USA 108, 20908–20912 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Walmsley, I. A. & Tang, C. L. The determination of electronic dephasing rates in time-resolved quantum-beat spectroscopy. J. Chem. Phys. 92, 1568–1574 (1990).

    Article  CAS  Google Scholar 

  11. Walmsley, I. A., Wise, F. W. & Tang, C. L. On the difference between quantum beats in impulsive stimulated Raman scattering and resonance Raman scattering. Chem. Phys. Lett. 154, 315–320 (1989).

    Article  CAS  Google Scholar 

  12. Pisliakov, A. V., Mančal, T. & Fleming, G. R. Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra. J. Chem. Phys. 124, 234505 (2006).

    Article  PubMed  CAS  Google Scholar 

  13. Nitzan, A. Chemical Dynamics in Condensed Phases (Oxford Univ. Press, 2006).

  14. Cohen-Tannoudji, C., Diu, B. & Laloe, F. Quantum Mechanics Vol. 2 (Wiley-VCH, 1986).

  15. Landau, L. Das dämpfungsproblem in der wellenmechanik [German]. Z. Physik 45, 430–441 (1927).

    Article  Google Scholar 

  16. Frenkel, J. On the transformation of light into heat in solids. I. Phys. Rev. 37, 17–44 (1931).

    Article  CAS  Google Scholar 

  17. Kasha, M., Rawls, H. R. & Ashraf El-Bayoumi, M. The exciton model in molecular spectroscopy. Pure Appl. Chem. 11, 371–392 (1965).

    Article  CAS  Google Scholar 

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

  19. Schlosshauer, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 76, 1267–1305 (2005).

    Article  Google Scholar 

  20. Zeh, H. D. On the interpretation of measurement in quantum theory. Found. Phys. 1, 69–76 (1970).

    Article  Google Scholar 

  21. Izmaylov, A. F. & Franco, I. Entanglement in the Born–Oppenheimer approximation. J. Chem. Theory Comput. 13, 20–28 (2017).

    Article  CAS  PubMed  Google Scholar 

  22. Hu, W., Gu, B. & Franco, I. Lessons on electronic decoherence in molecules from exact modeling. J. Chem. Phys. 148, 134304 (2018).

    Article  PubMed  CAS  Google Scholar 

  23. Yeh, S.-H., Hoehn, R. D., Allodi, M. A., Engel, G. S. & Kais, S. Elucidation of near-resonance vibronic coherence lifetimes by nonadiabatic electronic-vibrational state character mixing. Proc. Natl Acad. Sci. USA https://doi.org/10.1073/pnas.1701390115 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  24. Shankar, R. Principles of Quantum Mechanics 2nd edn (Springer, 1994).

  25. Mukamel, S. Principles of Nonlinear Optical Spectroscopy (Oxford Univ. Press, 1995).

  26. Born, M. & Oppenheimer, R. Zur quantentheorie der molekeln [German]. Ann. Phys. 389, 457–484 (1927).

    Article  Google Scholar 

  27. Pisana, S. et al. Breakdown of the adiabatic Born–Oppenheimer approximation in graphene. Nat. Mater. 6, 198 (2007).

    Article  CAS  PubMed  Google Scholar 

  28. Tully, J. C. Perspective: nonadiabatic dynamics theory. J. Chem. Phys. 137, 22A301 (2012).

    Article  PubMed  CAS  Google Scholar 

  29. Azumi, T. & Matsuzaki, K. What does the term “vibronic coupling” mean. Photochem. Photobiol. 25, 315–326 (1977).

    Article  CAS  Google Scholar 

  30. Lloyd, S. et al. No energy transport without discord. Preprint at arXiv https://arxiv.org/abs/1510.05035 (2015).

  31. Lee, M. K. & Coker, D. F. Modeling electronic-nuclear interactions for excitation energy transfer processes in light-harvesting complexes. J. Phys. Chem. Lett. 7, 3171–3178 (2016).

    Article  CAS  PubMed  Google Scholar 

  32. Allodi, M. A. et al. Redox conditions affect ultrafast exciton transport in photosynthetic pigment–protein complexes. J. Phys. Chem. Lett. 9, 89–95 (2018).

    Article  CAS  PubMed  Google Scholar 

  33. Shank, C. V. Measurement of ultrafast phenomena in the femtosecond time domain. Science 219, 1027–1031 (1983).

    Article  CAS  PubMed  Google Scholar 

  34. Perry, J. W., Scherer, N. F. & Zewail, A. H. Picosecond pump-probe multiphoton ionization of isolated molecules: IVR and coherence. Chem. Phys. Lett. 103, 1–8 (1983).

    Article  CAS  Google Scholar 

  35. Dantus, M., Rosker, M. J. & Zewail, A. H. Real-time femtosecond probing of “transition states” in chemical reactions. J. Chem. Phys. 87, 2395–2397 (1987).

    Article  CAS  Google Scholar 

  36. Savikhin, S. & Struve, W. S. Femtosecond pump-probe spectroscopy of bacteriochlorophyll a monomers in solution. Biophys. J. 67, 2002–2007 (1994).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. McClure, S. D., Turner, D. B., Arpin, P. C., Mirkovic, T. & Scholes, G. D. Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state. J. Chem. Phys. B 118, 1296–1308 (2014).

    Article  CAS  Google Scholar 

  38. Bai, S., Song, K. & Shi, Q. Effects of different quantum coherence on the pump–probe polarization anisotropy of photosynthetic light-harvesting complexes: a computational study. J. Phys. Chem. Lett. 6, 1954–1960 (2015).

    Article  CAS  PubMed  Google Scholar 

  39. Zhang, W. M., Chernyak, V. & Mukamel, S. Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitons. J. Chem. Phys. 110, 5011–5028 (1999).

    Article  CAS  Google Scholar 

  40. Hybl, J. D., Albrecht Ferro, A. & Jonas, D. M. Two-dimensional Fourier transform electronic spectroscopy. J. Chem. Phys. 115, 6606–6622 (2001).

    Article  CAS  Google Scholar 

  41. Cowan, M. L., Ogilvie, J. P. & Miller, R. J. D. Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes. Chem. Phys. Lett. 386, 184–189 (2004).

    Article  CAS  Google Scholar 

  42. Brixner, T., Manc˘al, T., Stiopkin, I. V. & Fleming, G. R. Phase-stabilized two-dimensional electronic spectroscopy. J. Chem. Phys. 121, 4221–4236 (2004).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  44. Jonas, D. M. Two-dimensional femtosecond spectroscopy. Annu. Rev. Phys. Chem. 54, 425–463 (2003).

    Article  CAS  PubMed  Google Scholar 

  45. Zhang, Z., Wells, K. L., Hyland, E. W. J. & Tan, H.-S. Phase-cycling schemes for pump–probe beam geometry two-dimensional electronic spectroscopy. Chem. Phys. Lett. 550, 156–161 (2012).

    Article  CAS  Google Scholar 

  46. Tekavec, P. F., Lott, G. A. & Marcus, A. H. Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation. J. Chem. Phys. 127, 214307 (2007).

    Article  PubMed  CAS  Google Scholar 

  47. Lott, G. A. et al. Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2D fluorescence spectroscopy. Proc. Natl Acad. Sci. USA 108, 16521–16526 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Pachón, L. A., Marcus, A. H. & Aspuru-Guzik, A. Quantum process tomography by 2D fluorescence spectroscopy. J. Chem. Phys. 142, 212442 (2015).

    Article  PubMed  CAS  Google Scholar 

  49. Draeger, S., Roeding, S. & Brixner, T. Rapid-scan coherent 2D fluorescence spectroscopy. Opt. Express 25, 3259–3267 (2017).

    Article  PubMed  Google Scholar 

  50. Mueller, S. et al. Fluorescence-detected two-quantum and one-quantum–two-quantum 2D electronic spectroscopy. J. Phys. Chem. Lett. 9, 1964–1969 (2018).

    Article  CAS  PubMed  Google Scholar 

  51. Harel, E. Four-dimensional coherent electronic Raman spectroscopy. J. Chem. Phys. 146, 154201 (2017).

    Article  PubMed  CAS  Google Scholar 

  52. Spencer, A. P., Hutson, W. O. & Harel, E. Quantum coherence selective 2D Raman–2D electronic spectroscopy. Nat. Commun. 8, 14732 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  53. Cho, M., Brixner, T., Stiopkin, I., Vaswani, H. & Fleming, G. R. Two dimensional electronic spectroscopy of molecular complexes. J. Chin. Chem. Soc. 53, 15–24 (2006).

    Article  CAS  Google Scholar 

  54. Turner, D. B., Wilk, K. E., Curmi, P. M. G. & Scholes, G. D. Comparison of electronic and vibrational coherence measured by two-dimensional electronic spectroscopy. J. Phys. Chem. Lett. 2, 1904–1911 (2011).

    Article  CAS  Google Scholar 

  55. Turner, D. B. et al. Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis. Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).

    Article  CAS  PubMed  Google Scholar 

  56. Wang, L. et al. Controlling quantum-beating signals in 2D electronic spectra by packing synthetic heterodimers on single-walled carbon nanotubes. Nat. Chem. 9, 219–225 (2017).

    Article  PubMed  CAS  Google Scholar 

  57. Gundogdu, K., Stone, K. W., Turner, D. B. & Nelson, K. A. Multidimensional coherent spectroscopy made easy. Chem. Phys. 341, 89–94 (2007).

    Article  CAS  Google Scholar 

  58. Turner, D. B., Stone, K. W., Gundogdu, K. & Nelson, K. A. Invited article: the coherent optical laser beam recombination technique (COLBERT) spectrometer: coherent multidimensional spectroscopy made easier. Rev. Sci. Instrum. 82, 081301 (2011).

    Article  PubMed  CAS  Google Scholar 

  59. Harel, E., Fidler, A. F. & Engel, G. S. Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy. Proc. Natl Acad. Sci. USA 107, 16444–16447 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Harel, E., Fidler, A. F. & Engel, G. S. Single-shot gradient-assisted photon echo electronic spectroscopy. J. Phys. Chem. A 115, 3787–3796 (2011).

    Article  CAS  PubMed  Google Scholar 

  61. Spokoyny, B. & Harel, E. Mapping the vibronic structure of a molecule by few-cycle continuum two-dimensional spectroscopy in a single pulse. J. Phys. Chem. Lett. 5, 2808–2814 (2014).

    Article  CAS  PubMed  Google Scholar 

  62. Tian, P., Keusters, D., Suzaki, Y. & Warren, W. S. Femtosecond phase-coherent two-dimensional spectroscopy. Science 300, 1553–1555 (2003).

    Article  CAS  PubMed  Google Scholar 

  63. Grumstrup, E. M., Shim, S.-H., Montgomery, M. A., Damrauer, N. H. & Zanni, M. T. Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping technology. Opt. Express 15, 16681–16689 (2007).

    Article  PubMed  Google Scholar 

  64. Myers, J. A., Lewis, K. L. M., Tekavec, P. F. & Ogilvie, J. P. Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper. Opt. Express 16, 17420–17428 (2008).

    Article  CAS  PubMed  Google Scholar 

  65. Brida, D., Manzoni, C. & Cerullo, G. Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line. Opt. Lett. 37, 3027–3029 (2012).

    Article  PubMed  Google Scholar 

  66. Fuller, F. D., Wilcox, D. E. & Ogilvie, J. P. Pulse shaping based two-dimensional electronic spectroscopy in a background free geometry. Opt. Express 22, 1018–1027 (2014).

    Article  PubMed  Google Scholar 

  67. Zheng, H. et al. Dispersion-free continuum two-dimensional electronic spectrometer. Appl. Opt. 53, 1909–1917 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  68. Ma, X., Dostál, J. & Brixner, T. Broadband 7-fs diffractive-optic-based 2D electronic spectroscopy using hollow-core fiber compression. Opt. Express 24, 20781–20791 (2016).

    Article  CAS  PubMed  Google Scholar 

  69. Son, M., Mosquera-Vázquez, S. & Schlau-Cohen, G. S. Ultrabroadband 2D electronic spectroscopy with high-speed, shot-to-shot detection. Opt. Express 25, 18950–18962 (2017).

    Article  CAS  PubMed  Google Scholar 

  70. Hochstrasser, R. M. Two-dimensional IR-spectroscopy: polarization anisotropy effects. Chem. Phys. 266, 273–284 (2001).

    Article  CAS  Google Scholar 

  71. Jonas, D. M., Lang, M. J., Nagasawa, Y., Joo, T. & Fleming, G. R. Pump−probe polarization anisotropy study of femtosecond energy transfer within the photosynthetic reaction center of Rhodobacter sphaeroides R26. J. Phys. Chem. 100, 12660–12673 (1996).

    Article  CAS  Google Scholar 

  72. Read, E. L. et al. Cross-peak-specific two-dimensional electronic spectroscopy. Proc. Natl Acad. Sci. USA 104, 14203–14208 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Thyrhaug, E., Žídek, K., Dostál, J., Bína, D. & Zigmantas, D. Exciton structure and energy transfer in the Fenna–Matthews–Olson complex. J. Phys. Chem. Lett. 7, 1653–1660 (2016).

    Article  CAS  PubMed  Google Scholar 

  74. Schlau-Cohen, G. S. et al. Spectroscopic elucidation of uncoupled transition energies in the major photosynthetic light-harvesting complex, LHCII. Proc. Natl Acad. Sci. USA 107, 13276–13281 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Zanni, M. T., Ge, N.-H., Kim, Y. S. & Hochstrasser, R. M. Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination. Proc. Natl Acad. Sci. USA 98, 11265–11270 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. Thyrhaug, E. et al. Identification and characterization of diverse coherences in the Fenna–Matthews–Olson complex. Nat. Chem. 10, 780–786 (2018).

    Article  CAS  PubMed  Google Scholar 

  77. Holdaway, D. I. H., Collini, E. & Olaya-Castro, A. Isolating the chiral contribution in optical two-dimensional chiral spectroscopy using linearly polarized light. Opt. Express 25, 6383–6401 (2017).

    Article  PubMed  Google Scholar 

  78. Holdaway, D. I. H., Collini, E. & Olaya-Castro, A. Coherence specific signal detection via chiral pump-probe spectroscopy. J. Chem. Phys. 144, 194112 (2016).

    Article  PubMed  CAS  Google Scholar 

  79. Fidler, A. F., Singh, V. P., Long, P. D., Dahlberg, P. D. & Engel, G. S. Dynamic localization of electronic excitation in photosynthetic complexes revealed with chiral two-dimensional spectroscopy. Nat. Commun. 5, 3286 (2014).

    Article  PubMed  CAS  Google Scholar 

  80. Dawlaty, J. M., Bennett, D. I. G., Huxter, V. M. & Fleming, G. R. Mapping the spatial overlap of excitons in a photosynthetic complex via coherent nonlinear frequency generation. J. Chem. Phys. 135, 044201 (2011).

    Article  PubMed  CAS  Google Scholar 

  81. Senlik, S. S., Policht, V. R. & Ogilvie, J. P. Two-color nonlinear spectroscopy for the rapid acquisition of coherent dynamics. J. Phys. Chem. Lett. 6, 2413–2420 (2015).

    Article  CAS  PubMed  Google Scholar 

  82. Novelli, F. et al. Vibronic resonances facilitate excited-state coherence in light-harvesting proteins at room temperature. J. Phys. Chem. Lett. 6, 4573–4580 (2015).

    Article  CAS  PubMed  Google Scholar 

  83. Richards, G. H., Wilk, K. E., Curmi, P. M. G. & Davis, J. A. Disentangling electronic and vibrational coherence in the phycocyanin-645 light-harvesting complex. J. Phys. Chem. Lett. 5, 43–49 (2014).

    Article  CAS  PubMed  Google Scholar 

  84. Hildner, R., Brinks, D., Nieder, J. B., Cogdell, R. J. & van Hulst, N. F. Quantum coherent energy transfer over varying pathways in single light-harvesting complexes. Science 340, 1448–1451 (2013).

    Article  CAS  PubMed  Google Scholar 

  85. Richards, G. H., Wilk, K. E., Curmi, P. M. G., Quiney, H. M. & Davis, J. A. Coherent vibronic coupling in light-harvesting complexes from photosynthetic marine algae. J. Phys. Chem. Lett. 3, 272–277 (2012).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  87. Hayes, D. & Engel, G. S. Extracting the excitonic Hamiltonian of the Fenna-Matthews-Olson complex using three-dimensional third-order electronic spectroscopy. Biophys. J. 100, 2043–2052 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  88. Cheng, Y.-C. & Fleming, G. R. Coherence quantum beats in two-dimensional electronic spectroscopy. J. Phys. Chem. A 112, 4254–4260 (2008).

    Article  CAS  PubMed  Google Scholar 

  89. Volpato, A., Bolzonello, L., Meneghin, E. & Collini, E. Global analysis of coherence and population dynamics in 2D electronic spectroscopy. Opt. Express 24, 24773–24785 (2016).

    Article  PubMed  Google Scholar 

  90. Rolczynski, B. S. et al. Correlated protein environments drive quantum coherence lifetimes in photosynthetic pigment-protein complexes. Chem 4, 138–149 (2018). Synchronized and correlated spectral motion of the excited states is observed, showing how coherence may be preserved among excited states.

    Article  CAS  Google Scholar 

  91. de A Camargo, F. V., Grimmelsmann, L., Anderson, H. L., Meech, S. R. & Heisler, I. A. Resolving vibrational from electronic coherences in two-dimensional electronic spectroscopy: the role of the laser spectrum. Phys. Rev. Lett. 118, 033001 (2017).

    Article  Google Scholar 

  92. Hayes, D., Wen, J., Panitchayangkoon, G., Blankenship, R. E. & Engel, G. S. Robustness of electronic coherence in the Fenna–Matthews–Olson complex to vibronic and structural modifications. Faraday Discuss. 150, 459–469 (2011).

    Article  CAS  PubMed  Google Scholar 

  93. Flanagan, M. L. et al. Mutations to R. sphaeroides reaction center perturb energy levels and vibronic coupling but not observed energy transfer rates. J. Phys. Chem. A 120, 1479–1487 (2016).

    Article  CAS  PubMed  Google Scholar 

  94. Maiuri, M., Ostroumov, E. E., Saer, R. G., Blankenship, R. E. & Scholes, G. D. Coherent wavepackets in the Fenna–Matthews–Olson complex are robust to excitonic-structure perturbations caused by mutagenesis. Nat. Chem. 10, 177–183 (2018).

    Article  CAS  PubMed  Google Scholar 

  95. Saer, R. et al. Perturbation of bacteriochlorophyll molecules in Fenna–Matthews–Olson protein complexes through mutagenesis of cysteine residues. Biochim. Biophys. Acta 1857, 1455–1463 (2016).

    Article  CAS  PubMed  Google Scholar 

  96. Caram, J. R., Fidler, A. F. & Engel, G. S. Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy. J. Chem. Phys. 137, 024507 (2012).

    Article  PubMed  CAS  Google Scholar 

  97. Christensson, N. et al. High frequency vibrational modulations in two-dimensional electronic spectra and their resemblance to electronic coherence signatures. J. Chem. Phys. B 115, 5383–5391 (2011).

    Article  CAS  Google Scholar 

  98. Manc˘al, T. et al. System-dependent signatures of electronic and vibrational coherences in electronic two-dimensional spectra. J. Phys. Chem. Lett. 3, 1497–1502 (2012).

    Article  CAS  Google Scholar 

  99. Hayes, D., Griffin, G. B. & Engel, G. S. Engineering coherence among excited states in synthetic heterodimer systems. Science 340, 1431–1434 (2013).

    Article  CAS  PubMed  Google Scholar 

  100. Halpin, A. et al. Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences. Nat. Chem. 6, 196–201 (2014).

    Article  CAS  PubMed  Google Scholar 

  101. Lim, J. et al. Vibronic origin of long-lived coherence in an artificial molecular light harvester. Nat. Commun. 6, 7755 (2015).

    Article  PubMed  Google Scholar 

  102. Milota, F. et al. Vibronic and vibrational coherences in two-dimensional electronic spectra of supramolecular J-aggregates. J. Phys. Chem. A 117, 6007–6014 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Bolzonello, L., Fassioli, F. & Collini, E. Correlated fluctuations and intraband dynamics of J-aggregates revealed by combination of 2DES schemes. J. Phys. Chem. Lett. 7, 4996–5001 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. Collini, E. & Scholes, G. D. Electronic and vibrational coherences in resonance energy transfer along MEH-PPV chains at room temperature. J. Phys. Chem. A 113, 4223–4241 (2009).

    Article  CAS  PubMed  Google Scholar 

  105. Collini, E. & Scholes, G. D. Coherent intrachain energy migration in a conjugated polymer at room temperature. Science 323, 369–373 (2009).

    Article  CAS  PubMed  Google Scholar 

  106. Butkus, V. et al. Discrimination of diverse coherences allows identification of electronic transitions of a molecular nanoring. J. Phys. Chem. Lett. 8, 2344–2349 (2017).

    Article  CAS  PubMed  Google Scholar 

  107. Ferretti, M. et al. The nature of coherences in the B820 bacteriochlorophyll dimer revealed by two-dimensional electronic spectroscopy. Phys. Chem. Chem. Phys. 16, 9930–9939 (2014).

    Article  CAS  PubMed  Google Scholar 

  108. Dahlberg, P. D. et al. Communication: coherences observed in vivo in photosynthetic bacteria using two-dimensional electronic spectroscopy. J. Chem. Phys. 143, 101101 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  109. Ryu, I. S., Dong, H. & Fleming, G. R. Role of electronic-vibrational mixing in enhancing vibrational coherences in the ground electronic states of photosynthetic bacterial reaction center. J. Chem. Phys. B 118, 1381–1388 (2014).

    Article  CAS  Google Scholar 

  110. Romero, E. et al. Quantum coherence in photosynthesis for efficient solar-energy conversion. Nat. Phys. 10, 676–682 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  111. Fuller, F. D. et al. Vibronic coherence in oxygenic photosynthesis. Nat. Chem. 6, 706–711 (2014).

    Article  CAS  PubMed  Google Scholar 

  112. Westenhoff, S., Palecek, D., Edlund, P., Smith, P. & Zigmantas, D. Coherent picosecond exciton dynamics in a photosynthetic reaction center. J. Am. Chem. Soc. 134, 16484–16487 (2012).

    Article  CAS  PubMed  Google Scholar 

  113. Parkinson, D. Y., Lee, H. & Fleming, G. R. Measuring electronic coupling in the reaction center of purple photosynthetic bacteria by two-color, three-pulse photon echo peak shift spectroscopy. J. Chem. Phys. B 111, 7449–7456 (2007).

    Article  CAS  Google Scholar 

  114. Wong, C. Y. et al. Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting. Nat. Chem. 4, 396–404 (2012).

    Article  CAS  PubMed  Google Scholar 

  115. Dostál, J., Pšenčík, J. & Zigmantas, D. In situ mapping of the energy flow through the entire photosynthetic apparatus. Nat. Chem. 8, 705–710 (2016).

    Article  PubMed  CAS  Google Scholar 

  116. Dahlberg, P. D. et al. Mapping the ultrafast flow of harvested solar energy in living photosynthetic cells. Nat. Commun. 8, 988 (2017).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  117. Duan, H.-G. et al. Nature does not rely on long-lived electronic quantum coherence for photosynthetic energy transfer. Proc. Natl Acad. Sci. USA 114, 8493–8498 (2017). Coherences assigned to vibrational ground-state signals due to the absence of signals within the excited-state absorption portion of the signal.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  118. Prior, J., Chin, A. W., Huelga, S. F. & Plenio, M. B. Efficient simulation of strong system–environment interactions. Phys. Rev. Lett. 105, 050404 (2010).

    Article  PubMed  CAS  Google Scholar 

  119. Womick, J. M. & Moran, A. M. Vibronic enhancement of exciton sizes and energy transport in photosynthetic complexes. J. Chem. Phys. B 115, 1347–1356 (2011).

    Article  CAS  Google Scholar 

  120. Christensson, N., Kauffmann, H. F., Pullerits, T. & Manc˘al, T. Origin of long-lived coherences in light-harvesting complexes. J. Chem. Phys. B 116, 7449–7454 (2012). Vibronic coupling model proposed shows how excitons can largely exist on the same chromophore, giving rise to signals of vibrational origin.

    Article  CAS  Google Scholar 

  121. Polyutov, S., Kühn, O. & Pullerits, T. Exciton-vibrational coupling in molecular aggregates: electronic versus vibronic dimer. Chem. Phys. 394, 21–28 (2012).

    Article  CAS  Google Scholar 

  122. Chenu, A., Christensson, N., Kauffmann, H. F. & Manc˘al, T. Enhancement of vibronic and ground-state vibrational coherences in 2D spectra of photosynthetic complexes. Sci. Rep. 3, 2029 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  123. Chin, A. W. et al. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment–protein complexes. Nat. Phys. 9, 113–118 (2013).

    Article  CAS  Google Scholar 

  124. Butkus, V., Valkunas, L. & Abramavicius, D. Vibronic phenomena and exciton–vibrational interference in two-dimensional spectra of molecular aggregates. J. Chem. Phys. 140, 034306 (2014).

    Article  PubMed  CAS  Google Scholar 

  125. Tiwari, V., Peters, W. K. & Jonas, D. M. Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework. Proc. Natl Acad. Sci. USA 110, 1203–1208 (2013). Quantum beating signals assigned to Raman-like signals on the ground state but dependent on vibronic couplings in the excited-state manifold relevant to energy transfer.

    Article  CAS  PubMed  Google Scholar 

  126. Plenio, M. B., Almeida, J. & Huelga, S. F. Origin of long-lived oscillations in 2D-spectra of a quantum vibronic model: electronic versus vibrational coherence. J. Chem. Phys. 139, 235102 (2013).

    Article  CAS  PubMed  Google Scholar 

  127. del Rey, M., Chin, A. W., Huelga, S. F. & Plenio, M. B. Exploiting structured environments for efficient energy transfer: the phonon antenna mechanism. J. Phys. Chem. Lett. 4, 903–907 (2013).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

  129. Ishizaki, A., Calhoun, T. R., Schlau-Cohen, G. S. & Fleming, G. R. Quantum coherence and its interplay with protein environments in photosynthetic electronic energy transfer. Phys. Chem. Chem. Phys. 12, 7319–7337 (2010).

    Article  CAS  PubMed  Google Scholar 

  130. Mohseni, M., Shabani, A., Lloyd, S. & Rabitz, H. Energy-scales convergence for optimal and robust quantum transport in photosynthetic complexes. J. Chem. Phys. 140, 035102 (2014). Identical energy scales of dephasing, energy gaps, thermal noise and reorganization energy described as optimal for transport, though frustrating for modelling and assignment.

    Article  CAS  PubMed  Google Scholar 

  131. Fassioli, F., Dinshaw, R., Arpin, P. C. & Scholes, G. D. Photosynthetic light harvesting: excitons and coherence. J. R. Soc. Interface 11, 20130901 (2014).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  132. Silbey, R. Description of quantum effects in the condensed phase. Procedia Chem. 3, 188–197 (2011).

    Article  CAS  Google Scholar 

  133. Redfield, A. G. On the theory of relaxation processes. IBM J. Res. Dev. 1, 19–31 (1957).

    Article  Google Scholar 

  134. 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  PubMed  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  137. Chin, A. W., Huelga, S. F. & Plenio, M. B. Coherence and decoherence in biological systems: principles of noise-assisted transport and the origin of long-lived coherences. Phil. Trans. R. Soc. A 370, 3638–3657 (2012).

    Article  CAS  PubMed  Google Scholar 

  138. Plenio, M. B. & Huelga, S. F. Dephasing-assisted transport: quantum networks and biomolecules. New J. Phys. 10, 113019 (2008). Dephasing-assisted quantum transport proposes how dephasing noise can enhance and influence energy transfer in quantum systems.

    Article  CAS  Google Scholar 

  139. Mohseni, M., Rebentrost, P., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008). Environmentally assisted quantum transport mechanism shows an optimal dephasing regime near where FMO dephasing is observed.

    Article  PubMed  CAS  Google Scholar 

  140. Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum transport. New J. Phys. 11, 033003 (2009).

    Article  CAS  Google Scholar 

  141. Bennett, D. I. G., Malý, P., Kreisbeck, C., van Grondelle, R. & Aspuru-Guzik, A. Mechanistic regimes of vibronic transport in a heterodimer and the design principle of incoherent vibronic transport in phycobiliproteins. J. Phys. Chem. Lett. 9, 2665–2670 (2018).

    Article  CAS  PubMed  Google Scholar 

  142. Womick, J. M. & Moran, A. M. Exciton coherence and energy transport in the light-harvesting dimers of allophycocyanin. J. Chem. Phys. B 113, 15747–15759 (2009).

    Article  CAS  Google Scholar 

  143. Meneghin, E. et al. Coherence in carotenoid-to-chlorophyll energy transfer. Nat. Commun. 9, 3160 (2018).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  144. Jin, X.-H. et al. Long-range exciton transport in conjugated polymer nanofibers prepared by seeded growth. Science 360, 897–900 (2018).

    Article  CAS  PubMed  Google Scholar 

  145. Abramavicius, D. & Mukamel, S. Quantum oscillatory exciton migration in photosynthetic reaction centers. J. Chem. Phys. 133, 064510 (2010).

    Article  PubMed  CAS  Google Scholar 

  146. McClung, R. E. D. Coherence transfer pathways and phase cycles: the decoding of a pulse sequence. Concepts Magn. Reson. 11, 1–28 (1998).

    Article  Google Scholar 

  147. Maier, C. et al. Environment-assisted quantum transport in a 10-qubit network. Phys. Rev. Lett. 122, 050501 (2019).

    Article  CAS  PubMed  Google Scholar 

  148. Carlo Andrea, R., Filippo, T. & Ivano, T. Quantum modeling of ultrafast photoinduced charge separation. J. Phys. Condens. Matter 30, 013002 (2018).

    Article  Google Scholar 

  149. Ma, F., Romero, E., Jones, M. R., Novoderezhkin, V. I. & van Grondelle, R. Vibronic coherence in the charge separation process of the Rhodobacter sphaeroides reaction center. J. Phys. Chem. Lett. 9, 1827–1832 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  150. Romero, E., Novoderezhkin, V. I. & van Grondelle, R. Quantum design of photosynthesis for bio-inspired solar-energy conversion. Nature 543, 355–365 (2017).

    Article  CAS  PubMed  Google Scholar 

  151. Tronrud, D. E., Wen, J., Gay, L. & Blankenship, R. E. The structural basis for the difference in absorbance spectra for the FMO antenna protein from various green sulfur bacteria. Photosynth. Res. 100, 79–87 (2009).

    Article  CAS  PubMed  Google Scholar 

  152. Harrop, S. J. et al. Single-residue insertion switches the quaternary structure and exciton states of cryptophyte light-harvesting proteins. Proc. Natl Acad. Sci. USA 111, E2666–E2675 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  153. Stowell, M. H. B. et al. Light-induced structural changes in photosynthetic reaction center: implications for mechanism of electron-proton transfer. Science 276, 812–816 (1997).

    Article  CAS  PubMed  Google Scholar 

  154. Doust, A. B. et al. Developing a structure–function model for the cryptophyte phycoerythrin 545 using ultrahigh resolution crystallography and ultrafast laser spectroscopy. J. Mol. Biol. 344, 135–153 (2004).

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

The authors thank Karen Watters for the scientific comments and scientific editing of the manuscript. This work is supported by the Vannevar Bush Fellowship (N00014-16-1-2513) and the Air Force Office of Scientific Research (FA9550-18-1-0099). G.S.E. acknowledges support from the Qatar National Research Foundation exceptional grant (NPRP-X-107-1-027). Additional support was provided by the University of Chicago Materials Research Science and Engineering Centers (MRSEC), which is funded by the National Science Foundation (NSF) through grant DMR-1420709. M.A.A. acknowledges support from an Arnold O. Beckman Postdoctoral Fellowship from the Arnold and Mabel Beckman Foundation.

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  1. These authors contributed equally: Lili Wang, Marco A. Allodi.

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  1. Department of Chemistry, The Institute for Biophysical Dynamics and The James Franck Institute, The University of Chicago, Chicago, IL, USA

    Lili Wang, Marco A. Allodi & Gregory S. Engel

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L.W. and M.A.A. researched data for the article. All authors contributed to the discussion of content, writing and editing of this manuscript.

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Glossary

Density matrix

An operator in quantum mechanics that contains all the physically relevant information about the statistical state of a quantum ensemble.

Decoherence

Fundamental quantum process that underlies dephasing and can lead to loss of coherences, even in a system without static disorder. The system can interact with its bath to exchange or transfer quantum information. The coherence is destroyed when such information cannot be regained by the system. The specifics of decoherence in a molecular system depends upon the coupling between electronic and nuclear degrees of freedom.

Dephasing

Decay of the macroscopic coherence across the ensemble. Includes both static and dynamic contributions. Because of differences in local environments, different members of the ensemble will accumulate phase at different rates, weakening the amplitude of measured quantum beats. Static disorder that leads to energy differences across the ensemble also contributes to the loss of quantum coherences. The overall dephasing envelope of these coherences is an exceptionally sensitive probe of ensemble system–bath interactions.

Reduced density matrix

A version of the density matrix operator that focuses specifically on the system of interest. This reduced density matrix requires a trace to be taken over the degrees of freedom that are defined as outside of the system of interest. The states that have been traced over are commonly referred to as bath degrees of freedom, or simply ‘the bath’.

Exciton basis

In pigment–protein complexes, coupling between molecules causes excitations to delocalize over several chromophores, forming Frenkel excitons that are the eigenstates of the system Hamiltonian.

Adiabatic dynamics

Dynamics that can be described by interactions within a single potential energy surface.

Nonadiabatic dynamics

Dynamics that need to consider interactions between several coupled potential energy surfaces.

Liouville space

A linear vector space, analogous to Hilbert space, that allows for the calculation of quantum dynamics. It is of higher dimensionality than Hilbert space and uses the density matrix to natively represent the state of the system. This allows for facile calculations of the statistical ensemble physics contained in the density operator.

Population states

Individual state or multiple states of the system when no coherent superposition between different quantum states exists and the system can be described as propagating along a single potential energy surface (that is, the excited state or the ground state). This is in contrast to coherences in which superpositions of prescribed phase are present.

Sliding window Fourier transform

A Fourier transform algorithm that employs some window size (N), where N is less than the total number of points (P) in the dataset to be Fourier transformed. This window can then be moved to find the Fourier transform of different sections of the full dataset, P. This technique can be useful to determine if different frequencies appear at different times in (or, more generally, in different parts of) the dataset, P.

Third-order nonlinear spectroscopy

A spectroscopic measurement that involves three interactions of the electric field of light with matter, thus generating a microscopic polarizability that has terms to the third order. In practice, this requires three laser pulses. Examples include 2DES and pump–probe spectroscopy. This measurement is also known as four-wave mixing (three input, one output) in the literature.

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Wang, L., Allodi, M.A. & Engel, G.S. Quantum coherences reveal excited-state dynamics in biophysical systems. Nat Rev Chem 3, 477–490 (2019). https://doi.org/10.1038/s41570-019-0109-z

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