Coherent or hopping like energy transfer in the chlorosome? Peter Nalbach

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1 Coherent or hopping like energy transfer in the chlorosome? Peter Nalbach

2 Photosynthesis 2

3 Photosynthesis Energy transfer incoherent Förster type or quantum coherent? Incoherent Förster type Strong environmental fluctuations Vibrations Solvent Quantum coherent recent experiments in FMO complex 3

4 What is special about photosythesis? Photosynthesis No recombination losses in excitonic transport 4

5 What is special about photosythesis? Photosynthesis No recombination losses in excitonic transport Organic solar cells Cheap but inefficient due to large recombination losses during excitonic energy transfer 5

6 What is special about photosythesis? Photosynthesis No recombination losses in excitonic transport To understand why might pave the way to cheap green energy 6

7 Overview Coherent or hopping like energy transfer in the chlorosome? Introduction What is the chlorosome? Why coherence? Random Walk Hierachical structure in the chlorosome Model Hamiltonian Master equation & Lindblad + Redfield tensors Results Conclusion & Summary 7

8 Green Sulfur Bacteria & Light Harvesting Chlorosome 8

9 Femtosecond Photon Echos in FMO signature of coherent oscillations interpretation as quantum coherence in the electronic exciton dynamics Engel / Fleming + al., Nature 446 (2007) & Panitchayangkoona / Engel + al., PNAS 107 (2010) 9

10 Femtosecond Photon Echos in FMO Quantum coherence functionally relevant for energy transport? How can coherence survive so long? Engel / Fleming + al., Nature 446 (2007) & Panitchayangkoona / Engel + al., PNAS 107 (2010) 10

11 How can coherence survive so long? We have given it some thoughts. P. Nalbach, I. Pugliesi, H. Langhals, and M. Thorwart, Phys. Rev. Lett. 108 (2012) P. Nalbach and M. Thorwart, J. Phys. B: At. Mol. Opt. Phys. 45 (2012) P. Nalbach and M. Thorwart, J. Phys.: Conf. Ser. 376 (2012) TIDS14 P. Nalbach, D. Braun, M. Thorwart, Phys. Rev. E 84 (2011) P. Nalbach, A. Ishizaki, G. R. Fleming, M. Thorwart, New J. Phys. 13 (2011) P. Nalbach, J. Eckel, M. Thorwart, New J. of Phys. 12 (2010) P. Nalbach and M. Thorwart, J. Chem. Phys. 132 (2010) P. Nalbach and M. Thorwart, in 'Quantum Efficiency in Complex Systems, Part I: Biomolecular systems', Semiconductors and Semimetals 83 (2010) M. Thorwart, J. Eckel, J.H. Reina, P. Nalbach, S. Weiss, Chem. Phys. Lett. 478 (2009) others too spatial or temporal correlations within the environmental fluctuations could do it! but don't! 11

12 How can coherence survive so long? Current believe Vibronic effects Vibrations coupled in Resonance! T. Mancal, N. Christensson, V. Lukes, F. Milota, O. Bixner, H. F. Kauffmann, and J. Hauer, J. Phys. Chem. Lett. 3, 1497 (2012). S. Polyutov, O. Kühn, and T. Pullerits, Chem. Phys. 394, 21 (2012). N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mancal, J. Phys. Chem. B 116, 7449 (2012). V. Tiwari, W.K. Peters, D.M. Jonas, Proc. Natl. Acad. Sci. USA, /pnas , (2013). A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, Nat. Phys. 9, 113 (2013). Population dynamics without vibration and with vibration! 12

13 Functional Relevance Chlorosome 10⁵ bacteriochlorophylls FMO 3 x 8 bacteriochlorophylls 13

14 Functional Relevance Chlorosome 10⁵ bacteriochlorophylls FMO 3 x 8 bacteriochlorophylls If then chlorosome should use. 14

15 Energy Transfer in Chlorosome Pump Probe Experiments Four distinct time scales at 1K ~ 0.1 / 1 / 10 / 100 ps Room temperature ~ 0.1 / / ps There are coherent clusters on a scale of ~5 nm Dynamics on this scale is 0.1 ps scale! Longest time scale is connected to energy transfer out of the chlorosome! 15

16 Energy Transfer in Chlorosome Pump Probe Experiments Four distinct time scales at 1K ~ 0.1 / 1 / 10 / 100 ps Room temperature ~ 0.1 / / ps There are coherent clusters on a scale of ~5 nm Dynamics on this scale is 0.1 ps scale! Longest time scale is connected to energy transfer out of the chlorosome! Energy pathways related to the intermediate time scales not clear! 16

17 Random walk Chlorosome Random walk reaches R after N steps with stepsize a ~ 5 nm diameter Experiments Coherent clusters a ~ 5 nm diameter 17

18 Random walk Chlorosome Random walk reaches R after N steps with stepsize a ~ 5 nm diameter Experiments Coherent clusters a ~ 5 nm diameter 480 x 0.1 ps = 48 ps relation between shortest and longest time scale Random walk cannot explain intermediate time scales but the total transfer time based on 5 nm coherent clusters 18

19 Structure of Chlorosome Due to strong disorder not finally known! some models are available 19

20 Structure of Chlorosome Due to strong disorder not finally known! some models are available 20

21 Chlorosome 21

22 Chlorosome Hamiltonian for a single ring Single excitation subspace j> means pigment j excited all others not Ej is Gaussian distributed with width 22

23 Chlorosome model (light)

24 Dynamics Quantum dynamics by von Neumann equation Destruction of quantum coherence by environmental fluctuations coupling to noise in the pigment energies dephasing & relaxation Thermal dephasing rate ~ kt leading to localization at pigment Redfield tensor pushing the system into thermal equilibrium according to H4R 24

25 Results 3 energy transfer time scales at room temperature: ~ 25 fs ring 1 & 2 come to an equilibrium inner tube transfer ~ 250 fs ring 1 & 2 & 4 come to an equilibrium tube in tube transfer ~ 2.5 ps ring 1 & 2 & 3 & 4 come to an equilibrium inter tube transfer ~150 fs coherent oscillating dynamics maximally intertube dynamics coherent 25

26 Conclusion & Summary Coherent or hopping like energy transfer in the chlorosome? Available structure model allows to understand all energy transfer time scales Hierarchical structure results in distinct energy transfer time scales Coherence only on shortest time & length scale inner tube maximally on that scale necessary see random walk!

27 Acknowlegdements Excitation Energy Transfer in Nonequilibrium Johannes Knörzer-Kühn Henning Kirchberg Aki Ishizaki (Japan) Graham R. Fleming (Berkeley) Daniel Braun (Toulouse) Adriana De Mendoza (Bogota) John Henry Reina (Cali) Igor Pugliesi (LMU) Heinz Langhals (LMU) Valentyn Prokhorenko Hendrik Papenjohann Timo Palm Moritz Frey Alexander Achner Hong-Guang Duan Martina Pola Cesar Mujica Tunneling Systems Doug Osheroff (Stanford) Danna Rosenberg Stefan Ludwig (LMU) Moshe Schechter (Ben Gurion University) Michael Thorwart Thanks to you! 27

28 System Environment models Interested in a small subsystem of a large total system exciton dynamics in a light-harvesting complex system environment approach useful An archtype problem particle in a double well Spin Boson model Phenomenological description Bloch equations 28

29 Methods RESPET (like Redfield + secular approx.): determine environmental influence in second order in results in Bloch dynamics with rates Environmental spectral function: detailed spectra Models: (Ohmic s = 1) 29

30 Results 30