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New Journal of Physics

Signatures of three-exciton correlations in the coherent and incoherent nonlinear optical response of photosynthetic complexes

Lijun Yang, Darius Abramavičius, Shaul Mukamel

Published Jun 30, 2010• 4 citations
Publisher

Abstract

We present a simulation study of population and coherence relaxation dynamics in the third-order nonlinear responses of the Fenna–Matthews–Olson (FMO) light-harvesting photosynthetic complex. Three-exciton correlations have been incorporated and the relevant six-point relaxation superoperator is calculated to second order in coupling to a phonon bath. The dynamics of three-exciton correlations induce new peaks that are absent or much weaker when the three-exciton variables are factorized. Such features were observed in a recent experiment (Engel G S et al 2007 Nature 446 782–6).

DOI
10.1088/1367-2630/12/6/065046

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We present a simulation study of population and coherence relaxation dynamics in the third-order nonlinear responses of the Fenna–Matthews–Olson (FMO) light-harvesting photosynthetic complex. Three-exciton correlations have been incorporated and the relevant six-point relaxation superoperator is calculated to second order in coupling to a phonon bath. The dynamics of three-exciton correlations induce new peaks that are absent or much weaker when the three-exciton variables are factorized. Such features were observed in a recent experiment (Engel G S et al 2007 Nature 446 782–6).
We theoretically investigate polarization-filtered two-photon correlations for the light emitted by a multichromophoric system undergoing excitation transport under realistic exciton-phonon interactions, and subject to continuous incoherent illumination. We show that for a biomolecular aggregate, such as the Fenna-Matthews Olson (FMO) photosynthetic complex, time-asymmetries in the cross-correlations of photons corresponding to different polarizations can be exploited to probe both quantum coherent transport mechanisms and steady-state coherence properties, which are not witnessed by zero-delay correlations. A classical bound on correlation asymmetry is obtained, which FMO is shown to violate using exact numerical calculations. Our analysis indicates that the dominant contributions to time-asymmetry in such photon cross-correlations are population to coherence transfer for Frenkel-Exciton models. Our results therefore put forward photon correlation asymmetry as a promising approach to investigate coherent contributions to excited-stated dynamics in molecular aggregates and other many-site quantum emitters.
We explore the feasibility of the coherent control of excitonic dynamics in light-harvesting complexes, analyzing the limits imposed by the open nature of these quantum systems. We establish feasible targets for phase and phase/amplitude control of the electronically excited state populations in the Fenna–Mathews–Olson (FMO) complex and analyze the robustness of this control with respect to orientational and energetic disorder, as well as the decoherence arising from coupling to the protein environment. We further present two possible routes to verification of the control target, with simulations for the FMO complex showing that steering of the excited state is experimentally verifiable either by extending excitonic coherence or by producing novel states in a pump–probe setup. Our results provide a first step toward coherent control of these complex biological quantum systems in an ultrafast spectroscopy setup.
We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.
In this article, we perform a systematic study of the global entanglement and exciton coherence length dynamics in natural light-harvesting system Fenna-Matthews-Olson (FMO) complex across various parameters of a dissipative environment from low to high temperatures, weak to strong system-environment coupling, and non-Markovian environments. A nonperturbative numerically exact hierarchical equations of motions method is employed to obtain the dynamics of the system. We found that entanglement is driven primarily by the strength of interaction between the system and environment, and it is modulated by the interplay between temperature and non-Markovianity. In contrast, coherence length is found to be insensitive to non-Markovianity. In agreement with previous studies, we do not observe a direct correlation between global entanglement and the efficiency of the excitation energy transfer in the FMO complex. As a new result, we found that the coherence length dynamics is correlated with the excitation energy transfer dynamics.
It has been suggested that excitation transport in photosynthetic light-harvesting complexes features speedups analogous to those found in quantum algorithms. Here we compare the dynamics in these light-harvesting systems to the dynamics of quantum walks, in order to elucidate the limits of such quantum speedups. For the Fenna–Matthews–Olson complex of green sulfur bacteria, we show that while there is indeed speedup at short times, this is short lived (70 fs) despite longer-lived (ps) quantum coherence. Remarkably, this timescale is independent of the details of the decoherence model. More generally, we show that the distinguishing features of light-harvesting complexes not only limit the extent of quantum speedup but also reduce the rates of diffusive transport. These results suggest that quantum coherent effects in biological systems are optimized for efficiency or robustness rather than the more elusive goal of quantum speedup.
The dynamics of energy transfer in Fenna–Matthews–Olson (FMO) light-harvesting complex interacting with a phonon bath is investigated. In this contribution, by considering the phonon bath as a source of stochastic noise, a new approach is proposed. Also, by calculating the global quantum entanglement and global quantum discord, the time evolution of the quantum correlation during the process is evaluated. The effects of temperature and initial excited state on the energy transfer and the quantum correlation are studied. It is shown, in agreement with the previous results, that the increasing of the temperature gives rise to the faster delocalisation of energy transfer and global quantum entanglement in the FMO complex. The proposed model predicts that the global discord is resistance versus the raising temperature. Furthermore, it is demonstrated that the quantum entanglement with respect to the global quantum discord has a significant role in the process of energy transfer in the FMO complex.