Session H38: Focus Session: Quantum Coherence in Biology I

Indicators of quantum coherence in light-harvesting dynamics

Characterizing quantum dynamics of electronic excitations in a variety of light-harvesting systems is currently of much interest [1]. In particular, it is important to identify measures that appropriately quantify the strength of coherent dynamics and its impact on different time scales of the light-harvesting process. In this talk I will discuss quantum transport performance measures that are defined based on the probability for the dynamics to successfully distinguish different initial photo-excitation conditions. I will also discuss how initial state distinguisability can provide information on spatially correlated phonon fluctuations as well as on the non-markovian character of the quantum dynamics. The prototype systems considered here are cryptophyte light-harvesting antennae isolated from marine algae [2, 3]. Experimental quantification of state distinguishability can be realized by monitoring the evolution of selected off-diagonal density matrix elements and therefore it could be achieved with current two-dimensional spectroscopy techniques. \\[4pt] [1] A. Olaya-Castro and G. D. Scholes, ``Energy transfer from F\"{o}rster-Dexter theory to quantum coherent light-harvesting'', to appear in Int. Rev. Phys. Chem. (2010) \\[0pt] [2] E. Collini, C.Y. Wong, K.E. Wilk, P.M.G. Curmi, P. Brumer and G.D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature, 463, 644-647 (2010) \\[0pt] [3] A. Kolli, A Nazir, F. Fassioli, R. Dinshaw, G D Scholes, and A Olaya-Castro, ``Energy transfer dynamics in cryptophyte antennae proteins'', submitted for publication (2010)   

Phonon-mediated path-interference in electronic energy transfer

Motivated by the recent observations of quantum coherence in light-harvesting antennae, we present a formalism to quantify the contribution of path-interference in phonon-mediated electronic energy transfer. The transfer rate between two molecules is computed by considering the quantum mechanical amplitudes associated with pathways connecting the initial and final sites. This includes contributions from classical pathways, but also terms arising from their interference. By treating the vibrational modes of the molecules as a non-Markovian harmonic oscillator bath, we compute the first-order path-interference correction to the classical transfer rate. We show that the correction due to path-interference may have either a vibrational or an electronic character, and may exceed the contribution of the indirect classical pathways.   

Efficiency of the energy transfer in the FMO complex using hierarchical equations on Graphics Processing Units

We study the efficiency of the energy transfer in the Fenna-Matthews-Olson complex solving the non-Markovian hierarchical equations (HE) proposed by Ishizaki and Fleming in 2009, which include properly the reorganization process. We compare it to the Markovian approach and find that the Markovian dynamics overestimates the thermalization rate, yielding higher efficiencies than the HE. Using the high-performance of graphics processing units (GPU) we cover a large range of reorganization energies and temperatures and find that initial quantum beatings are important for the energy distribution, but of limited influence to the efficiency. Our efficient GPU implementation of the HE allows us to calculate nonlinear spectra of the FMO complex. References see www.quantumdynamics.de   

Efficient GPU calculation of 2D-echo spectra of excitonic energy-transfer in systems with large reorganization energy

Using the Fenna-Matthews-Olson light harvesting complex as example, we calculate the two dimensional echo spectra (2D echo) of a multi-site system coupled to phonon baths using the propagation scheme suggested by Ishizaki and Fleming in 2009 which works for large system-bath couplings. We study the anti-correlations in the shapes of the 2D spectrum peaks which are seen as evidence for exciton energy transfer. This computationally demanding calculation uses 2.6 h GPU (graphics processing unit) time compared to 2.8 weeks time on a high performance conventional CPU cluster. The efficient implementation of the exact hierarchical equations obliterates the need for approximative methods and facilitates the interpretation and comparison of theory and experiment for systems with large reorganization energies. References see www.quantumdynamics.de   

Simulation of dissipative quantum dynamics in the presence of strongly-interacting and structured environments: a many-body approach to memory effects

Quantum systems which interact strongly with complex and structured environments are receiving increasing attention due to their importance in contexts such as solid-state quantum information processing and bio-molecular quantum dynamics. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively, and standard approaches are invalid or inefficient. Here we combine time-dependent density matrix renormalization group methods with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems at zero and finite temperatures. Using this technique we demonstrate a number of novel dynamical effects which result from long bath memories induced by either sharp spectral structures or strong coupling, and comment on how these can be exploited to drive efficient transport in small networks. We also show how our technique can be used to find the equilibrium properties of excitations in strongly renormalizing environments, and present some results on the quantum phase transition in the sub-Ohmic spin-boson model.   

Optimal Excitation energy transfer dynamics in light-harvesting systems

With the facilitation of surrounding protein environments, excitation energy transfer (EET) in photosynthetic systems can be highly efficient and robust. This talk compares different descriptions of dissipative exciton dynamics, discusses the generic mechanism of optimal energy transfer, and explores its implications for light-harvesting systems. (i) The generalized Bloch-Redfield equation provides a reliable description of exciton dynamics over a broad range of parameter space. (ii) The generic mechanism of optimal efficiency allows us to examine the interplay of quantum coherence, dynamics noise, and static disorder in a unified conceptual framework. (iii) The topological symmetry and network structures in photosynthetic systems reveal useful insights for the optimal design of artificial energy transfer systems.   

A quantum landscape study of energy transfer efficiency in light-harvesting complexes

Over billion years of evolution some photosynthetic complexes have turned into highly efficient light energy harvesting systems. In this work, we demonstrate optimality and robustness of energy transfer in the Fenna-Matthews-Olson (FMO) protein complex with respect to all the relevant parameters of system and environmental interactions. To this end we developed an efficient technique for studying the dynamics of energy transfer in a non-Markovian and non-perturbative regime. For the FMO protein of green sulfur bacteria we find that all the relevant natural parameters to lay within the optimal and robust regimes of energy transfer process. This suggests a peculiar interplay of internal and external forces in order to have a system that functions optimally while being robust under physiological conditions.   

Fast and efficient excitation transfer across disordered molecular networks

In this talk, we will present our statistical investigations on coherent excitation transfer through finite-size disordered molecular networks. As we have found, there exist certain molecular conformations that exhibit fast and highly efficient transport -- mediated by constructive quantum interference. We will discuss the properties of these optimal conformations which go along with the enhancement of efficiency. These insights may be relevant for explaining efficient energy transfer in the photosynthetic FMO complex.   

Regenerative quantum coherence in photosynthesis under natural conditions

Recent experiments provide compelling evidence for the feasibility of quantum coherent beating in photosynthetic light harvesting complexes, even at room temperature. However, whether this coherence arises \emph{in vivo} and its biological function (if any) have remained unclear. Here we present theoretical evidence for the creation and regeneration of electronic coherence under natural conditions. We show how such regenerated coherence may contribute to energy transfer efficiency in the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria.   

Enhanced exciton diffusion length via cooperative quantum transport

The energy transfer rate in biomolecular systems is typically calculated from the transition probability of an excitation hopping from one molecule to another using F\"orster energy transfer based on dipole-dipole interaction of individual molecules in the perturbative regime. However, due to strong interactions of among a group of molecules the excitation can become highly delocalized leading to an effective large dipole moment with an enhanced oscillator strength. Under certain symmetries, this could lead to an enhancement in exicton transfer rate via cooperative donation or acceptance of an excitation. Here, we explore this phenomenon in various multichromophoric geometries, under different symmetries, initial conditions, and dynamics. We study the behavior of the exciton diffusion length under the effects of disorders and environmental fluctuations and quantify the crossover from ballistic to diffusive regimes. Specifically, for a quasi-1 D array of rings containing N chromophores interacting with a bosonic bath, an interplay of time scales dictates the exciton dynamics. In the ``far-field'' regime, environmental interactions are dominating and the system properties are approaching those of the incoherent equilibrium Gibbs state. However, in the ``near-field'' the coherent interactions among dipole aggregates dominate other time scales and exciton diffusion length is enhanced by a factor of $\sqrt{N}$.   

Concatenated quantum codes in biological systems

This talk investigates how biological systems such as photosynthetic bacteria use quantum coding techniques such as decoherent subspaces, noiseless subsystems, and concatenated quantum codes to engineer long exitonic lifetimes and rapid energy transport. The existence of hierarchical structures in photosynthetic complexes is associated with concatenated quantum codes. A concatenated code is one that combines two or more codes to construct a hierarchical code that possesses features of all its constituent codes. In photosynthetic complexes, structures at the smallest level use quantum coding techniques to enhance exciton lifetimes, and structures at higher scales possess symmetries that enhance exciton hopping rates. The result is a concatenated quantum code that simultaneously protects excitons and enhances their transport rate. All known quantum codes can be described within the framework of group representation theory. This talk reviews the relationship between symmetry and quantum codes, and shows how photosynthetic bacteria and plants put quantum coding techniques to use to improve the efficiency of photosynthetic transport.   

A possible mechanisms for quantum coherence assisted ion transport in ion channels

Recently it was demonstrated that long-lived quantum coherence exists during excitation energy transport in photosynthesis. It is a valid question up to which length, time and mass scales quantum coherence may extend, how to one may detect this coherence and what if any role it plays for the dynamics of the system. Ion-channels are involved in many physiological processes. In the nervous system their coordinated opening and closing generates action potentials that form the basis for intra-neural communication which are essential for information representation and processing. We have recently suggested that the selectivity filter of ion channels may exhibit quantum coherence which might be relevant for the process of ion selectivity and conduction. I will discuss some of our current experimental efforts in this direction and show that quantum resonances could provide a viable approach to probe these quantum coherences. The emergence of resonances in the conduction of ion channels that are modulated periodically by time varying external fields can serve as signatures of quantum coherence in such a system.