Exciton-phonon information flow in the energy transfer process of photosynthetic complexes

Non-Markovian and non-equilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton-phonon coupling. In this work, we utilize a recently-developed measure for non-Markovianity to elucidate the exciton-phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong system-bath coupling effects and non-equilibrium molecular reorganization. We propose an additional trace-distance measure for the information flow that could be extended to other master equations. We find that for a model dimer system and the Fenna-Matthews-Olson complex that non-Markovianity is significant under physiological conditions.Comment: 4 pages, 2 figure

Environment-assisted quantum transport in ordered systems

Noise-assisted transport in quantum systems occurs when quantum time-evolution and decoherence conspire to produce a transport efficiency that is higher than what would be seen in either the purely quantum or purely classical cases. In disordered systems, it has been understood as the suppression of coherent quantum localisation through noise, which brings detuned quantum levels into resonance and thus facilitates transport. We report several new mechanisms of environment-assisted transport in ordered systems, in which there is no localisation to overcome and where one would naively expect that coherent transport is the fastest possible. Although we are particularly motivated by the need to understand excitonic energy transfer in photosynthetic light-harvesting complexes, our model is general---transport in a tight-binding system with dephasing, a source, and a trap---and can be expected to have wider application

Efficiency of energy funneling in the photosystem II supercomplex of higher plants

The investigation of energy transfer properties in photosynthetic multi-protein networks gives insight into their underlying design principles.Here, we discuss excitonic energy transfer mechanisms of the photosystem II (PS-II) C$_2$S$_2$M$_2$ supercomplex, which is the largest isolated functional unit of the photosynthetic apparatus of higher plants.Despite the lack of a decisive energy gradient in C$_2$S$_2$M$_2$, we show that the energy transfer is directed by relaxation to low energy states. C$_2$S$_2$M$_2$ is not organized to form pathways with strict energetic downhill transfer, which has direct consequences on the transfer efficiency, transfer pathways and transfer limiting steps. The exciton dynamics is sensitive to small structural changes, which, for instance, are induced by the reorganization of vibrational coordinates. In order to incorporate the reorganization process in our numerical simulations, we go beyond rate equations and use the hierarchically coupled equation of motion approach (HEOM). While transfer from the peripherical antenna to the proteins in proximity to the reaction center occurs on a faster time scale, the final step of the energy transfer to the RC core is rather slow, and thus the limiting step in the transfer chain. Our findings suggest that the structure of the PS-II supercomplex guarantees photoprotection rather than optimized efficiency.Comment: 23 pages, 6 figure

Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground states are quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev Clock with FCIQMC to formulate a new technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique

Path integral Monte Carlo with importance sampling for excitons interacting with an arbitrary phonon bath

The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropolis-adjusted Langevin algorithm. The analytic expression for the gradient of the target probability density function associated with the population-normalized estimator cannot be obtained in closed form without a matrix power series. An approximated gradient that can be efficiently calculated is explored to achieve better computational scaling and efficiency. Application to a simple one-dimensional model system from the previous literature confirms the correctness of the method developed in this manuscript. The displaced harmonic model system within the single exciton manifold shows the numerically exact temperature dependence of the coherence and population of the excitonic system. The sampling scheme can be applied to an arbitrary anharmonic environment, such as multichromophoric systems embedded in the protein complex. The result of this study is expected to stimulate further development of real time propagation methods that satisfy the detailed balance condition for exciton populations.Comment: 16 pages, 5 figure