Excitation energy transfer: study with non-Markovian dynamics

Excitation transport in molecular aggregates with thermal motion

Molecular aggregates can under certain conditions transport electronic excitation energy over large distances due to dipole-dipole interactions. Here, we explore to what extent thermal motion of entire monomers can guide or enhance this excitation transport. The motion induces changes of aggregate geometry and hence modifies exciton states. Under certain conditions, excitation energy can thus be transported by the aggregate adiabatically, following a certain exciton eigenstate. While such transport is always slower than direct migration through dipole-dipole interactions, we show that transport through motion can yield higher transport efficiencies in the presence of on-site energy disorder than the static counterpart. For this we consider two simple models of molecular motion: (i) longitudinal vibrations of the monomers along the aggregation direction within their inter-molecular binding potential and (ii) torsional motion of planar monomers in a plane orthogonal to the aggregation direction. The parameters and potential shapes used are relevant to dye-molecule aggregates. We employ a quantum-classical method, in which molecules move through simplified classical molecular dynamics, while the excitation transport is treated quantum mechanically using Schrödinger's equation. For both models we find parameter regimes in which the motion enhances excitation transport, however these are more realistic for the torsional scenario, due to the limited motional range in a typical Morse type inter-molecular potential. We finally show that the transport enhancement can be linked to adiabatic quantum dynamics. This transport enhancement through adiabatic motion appears a useful resource to combat exciton trapping by disorder.

Coherent and incoherent theories for photosynthetic energy transfer

There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Förster theory and modified Redfield theory (MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion (HEOM), quantum path integral, coherent modified Redfield theory (CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer (EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.

Simulating signatures of two-dimensional electronic spectra of the Fenna-Matthews-Olson complex: By using a numerical path integral

A framework for simulating electronic spectra from photon-echo experiments is constructed by using a numerical path integral technique. This method is non-Markovian and nonperturbative and, more importantly, is not limited by a fixed form of the spectral density functions of the environment. Next, a two-dimensional (2D) third-order electronic spectrum of a dimer system is simulated. The spectrum is in agreement with the experimental and theoretical results previously reported [for example, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 90, 047401 (2003)]. Finally, a 2D third-order electronic spectrum of the Fenna-Matthews-Olson (FMO) complex is simulated by using the Debye, Ohmic, and Adolphs and Renger spectral density functions. It is shown that this method can clearly produce the spectral signatures of the FMO complex by using only the Adolphs and Renger spectral density function. Plots of the evolution of the diagonal and cross-peaks show that they are oscillating with the population time.

General non-markovian structure of Gaussian master and stochastic Schrödinger equations

General open quantum systems display memory features, their master equations are non-Markovian. We show that the subclass of Gaussian non-Markovian open system dynamics is tractable in a depth similar to the Markovian class. The structure of master equations exhibits a transparent generalization of the Lindblad structure. We find and parametrize the class of stochastic Schrödinger equations that unravel a given master equation, such a class was previously known for Markovian systems only. We show that particular non-Markovian unravelings known in the literature are special cases of our class.

Complex quantum network model of energy transfer in photosynthetic complexes

The quantum network model with real variables is usually used to describe the excitation energy transfer (EET) in the Fenna-Matthews-Olson (FMO) complexes. In this paper we add the quantum phase factors to the hopping terms and find that the quantum phase factors play an important role in the EET. The quantum phase factors allow us to consider the space structure of the pigments. It is found that phase coherence within the complexes would allow quantum interference to affect the dynamics of the EET. There exist some optimal phase regions where the transfer efficiency takes its maxima, which indicates that when the pigments are optimally spaced, the exciton can pass through the FMO with perfect efficiency. Moreover, the optimal phase regions almost do not change with the environments. In addition, we find that the phase factors are useful in the EET just in the case of multiple pathways. Therefore, we demonstrate that the quantum phases may bring the other two factors, the optimal space of the pigments and multiple pathways, together to contribute the EET in photosynthetic complexes with perfect efficiency.

Efficient estimation of energy transfer efficiency in light-harvesting complexes

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.