Long-lived quantum coherence in photosynthetic pigment-protein complexes has recently been reported at physiological temperature. It has been pointed out that the discrete vibrational modes may be responsible for the long-lived coherence. Here, we propose an analytical non-Markovian model to explain the origin of the long-lived coherence in pigment-protein complexes. We show that the memory effect of the discrete vibrational modes produces a long oscillating tail in the coherence. We further use the recently proposed measure to quantify the non-Markovianity of the system and find out the prolonged coherence is highly correlated to it.
Long-lived quantum coherence in photosynthetic pigment-protein complexes has recently been reported at physiological temperature. It has been pointed out that the discrete vibrational modes may be responsible for the long-lived coherence. Here, we propose an analytical non-Markovian model to explain the origin of the long-lived coherence in pigment-protein complexes. We show that the memory effect of the discrete vibrational modes produces a long oscillating tail in the coherence. We further use the recently proposed measure to quantify the non-Markovianity of the system and find out the prolonged coherence is highly correlated to it.
Recently, long-lasting quantum effects in a number of photosynthetic complexes, which are pigment-protein molecular aggregates (PPMAs), were experimentally verified. These findings created an interest in trying to connect the known highly efficient excitation energy transfer (EET) in these systems to the existence of quantum effects such as quantum coherence and quantum correlations. It also raised the question of how these sensitive quantum effects can survive in such a macroscopic system. This thesis explores the existence and possible role of quantum effects in the EET in PPMAs. These systems can be modeled as non-Markovian open quantum systems and quantum effects can be investigated and quantified by methods developed in quantum information theory. Firstly, it is found that quantum nonlocal correlations in the EET in the Fenna-Matthews-Olson complex - a PPMA found in nature - are unlikely to exist when the initial excitation occurs in a natural manner. When the initial excitation occurs in an artificial manner by localization of the excitation on one pigment, nonlocal correlations exist on a short time scale. It is further found that in order for nonlocal correlations to be preserved in such a system, the excitation must be trapped on two pigments at the time and these pigments must not interact strongly with other pigments in the complex. Secondly, it is shown that quantum coherence is not in general a resource for efficient EET in model systems consisting of a network of pigments; systems optimized with respect to the amount of coherence do not coincide with systems with optimal EET efficiency between two end-site pigments. Thirdly, it is found that environmental effects and system-environment interactions can be tuned to optimize the EET efficiency in model PPMAs. The features of optimal environments highly depends on the structure of the pigment system and in particular, the relationship between the pigments excitation energies. It is further shown that a non-Markovian dynamics cannot be connected to an increased EET efficiency in these systems.
Long lasting coherence in photosynthetic pigment-protein complexes has been observed even at physiological temperatures. Experiments have demonstrated quantum coherent behaviour in the long-time operation of the D-Wave quantum computer as well. Quantum coherence is the common feature between the two phenomena. An explanations for eight orders of magnitude discrepancy between the single flux qubit coherence time and the long-time quantum behaviour of an array of thousand flux qubits in the quantum computer was suggested within a theory where the flux qubits are coupled to an environment of particles called gravonons of high density of states The coherent evolution is in high dimensional spacetime and can be understood as a solution of Schroedinger's time-dependent equation. Explanations for the quantum beats observed in 2D Fourier transform electronic spectroscopy of the Fenna-Matthews-Olson (FMO) protein complex in the green sulfur bacteria are presently sought in constructing transport theories based on quantum master equations where 'good' molecular vibrations ('coloured noise') in the chlorophyll and the surrounding protein scaffold knock the exciton oscillations back into coherence. These 'good' vibrations are claimed to have developed in three billion years of natural selection. These theories, however, face the discomforting experimental observation that "attempts to scramble vibrational modes or to shift resonances with isotopic substitution miserably failed to affect the beating signals". As a possible way out of this dilemma we adopted the formalism of the quantum computation to the quantum beats in the FMO protein complex.
In this work, an exact analytical approach for the dynamics of excitation energy transfer and quantum entanglement in a photosynthetic dimer system is presented. In this approach, the protein environment is investigated as non-Markovian stochastic noise around each pigment molecule. The exact analytical expressions for the population of two pigments and their quantum entanglement is obtained. It is shown that numerical results have a good matching with the experimental results at cryogenic and physiological temperatures.
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment.
Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.
Understanding the non-Markovian dynamics of dissipative processes induced by memory effects of the environment is a fundamental subject of open quantum systems. Because of the complexity of open quantum systems, e.g., the multiple energy scales involving that of the system, the environment, and their mutual coupling, it is generally a challenging task to characterize the relationship among the parameters of the system dynamics and the reservoir spectra. For the two-level spontaneous emission model within structured environments, it was shown in a recent literature (Opt. Lett. 38, 3650) that a functional relation could be established between the asymptotically non-decaying population and the spectral density of the reservoir as the system undergoes a long-time evolution. It hence renders a distinct perspective to look into the character of long-lived quantum coherence in the corresponding non-Markovian process. This article is devoted to further investigate the phenomena of limit cycle oscillations possibly occurring in such non-Markovian dissipative systems in a long-time evolution. For a two-level system subjected to an environment with Ohmic class spectra, due to the presence of a unique bound-state mode of the system, the evolution trajectory of the given initial states will converge to a limit cycle in the Bloch space. The dependence of the radius and the location of the limit cycle on the spectral density function of the reservoir are manifested by virtue of the described functional relation. For the model subjected to a photonic crystal environment with multiple bands, our studies reveal that, owing to the presence of two or more bound states, the evolution trajectory of the system will converge to a toric curve of a paraboloid in the Bloch space and the phenomena of periodic or quasi-periodic oscillations could exhibit. While the equation of the parabolic curve is fully determined by the initial values of the state vector in the Bloch space, our results reveal that the scope of the evolution trajectory inside the toric curve is related to the spectral density of the reservoir and their quantified relation is distinctly characterized. Finally, the asymptotic dynamics of the correlations of a two-qubit system is discussed when it is subjected locally to the non-Markovian dissipative process.