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Quantum Resources for Efficient Excitation Energy Transfer in Natural and Artificial Pigment-Protein Molecular Aggregates

Charlotta Bengtson

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

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.

Related papers

Quantum nonlocality in the excitation energy transfer in the Fenna-Matthews-Olson complex

Charlotta Bengtson, Michael Stenrup, Erik Sjöqvist

The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.

arXiv:1502.07842•Feb 27, 2015•0 citations

Nonlocality in the excitation energy transfer in the Fenna-Matthews-Olson complex

Charlotta Bengtson, Michael Stenrup, Erik Sjöqvist

The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.

•Feb 27, 2015•0 citations

Quantum nonlocality in the excitation energy transfer in the F enna– M atthews– O lson complex

Charlotta Bengtson, Michael Stenrup, Erik Sjöqvist

Abstract The Fenna–Matthews–Olson (FMO) complex—a pigment protein complex involved in photosynthesis in green sulfur bacteria—is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger‐than‐entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs, on the other hand, is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.

International Journal of Quantum Chemistry•Sep 8, 2016•5 citations

Understanding and manipulating electronic quantum coherence in photosynthetic light-harvesting

Stephan Hoyer

Ultrafast spectroscopy experiments show that photosynthetic systems can preserve quantum beats in the process of electronic energy transfer between pigments, even at room temperature. But what does this discovery imply for biology - and for quantum mechanics? This dissertation examines photosynthesis through the tools of quantum information science. We evaluate to what extent photosynthesis can be thought of as a type of quantum technology, and consider how we can apply experimental tools widely used for quantum technologies (state tomography and coherent control) to photosynthesis. Throughout, we use the Fenna-Matthews-Olson (FMO) complex of greens sulfur bacteria as a model photosynthetic pigment-protein complex.In Part I, we evaluate two mechanisms for the possible biological relevance of quantum coherent motion. First, we consider the extent to which dynamics in light-harvesting systems exhibit the quantum speedups characteristic of quantum algorithms and quantum walks. Second, we demonstrate a ratchet effect in electronic energy transfer enabled by partially coherent dynamics. To do so, we build a new model of energy transfer between weakly coupled light-harvesting complexes to understand how electronic coherence arises under natural conditions.In Part II, we present proposals for experimental probes of light harvesting dynamics with ultrafast spectroscopy. We show how the signal from pump-probe spectroscopy can be formally inverted to determine the excited state electronic density matrix. Finally, we examine the feasiblity of coherent control experiments on light-harvesting systems, and provide two realistic targets feasible with present-day technology.

•Jan 1, 2013•0 citations

Quantum population and entanglement evolution in photosynthetic process

Jing Zhu

Applications of the concepts of quantum information theory are usually related to the powerful and counter-intuitive quantum mechanical effects of superposition, interference and entanglement. In this thesis, I examine the role of coherence and entanglement in complex chemical systems. The research has focused mainly on two related projects: The first project is developing a theoretical model to explain the recent ultrafast experiments on excitonic migration in photosynthetic complexes that show long-lived coherence of the order of hundreds of femtoseconds and the second project developing the Grover algorithm for global optimization of complex systems. The first part can be divided into two sections. The first section is investigating the theoretical frame about the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex. The new developed modified scaled hierarchical equation of motion (HEOM) approach is employed for simulating the open quantum system. The second section is investigating the evolution of entanglement in the FMO complex based on the simulation result via scaled HEOM approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of different measures, including pairwise, triplet, quadruple and quintuple sites entanglement. Our results support the hypothesis that multipartite entanglement is maximum primary along the two distinct electronic energy transfer pathways. The second part of this thesis can be separated into two sections. The first section demonstrated that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The second section is implementing the basic quantum logical gates upon arrays of trapped ultracold polar molecules as qubits for the quantum computer. Utilized herein is the Multi-Target Optimal Control Theory (MTOCT) as a means of manipulating the initial-to-target transition probability via external laser field. The detailed calculation is applied for the SrO molecule, an ideal candidate in proposed quantum computers using arrays of trapped ultra-cold polar molecules.

•Jan 1, 2012•0 citations

Quantum Entanglement in Fenna—Matthews—Olson Photosynthetic Light—Harvesting complexes: A Short Review of Analysis Methods

Bruno González-Soria, Francisco Delgado

Abstract The Fenna-Matthews-Olson light-harvesting complexes have become a center of attention due to their high excitation energy transfer efficiency, which may surpass 98%. Experimental results reveal the presence of quantum entanglement in the protein structure, which seems to be associated to such a remarkably high efficiency. Notably, Redfield and Lindblad master equations have been already used to model the chromophore excitation in the protein complex as well as its interactions with the environment. The entanglement arising during the process has been quantified through several measures. This work provides a short review of methods used to model the above described system. It is also discussed the introduction of two nonconventional measures addresed to quantify the emergent entanglement.

Journal of Physics Conference Series•Apr 1, 2020•6 citations
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.
The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.
The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.
Abstract The Fenna–Matthews–Olson (FMO) complex—a pigment protein complex involved in photosynthesis in green sulfur bacteria—is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger‐than‐entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs, on the other hand, is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.
Ultrafast spectroscopy experiments show that photosynthetic systems can preserve quantum beats in the process of electronic energy transfer between pigments, even at room temperature. But what does this discovery imply for biology - and for quantum mechanics? This dissertation examines photosynthesis through the tools of quantum information science. We evaluate to what extent photosynthesis can be thought of as a type of quantum technology, and consider how we can apply experimental tools widely used for quantum technologies (state tomography and coherent control) to photosynthesis. Throughout, we use the Fenna-Matthews-Olson (FMO) complex of greens sulfur bacteria as a model photosynthetic pigment-protein complex.In Part I, we evaluate two mechanisms for the possible biological relevance of quantum coherent motion. First, we consider the extent to which dynamics in light-harvesting systems exhibit the quantum speedups characteristic of quantum algorithms and quantum walks. Second, we demonstrate a ratchet effect in electronic energy transfer enabled by partially coherent dynamics. To do so, we build a new model of energy transfer between weakly coupled light-harvesting complexes to understand how electronic coherence arises under natural conditions.In Part II, we present proposals for experimental probes of light harvesting dynamics with ultrafast spectroscopy. We show how the signal from pump-probe spectroscopy can be formally inverted to determine the excited state electronic density matrix. Finally, we examine the feasiblity of coherent control experiments on light-harvesting systems, and provide two realistic targets feasible with present-day technology.
Applications of the concepts of quantum information theory are usually related to the powerful and counter-intuitive quantum mechanical effects of superposition, interference and entanglement. In this thesis, I examine the role of coherence and entanglement in complex chemical systems. The research has focused mainly on two related projects: The first project is developing a theoretical model to explain the recent ultrafast experiments on excitonic migration in photosynthetic complexes that show long-lived coherence of the order of hundreds of femtoseconds and the second project developing the Grover algorithm for global optimization of complex systems. The first part can be divided into two sections. The first section is investigating the theoretical frame about the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex. The new developed modified scaled hierarchical equation of motion (HEOM) approach is employed for simulating the open quantum system. The second section is investigating the evolution of entanglement in the FMO complex based on the simulation result via scaled HEOM approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of different measures, including pairwise, triplet, quadruple and quintuple sites entanglement. Our results support the hypothesis that multipartite entanglement is maximum primary along the two distinct electronic energy transfer pathways. The second part of this thesis can be separated into two sections. The first section demonstrated that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The second section is implementing the basic quantum logical gates upon arrays of trapped ultracold polar molecules as qubits for the quantum computer. Utilized herein is the Multi-Target Optimal Control Theory (MTOCT) as a means of manipulating the initial-to-target transition probability via external laser field. The detailed calculation is applied for the SrO molecule, an ideal candidate in proposed quantum computers using arrays of trapped ultra-cold polar molecules.
Abstract The Fenna-Matthews-Olson light-harvesting complexes have become a center of attention due to their high excitation energy transfer efficiency, which may surpass 98%. Experimental results reveal the presence of quantum entanglement in the protein structure, which seems to be associated to such a remarkably high efficiency. Notably, Redfield and Lindblad master equations have been already used to model the chromophore excitation in the protein complex as well as its interactions with the environment. The entanglement arising during the process has been quantified through several measures. This work provides a short review of methods used to model the above described system. It is also discussed the introduction of two nonconventional measures addresed to quantify the emergent entanglement.