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arXiv:1012.4059 · Procedia Chemistry

Quantum entanglement phenomena in photosynthetic light harvesting complexes

K. Birgitta Whaley, Mohan Sarovar, Akihito Ishizaki

Published Jan 1, 2011• 30 citations
arXivHTMLPDF

Abstract

We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.

DOI
10.1016/j.proche.2011.08.021

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We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.
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.
Recent evidence of electronic coherence during energy transfer in photosynthetic antenna complexes has reinvigorated the discussion about whether coherence and/or entanglement have any practical functionality for these molecular systems. Here we investigate quantitative relationships between the quantum yield of a light-harvesting complex and the distribution of entanglement among its components. Our study focuses on the entanglement yield or average entanglement surviving a time scale comparable to the average excitation trapping time. We consider the Fenna–Matthews–Olson (FMO) protein of green sulfur bacteria as a prototype system and show that there is an inverse relationship between the quantum efficiency and the average entanglement between distant donor sites. Our results suggest that long-lasting electronic coherence among distant donors might help in the modulation of the light-harvesting function.
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.
We study the evolution of quantum entanglement during exciton energy transfer (EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a biological pigment-protein complex involved in the early steps of photosynthesis in sulfur bacteria. The influence of Markovian as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct chromophores (site entanglement) and different excitonic eigenstates (mode entanglement) is studied for different injection mechanisms, including thermal and coherent laser excitation. Additionally, we study the entangling power of the FMO complex under natural operating conditions. While quantum information processing tends to favor maximal entanglement, near unit EET is achieved as the result of an intricate interplay between coherent and noisy processes where the initial part of the evolution displays intermediate values of both forms of entanglement.
A study published on arXiv has strictly demonstrated the existence of true multipartite quantum entanglement between bacteriochlorophyll-a (BChl a) molecules within the Fenna-Matthews-Olson (FMO) light-harvesting complex of green sulfur bacteria. Using entanglement measures in the single-excitation subspace (bipartite concurrence and a global entanglement measure), the study proved for the first time in a biological system that these entanglement states persist for approximately 2 picoseconds (ps) not only at cryogenic temperatures but also at physiological temperatures (300 K, room temperature), surviving macroscopically. The findings suggest that strong quantum entanglement between distant molecules can enhance the robustness and efficiency of the energy transfer network as the exciton moves toward the reaction center, even amidst environmental noise (decohering effects). [Quantum Biology Society] Photosynthesis, known as one of the most efficient energy conversion processes in nature, has long been a subject of wonder for scientists. While previous research focused on quantum coherence at the single-particle level, a groundbreaking study has recently been published mathematically proving that "true quantum entanglement"—the non-local correlation between multiple pigment molecules—actually operates within living organisms, drawing global attention. The paper titled "Quantum entanglement in photosynthetic light harvesting complexes," published in the preprint repository arXiv, is evaluated as a monumental achievement in elucidating macroscopic quantum phenomena in biological systems. An international joint research team led by Mohan Sarovar, Akihito Ishizaki, Graham R. Fleming, and K. Birgitta Whaley from UC Berkeley and Lawrence Berkeley National Laboratory (LBNL) in the USA spearheaded this innovative research. ■ Demonstration of Multipartite Quantum Entanglement within the FMO Complex The researchers focused on the FMO (Fenna-Matthews-Olson) light-harvesting complex of green sulfur bacteria (Chlorobium tepidum). By precisely analyzing the exciton dynamics between the pigment molecules within the complex using a non-Markovian quantum master equation, they proved through bipartite concurrence and a measure of global entanglement that true multipartite quantum entanglement is formed, going beyond simple individual coherence. This marks the first rigorous instance of quantifying quantum entanglement in a biological system. ■ Quantum Information Maintained Through Room-Temperature Noise The most surprising discovery is that these delicate quantum entanglement states survive meaningfully even at warm and wet physiological temperatures. While it was generally thought that quantum states are instantly destroyed by the thermal fluctuations of the surrounding proteins and solvent (decohering effects), the study's results confirmed that the natural FMO complex maintains bipartite entanglement between dimerized pigments and even a small amount of long-range and multipartite entanglement at 300 K. This entanglement plays a crucial role in enhancing the efficiency and robustness of the energy transfer network as the exciton travels to the reaction center. ■ Living Organisms as Optimized Quantum Machines This study suggests that living organisms are not merely losing quantum phenomena in harsh environmental noise but are rather highly designed, optimized quantum machines that endure and actively utilize them. Mimicking these perfect energy transfer mechanisms of nature is expected to provide key physical clues for maximizing the efficiency of next-generation solar cells or developing innovative quantum communication and metrology devices that operate robustly even at room temperature. https://arxiv.org/abs/0905.3787
It has been suggested that excitation transport in photosynthetic light-harvesting complexes features speedups analogous to those found in quantum algorithms. Here we compare the dynamics in these light-harvesting systems to the dynamics of quantum walks, in order to elucidate the limits of such quantum speedups. For the Fenna–Matthews–Olson complex of green sulfur bacteria, we show that while there is indeed speedup at short times, this is short lived (70 fs) despite longer-lived (ps) quantum coherence. Remarkably, this timescale is independent of the details of the decoherence model. More generally, we show that the distinguishing features of light-harvesting complexes not only limit the extent of quantum speedup but also reduce the rates of diffusive transport. These results suggest that quantum coherent effects in biological systems are optimized for efficiency or robustness rather than the more elusive goal of quantum speedup.