We explore quantum entanglement among the chlorophyll molecules in light-harvesting complex II, which is the most abundant photosynthetic antenna complex in plants containing over 50% of the world's chlorophyll molecules. Our results demonstrate that there exists robust quantum entanglement under physiological conditions for the case of a single elementary excitation. However, this nonvanishing entanglement is not unexpected because entanglement in the single-excitation manifold is conceptually the same as quantum delocalized states, which are the spectroscopically detectable energy eigenstates of the system. We discuss the impact of the surrounding environments and correlated fluctuations in electronic energies of different pigments upon quantum delocalization and quantum entanglement. It is demonstrated that investigations with tools quantifying the entanglement can provide us with more detailed information on the nature of quantum delocalization, in particular the so-called dynamic localization, which is difficult for a traditional treatment to capture.
We explore quantum entanglement among the chlorophyll molecules in light-harvesting complex II, which is the most abundant photosynthetic antenna complex in plants containing over 50% of the world's chlorophyll molecules. Our results demonstrate that there exists robust quantum entanglement under physiological conditions for the case of a single elementary excitation. However, this nonvanishing entanglement is not unexpected because entanglement in the single-excitation manifold is conceptually the same as quantum delocalized states, which are the spectroscopically detectable energy eigenstates of the system. We discuss the impact of the surrounding environments and correlated fluctuations in electronic energies of different pigments upon quantum delocalization and quantum entanglement. It is demonstrated that investigations with tools quantifying the entanglement can provide us with more detailed information on the nature of quantum delocalization, in particular the so-called dynamic localization, which is difficult for a traditional treatment to capture.
The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar correlations can be observed when considering different degrees of freedom of a single system, even a classical one. Surprisingly, it has also been suggested that entanglement might be playing a relevant role in certain biological processes, such as the functioning of pigment-proteins that constitute light-harvesting complexes of photosynthetic bacteria. The aim of this work is to show that the presence of entanglement in all of these different scenarios should not be unexpected, once it is realized that the very same mathematical structure can describe all of them. We show this by considering three different, realistic cases in which the only condition for entanglement to exist is that a single excitation is coherently delocalized between the different subsystems that compose the system of interest.
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.
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.
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
This thesis is a compilation of studies on delocalization measures, entanglement, and the role of quantum coherence in electronic energy transfer (EET) in light-harvesting complexes. The first two chapters after the introduction provide foundational knowledge of quantum information and light-harvesting, respectively. Chapter 2 introduces concepts from quantum information such as purity, bipartite entanglement and criteria for its measurement. The peripheral light-harvesting complex LH2, isolated from the anoxygenic purple bacterium Rhodopseudomonas acidophila, is employed as model system of interest. This light-harvesting complex, along with a description of the process of light-harvesting, the presence of quantum coherence, and the different models used to simulate EET, are described in chapter 3. In combination these two chapters lay the foundation for chapter 4, a critical assessment of the current measures of delocalization employed in EET studies, their relationship, and overall effectiveness. The conclusion is that entanglement based measures are most effective at measuring quantum effects, and that they can be related to more conventional delocalization measures such as the inverse participation ratio (IPR) by taking into account the entropy of the system under study. All the measures within this chapter are known as bipartite measures, and only measure the strength of correlation between two sites. The fifth chapter presents the core of this thesis. Following a brief introduction to the concept of multipartite entanglement, the development of multipartite delocalization measures that give high-resolution information on quantum coherence in light-harvesting complexes is detailed. In contrast to other measures, these analytical measures can detect many body correlations in large systems undergoing decoherence. We determine that, much like the bipartite entanglement based measures of chapter 4, these measures are also a function of system entropy, and have a similar hierarchial structure as that of multipartite entanglement measures. The final chapter applies these measures to our model LH2 complex, and draws conclusions on the role of bipartite delocalization and multipartite delocalization in EET.
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.