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Scientific Reports

Investigation of quantum trajectories in photosynthetic light harvesting through a quantum stochastic approach

Teerapat Uthailiang, Ongart Suntijitrungruang, Purin Issarakul, Peera Pongkitiwanichakul, Sutee Boonchui

Published Feb 12, 2025• 6 citations
Publisher

Abstract

In natural photosynthesis systems, pigment-protein complexes harvest the photon from sunlight with near-unity quantum efficiency. These complexes show incredible properties that cannot be merely extrapolated from knowledge of their composition. Additionally, the environment perturbing the light-harvesting process significantly affects the mechanism of photosynthesis. This research investigates the photosystem II reaction center (PSII RC) from a new perspective which considers the restricted path of the exciton transfer, in the photosynthesis system, as a quantum trajectory picture with the quantum continuous measurement. In this work, the corridor path of exciton transfer dynamics satisfies the equation of motion, as the spin dynamics, which consists of precession, relaxation, and random force rapidly fluctuating spin splitting arising from the bath. Moreover, the width of the corridor is an important factor for restricting path dynamics resulting in the localization and decoherence phenomenon. Our method is to analyze exciton transfer dynamics through paths on the Bloch sphere, in order to investigate the propagating states in accordance with the weight functional which depends on the coupling parameter between the system and environment as the phonon bath. Our results show that the paths outside the width of the corridor have a considerably lower weight functional and decoherence functional than those inside the width. Therefore, the degrees of localization, the weight functional, and the decoherence functional are related. Furthermore, the simulation reveals three characteristics of exciton transfer: gradual transfer, no transfer, and rapid transfer, relying significantly on the coupling between the system and phonons.

DOI
10.1038/s41598-025-89474-3

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In natural photosynthesis systems, pigment-protein complexes harvest the photon from sunlight with near-unity quantum efficiency. These complexes show incredible properties that cannot be merely extrapolated from knowledge of their composition. Additionally, the environment perturbing the light-harvesting process significantly affects the mechanism of photosynthesis. This research investigates the photosystem II reaction center (PSII RC) from a new perspective which considers the restricted path of the exciton transfer, in the photosynthesis system, as a quantum trajectory picture with the quantum continuous measurement. In this work, the corridor path of exciton transfer dynamics satisfies the equation of motion, as the spin dynamics, which consists of precession, relaxation, and random force rapidly fluctuating spin splitting arising from the bath. Moreover, the width of the corridor is an important factor for restricting path dynamics resulting in the localization and decoherence phenomenon. Our method is to analyze exciton transfer dynamics through paths on the Bloch sphere, in order to investigate the propagating states in accordance with the weight functional which depends on the coupling parameter between the system and environment as the phonon bath. Our results show that the paths outside the width of the corridor have a considerably lower weight functional and decoherence functional than those inside the width. Therefore, the degrees of localization, the weight functional, and the decoherence functional are related. Furthermore, the simulation reveals three characteristics of exciton transfer: gradual transfer, no transfer, and rapid transfer, relying significantly on the coupling between the system and phonons.
Understanding how quantum coherence is regulated by structured environments is essential for elucidating energy-transfer mechanisms in photosynthetic light-harvesting complexes. In this work, we present a trajectory-based computational analysis of the quantum-classical transition in asymmetrically coupled spin-boson models, motivated by exciton-phonon interactions in the phycobiliprotein PC645 complex. The model captures site-dependent environmental coupling that mimics pigment-specific dissipation pathways in biological systems. We employ three complementary approaches: a Redfield master equation in the Bloch-vector representation, numerically exact hierarchical equations of motion (HEOM), and a stochastic Schrödinger equation that generates ensembles of quantum trajectories. Within the stochastic framework, environmental backaction is interpreted as a continuous measurement process, giving rise to a time-dependent dynamical corridor on the Bloch sphere. The corridor width provides a quantitative measure of coherence loss and defines the quantum-classical crossover time. Our results show that moderate asymmetric coupling can sustain coherence and enhance directional population transfer, whereas strong coupling rapidly suppresses quantum trajectories. These findings offer mechanistic insight into environmentally assisted energy transfer and coherence regulation in photosynthetic pigment-protein 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.
Open quantum system approaches are widely used in the description of physical, chemical and biological systems. A famous example is electronic excitation transfer in the initial stage of photosynthesis, where harvested energy is transferred with remarkably high efficiency to a reaction center. This transport is affected by the motion of a structured vibrational environment, which makes simulations on a classical computer very demanding. Here we propose an analog quantum simulator of complex open system dynamics with a precisely engineered quantum environment. Our setup is based on superconducting circuits, a well established technology. As an example, we demonstrate that it is feasible to simulate exciton transport in the Fenna–Matthews–Olson photosynthetic complex. Our approach allows for a controllable single-molecule simulation and the investigation of energy transfer pathways as well as non-Markovian noise-correlation effects.
Many biological phenomena including avian navigation and photosynthesis manifest quantum coherent effects. In avian navigation, the weak geomagnetic field and spin-dependent chemical reactions are utilized for navigation. As one of the most important energy sources on earth, photosynthesis has always been a point of discussion for scientists. The study of energy transmission in photosynthetic systems can support the design or performance optimization of artificial light-harvesting devices. Currently, the quantum coherent effect has been observed in photosynthetic complexes, and the quantum efficiency of energy transmission in photosynthetic complexes is close to 100%. These important findings prompted many experts in different disciplines to use quantum physical methods to explore the physical mechanism behind the energy transmission in photosynthetic systems and the role of the quantum coherent effect in the exciton energy transmission in photosynthetic complexes. It has been proven that energy transfer in pigment-protein complexes is mainly in the form of coherent energy transfer. Moreover, the importance of the quantum coherent effect in energy transmission has been proven. Furthermore, several researchers have used the quantum coherent effect to improve energy transmission in photosynthetic systems and achieved some progress. For open quantum systems, such as photosynthetic systems, many theoretical methods have been proposed to analyze their quantum dynamics. These theoretical methods can be divided into two categories according to whether they can describe the diagonal term of the system density matrix, namely, coherent and incoherent theories. Moreover, the application conditions of these theoretical methods differ according to their established processes. Recently, with the progress in research, several groups have proposed several quantum simulation methods based on different quantum computing systems, including quantum simulation methods based on nuclear magnetic resonance systems, superconducting quantum circuit systems, and ion trap systems, to analyze the phenomena in photosynthetic systems. Compared with the traditional theoretical calculation methods, these quantum simulation methods have higher computational efficiency and lower computational complexity. This paper mainly reviews the progress in research on quantum coherent effects in photosynthesis and the related theoretical calculation and quantum simulation methods.
Abstract The process of photosynthesis, the main source of energy in the living world, converts sunlight into chemical energy. The high efficiency of this process is believed to be enabled by an interplay between the quantum nature of molecular structures in photosynthetic complexes and their interaction with the environment. Investigating these effects in biological samples is challenging due to their complex and disordered structure. Here we experimentally demonstrate a technique for studying photosynthetic models based on superconducting quantum circuits, which complements existing experimental, theoretical, and computational approaches. We demonstrate a high degree of freedom in design and experimental control of our approach based on a simplified three-site model of a pigment protein complex with realistic parameters scaled down in energy by a factor of 105. We show that the excitation transport between quantum-coherent sites disordered in energy can be enabled through the interaction with environmental noise. We also show that the efficiency of the process is maximized for structured noise resembling intramolecular phononic environments found in photosynthetic complexes.
In this thesis we study the coherent energy transfer in photosynthetic systems. This resonant energy transfer has proven to be a coherent transfer in some light harvest complexes. The model which we suggest to describe this mechanism is an exciton hopping on an N-site ring coupled to a spin bath. Analytic results are found for both the dynamics of the influence functional and of the reduced density matrix of the excitons.We also give results for the dynamics of the current as a function of time. By setting states splitting initially into 2 separate wave-packets moving at different velocities, we reproduce the coherent beating phenomenon in experiments.