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Frontiers in Optics

Dissipative Five-level Quantum Systems: A Quantum Model of Photosynthetic Reaction Centers

Zibo Wang, Imran M. Mirza

Published Jan 1, 2020• 4 citations
Publisher

Abstract

Recent studies suggested that coherence can enhance the photosynthetic yield. In this work, we show how photosynthesis can be modeled as a five-level quantum heat engine and how its environmental interaction leads to noise-induced coherence.
DOI
10.1364/fio.2020.jm6b.26

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Abstract Quantum coherence is increasingly recognized as a foundational resource in quantum thermodynamics, serving as a key driver of thermodynamic performance in quantum heat engines (QHEs). However, a central paradox remains unresolved: how do natural photosynthetic systems achieve exceptionally high and robust energy-conversion efficiencies, even within noisy, dissipative environments where quantum coherence typically decays rapidly? Here, we present a coherently driven four-level QHE model, inspired by photosystem II—the primary energy-harvesting complex in plants, to elucidate the mechanisms by which quantum coherence and system topology jointly enable extraordinary efficiency and resilience. By performing spectral analysis of the system’s non-Hermitian Liouvillian superoperator, we reveal a topological phase transition characterized by a quantized change in the winding number. This transition separates two operational regimes: in the topologically trivial phase, stronger driving enhances coherence and boosts efficiency, whereas in the topologically nontrivial phase, topological protection preserves optimal efficiency even as coherence is largely destroyed. Our results establish a direct connection between topological effects and photosynthetic energy conversion, providing a new framework for understanding the resilience of biological energy harvesting and informing the design of robust, high-efficiency quantum energy conversion devices.
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In this paper, we present a theoretical description to the quantum coherence and decoherence phenomena of energy transfer in photosynthesis observed in a recent experiment [Science 316, 1462 (2007)]. As a successive two-color laser pulses with selected frequencies cast on a sample of the photosynthetic purple bacterium Rb. sphaeroides two resonant excitations of electrons in chromophores can be generated. However, this effective two-level subsystem will interact with its protein environment and decoherence is inevitable. We describe this subsystem coupled with its environment as a dynamical spin-boson model. The non-Markovian decoherence dynamics is described using a quasiadiabatic propagator path integral (QUAPI) approach. With the photon-induced effective time-dependent level splitting energy and level flip coupling coefficient between the two excited states and the environment-induced non-Markovian decoherence dynamics, our theoretical result is in good agreement with the experimental data.
Assessing the role of interference in natural and artificial quantum dynamical processes is a crucial task in quantum information theory. To this aim, an appropriate formalism is provided by the decoherent histories framework. While this approach has been deeply explored from different theoretical perspectives, it still lacks of a comprehensive set of tools able to concisely quantify the amount of coherence developed by a given dynamics. In this paper, we introduce and test different measures of the (average) coherence present in dissipative (Markovian) quantum evolutions, at various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we apply them to a paradigmatic quantum process where the role of coherence is being hotly debated: exciton transport in photosynthetic complexes. To spot out the essential features that may determine the performance of the transport, we focus on a relevant trimeric subunit of the Fenna-Matthews-Olson complex and we use a simplified (Haken-Strobl) model for the system-bath interaction. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to a quantum recoil avoiding effect on the exciton dynamics, that preserves and sustains the benefits of the initial fast quantum delocalization of the exciton over the network. Indeed, for intermediate levels of decoherence, the bath is seen to selectively kill the negative interference between different exciton pathways, while retaining the initial positive one. The concepts and tools here developed show how the decoherent histories approach can be used to quantify the relation between coherence and efficiency in quantum dynamical processes.
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.