Entanglement and entangling power of the dynamics in light-harvesting complexes
📝 Abstract
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 sulphur 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.
💡 Analysis
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 sulphur 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.
📄 Content
arXiv:0912.0122v2 [quant-ph] 14 Jun 2010 Entanglement and entangling power of the dynamics in light-harvesting complexes Filippo Caruso1,2,3, Alex W. Chin1,4, Animesh Datta2,3, Susana F. Huelga1,4, Martin B. Plenio1,2,3 1 Institut f¨ur Theoretische Physik, Universit¨at Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany 2 QOLS, The Blackett Laboratory, Prince Consort Road, Imperial College, London, SW7 2BW, UK 3 Institute for Mathematical Sciences, 53 Prince’s Gate, Imperial College, London, SW7 2PG, UK and 4 School of Physics, Astronomy & Mathematics, University of Hertfordshire, Hatfield, AL10 9AB, UK 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 sulphur 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. I. INTRODUCTION Photosynthesis, at its simplest, is the absorbtion of sunlight by photosensitive antennae and its subsequent conversion into chemical energy at a reaction center. The locations for these processes are physically and physiologically separated, which forces nature to devise a way for transferring the solar energy from the antennae to the reaction center (RC). Exciton en- ergy transfer (EET) is facilitated by certain protein molecules called light-harvesting complexes, and occurs at efficiencies of about 99%. EET has been a subject of continual interest for decades, not only for its phenomenal efficiency but also for its fundamental role in Nature [1]. Recently, ultrafast optics and nonlinear spectroscopy experiments have provided new insights into the process of EET in light-harvesting complexes like the one found in purple bacteria (LH-I) and the Fenna- Matthew-Olson (FMO) complex [2, 3]. In particular, evidence of quantum coherence has been presented, with the idea that nontrivial quantum effects may be at the root of its remarkable efficiency [4]. Following this, several studies have attempted to unravel the precise role of quantum coherence in the EET of light-harvesting complexes [5–11], and have, perhaps surpris- ingly, found that environmental decoherence and noise plays a crucial role [5–8, 12]. Light-harvesting complexes consist of several chro- mophores mutually coupled by dipolar interactions residing within a protein scaffold. Due to their mutual coupling, light-induced excitations on individual chromophores (sites) can undergo coherent transfer from site to site, and the typ- ical eigenstates are therefore delocalized over multiple chro- mophores. It is in these eigenstates, henceforth referred to as exciton states, that one finds evidence of quantum coher- ence. Here, we will study the role of quantum coherence in the process of EET in the FMO complex, as quantified by quantum entanglement, and investigate the sensitivity of the entanglement dynamics to variables that have not been di- rectly measured, such as the microscopic interaction strength between the complex and the surrounding environment, and the possible existence of spatial and temporal correlations in the bath. In this context, the first analysis of the entangle- ment behaviour in light-harvesting complexes was presented in Ref. [7], in which we analyzed the evolution of an entan- glement measurement, i.e. logarithmic negativity [13, 14], in a Markovian model of the FMO complex. The scope of the present work is two-fold, on the one hand it aims to make the study of coherence and entanglement in such systems quan- titative by considering spatial and temporal (non-Markovian) noise correlations, and secondly, it uses this quantitative ap- proach to show that maximal entanglement is not correlated with optimal transport, a result that may shed light on the pos- sible functional role of entanglement in EET. Entanglement is defined between subsystems of a global system. When considering entanglement in a composite sys- tem whose components are closely spaced and strongly inter- acting, as in the FMO complex, this choice of subsystems is, to some extent, dictated by the way we interrogate the sys- tem. If the sites can be addressed individually, then it is oper- ationally well justified to speak about site-entanglement, i.e. quantum correlations across distinguishable locations. How- ever, if
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