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arXiv:1706.10238 · New Journal of Physics

The role of quantum coherence in dimer and trimer excitation energy transfer

Charlotta Bengtson, Erik Sjöqvist

Published Oct 5, 2017• 5 citations
arXivHTMLPDF

Abstract

Recent progress in resource theory of quantum coherence has resulted in measures to quantify coherence in quantum systems. Especially, the l 1 -norm and relative entropy of coherence have been shown to be proper quantifiers of coherence and have been used to investigate coherence properties in different operational tasks. Since long-lasting quantum coherence has been experimentally confirmed in a number of photosynthetic complexes, it has been debated if and how coherence is connected to the known efficiency of population transfer in such systems. In this study, we investigate quantitatively the relationship between coherence, as quantified by l 1 -norm and relative entropy of coherence, and efficiency, as quantified by fidelity, for population transfer between end-sites in a network of two-level quantum systems. In particular, we use the coherence averaged over the duration of the population transfer in order to carry out a quantitative comparison between coherence and fidelity. Our results show that although coherence is a necessary requirement for population transfer, there is no unique relation between coherence and the efficiency of the transfer process.

DOI
10.1088/1367-2630/aa916b

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Recent progress in resource theory of quantum coherence has resulted in measures to quantify coherence in quantum systems. Especially, the l 1 -norm and relative entropy of coherence have been shown to be proper quantifiers of coherence and have been used to investigate coherence properties in different operational tasks. Since long-lasting quantum coherence has been experimentally confirmed in a number of photosynthetic complexes, it has been debated if and how coherence is connected to the known efficiency of population transfer in such systems. In this study, we investigate quantitatively the relationship between coherence, as quantified by l 1 -norm and relative entropy of coherence, and efficiency, as quantified by fidelity, for population transfer between end-sites in a network of two-level quantum systems. In particular, we use the coherence averaged over the duration of the population transfer in order to carry out a quantitative comparison between coherence and fidelity. Our results show that although coherence is a necessary requirement for population transfer, there is no unique relation between coherence and the efficiency of the transfer process.
Recent progress in resource theory of quantum coherence has resulted in measures to quantify coherence in quantum systems. Especially, the l1-norm and relative entropy of coherence have been shown to be proper quantifiers of coherence and have been used to investigate coherence properties in different operational tasks. Since long-lasting quantum coherence has been experimentally confirmed in a number of photosynthetic complexes, it has been debated if and how coherence is connected to the known efficiency of population transfer in such systems. In this study, we investigate quantitatively the relationship between coherence, as quantified by l1-norm and relative entropy of coherence, and efficiency, as quantified by fidelity, for population transfer between end-sites in a network of two-level quantum systems. In particular, we use the coherence averaged over the duration of the population transfer in order to carry out a quantitative comparision between coherence and fidelity. Our results show that although coherence is a necessary requirement for population transfer, there is no unique relation between coherence and the efficiency of the transfer process.
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.
Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from spectroscopic signatures, whereas transport performance is assessed through specific observables and depends on both the open system dynamics and the initial state preparation. Here we develop a resource theoretic approach that quantifies the maximum change that initial site-basis coherence can induce in a chosen readout under fixed reduced dynamics. The central quantity is the resource impact functional, which yields state independent, readout specific bounds on coherence-induced changes in signals and transport figures of merit. We apply the framework to two models. For a donor-acceptor dimer, we analyse coherence sensitivity across coupling and bath-timescale regimes and bound trapping efficiency and average transfer time in terms of the impact functional. For a multi-site chain with terminal trapping, we derive rigorous criteria that distinguish population placement from sensitivity to initial state site-basis coherence. These include upper bounds on the largest advantage over incoherent preparations, necessary delocalization requirements for achieving a prescribed improvement, and a simple pairwise sufficient condition that can be checked from local information. For quasi-local reduced dynamics, we further obtain a Lieb-Robinson-type bound that constrains when coherence prepared in a distant region can influence a localized readout at finite times. Together, these results provide operational diagnostics and rigorous bounds for benchmarking coherence effects and for identifying regimes in which they are necessarily negligible or potentially relevant in excitonic transport models.
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.
Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from spectroscopic signatures, whereas transport performance is assessed through specific observables and depends on both the open system dynamics and the initial state preparation. Here, we develop a resource theoretic approach that quantifies the maximum change that initial site-basis coherence can induce in a chosen readout under fixed reduced dynamics. The central quantity is the resource impact functional, which yields state independent, readout specific bounds on coherence-induced changes in signals and transport figures of merit. We apply the framework to two models. For a donor-acceptor dimer, we analyze coherence sensitivity across coupling and bath-timescale regimes and bound trapping efficiency and average transfer time in terms of the impact functional. For a multi-site chain with terminal trapping, we derive rigorous criteria that distinguish population placement from sensitivity to initial state site-basis coherence. These include upper bounds on the largest advantage over incoherent preparations, necessary delocalization requirements for achieving a prescribed improvement, and a simple pairwise sufficient condition that can be checked from local information. For quasi-local reduced dynamics, we further obtain a Lieb-Robinson-type bound that constrains when coherence prepared in a distant region can influence a localized readout at finite times. Together, these results provide operational diagnostics and rigorous bounds for benchmarking coherence effects and for identifying regimes in which they are necessarily negligible or potentially relevant in excitonic transport models.
Quantum coherence has been suggested to play a role in excitation energy transfer in open quantum systems, yet a quantitative approach to assessing its influence on the transfer process is still missing. Using Nakajima-Zwanzig projection operators, we derive a general memory kernel identity that enables us to characterize and quantify the impact of coherence in the eigenenergy basis on a generalized rate of energy transfer. Applying our approach to the electronic dynamics of a dimer coupled to a structured phonon bath, we demonstrate how quantum coherence acts to modulate energy transfer.