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arXiv:1305.6860 · New Journal of Physics

Stationary quantum coherence and transport in disordered networks

Björn Witt, Florian Mintert

Published Sep 13, 2013• 36 citations
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Abstract

We examine the excitation transport across quantum networks that are continuously driven by a constant and incoherent source. In particular we investigate the coherence properties of incoherently driven networks by employing recent tools from entanglement theory that enable a rigorous interpretation of coherence in the site basis. With these tools at hand we identify coherent delocalization of excitations over several sites to be a crucial prerequisite for highly efficient transport across networks driven by an incoherent source. These results are set into context with the latest discussion of the occurrence of coherence in molecular complexes that are driven by incoherent sun light.

DOI
10.1088/1367-2630/15/9/093020

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We examine the excitation transport across quantum networks that are continuously driven by a constant and incoherent source. In particular we investigate the coherence properties of incoherently driven networks by employing recent tools from entanglement theory that enable a rigorous interpretation of coherence in the site basis. With these tools at hand we identify coherent delocalization of excitations over several sites to be a crucial prerequisite for highly efficient transport across networks driven by an incoherent source. These results are set into context with the latest discussion of the occurrence of coherence in molecular complexes that are driven by incoherent sun light.
A variety of open quantum networks are currently under intense examination to model energy transport in photosynthetic systems. Here, we study the coherent transfer of a quantum excitation over a network incoherently coupled with a structured and small environment that effectively models the photosynthetic reaction center. Our goal is to distill a few basic, possibly universal, mechanisms or effects that are featured in simple energy-transfer models. In particular, we identify three different phenomena: the congestion effect, the asymptotic unitarity, and the staircase effects. We begin with few-site models, in which these effects can be fully understood, and then proceed to study more complex networks similar to those employed to model energy transfer in light-harvesting complexes.
We study the environment-assisted enhancement of the excitation-transport efficiency across a network of interacting quantum particles or sites. Our study reveals a crucial influence of the network configuration - and especially its degree of connectivity - on the amount of environment-supported enhancement. In particular, we find a significant interplay of direct and indirect connections between excitation sending and receiving sites. On the other hand, the non-Markovianity induced by memory-bearing, finite sized environments does not seem to provide a critical resource for the enhanced excitation-transport mechanism.
Selective energy transport throughout a quantum network connected to more than one reaction center can play an important role in many natural and technological considerations in photosystems. In this work, we propose a method in which an excitation can be transported from the original site of the network to one of the reaction centers arbitrarily using independent sources of dephasing noises. We demonstrate that in the absence of dephasing noises, the coherent evolution of the system does not have any role in energy transport in the network. Therefore, incoherent evolution via application of dephasing noises throughout a selected path of the network leads to complete transferring of the excitation to a desired reaction center.
One of the most pertinent problems in the debate on non-trivial quantum effects in biology concerns natural photosynthesis. Since sunlight is composed of thermal photons, it was argued to be unable to induce quantum coherence in matter, and that quantum mechanics is therefore irrelevant for the dynamical processes following photoabsorption. Our present analysis of a toy 'molecular aggregate'—composed of two dipole–dipole interacting two-level atoms treated as an open quantum system—however shows that incoherent excitations indeed can trigger persistent, coherent dynamics in both the site and the exciton bases: we demonstrate that collective decay processes induced by the dipole–dipole interactions create coherent intermolecular transport—regardless of the coherence properties of the incoming radiation. Our analysis shows that the steady state coherence is mediated by the population imbalance between the molecules and, therefore, increases with the energy difference between the two-level atoms. Our results establish the importance of collective decay processes in the study of ultrafast photophysics, and especially their potential role to generate stationary coherence in incoherently driven quantum transport.
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.