Macroscopic coherence as an emergent property in molecular nanotubes

Marco Gullì,Alessia Valzelli,Francesco Mattiotti,Fausto Borgonovi,Giuseppe Luca Celardo,Mattia Angeli

doi:10.1088/1367-2630/aaf01a

Abstract

Nanotubular molecular self-aggregates are characterized by a high degree of symmetry and they are fundamental systems for light-harvesting and energy transport. While coherent effects are thought to be at the basis of their high efficiency, the relationship between structure, coherence and functionality is still an open problem. We analyse natural nanotubes present in Green Sulphur Bacteria. We show that they have the ability to support macroscopic coherent states, i.e. delocalized excitonic states coherently spread over many molecules, even at room temperature. Specifically, assuming a canonical thermal state we find, in natural structures, a large thermal coherence length, of the order of 1000 molecules. By comparing natural structures with other mathematical models, we show that this macroscopic coherence cannot be explained either by the magnitude of the nearest-neighbour coupling between the molecules, which would induce a thermal coherence length of the order of 10 molecules, nor by the presence of long-range interactions between the molecules. Indeed we prove that the existence of macroscopic coherent states is an emergent property of such structures due to the interplay between geometry and cooperativity (superradiance and super-transfer). In order to prove that, we give evidence that the lowest part of the spectrum of natural systems is determined by a cooperatively enhanced coupling (super-transfer) between the eigenstates of modular sub-units of the whole structure. Due to this enhanced coupling strength, the density of states is lowered close to the ground state, thus boosting the thermal coherence length. As a striking consequence of the lower density of states, an energy gap between the excitonic ground state and the first excited state emerges. Such energy gap increases with the length of the nanotube (instead of decreasing as one would expect), up to a critical system size which is close to the length of the natural complexes considered.

Highlights

Cooperativity is the ability of many elements in a system to act in coordination, so that some physical property of the system results different from that of a single element
We show that the presence of a gapped, collective state affects the whole spectrum of the system, generating quite counter-intuitive disorder-enhanced and disorder-independent transport regimes, that extend over many orders of magnitude of the disorder strength
In particular the discovery of the role of cooperative effects in biological systems, for instance superradiance and super-transfer in photosynthetic systems, have inspired different proposals of bio-mimetic devices. Following this line of research on bio-mimetic quantum devices, we have proposed a design for a bio-inspired sunlight-pumped laser

Summary

Introduction

Cooperativity is the ability of many elements in a system to act in coordination, so that some physical property of the system results different from that of a single element. SR has been observed in a variety of systems [17], with some of the most recent examples being cold atomic clouds [18], photosynthetic antenna complexes [19], molecular aggregates [20, 21], quantum dots [22, 23] and nitrogen vacancies in nanodiamonds [24] This effect is relevant in enhancing absorption and energy transfer, which has been proposed to improve the efficiency of light-harvesting systems [1,2,3,4,5]. Contrary to the common lore that long-range should destroy Anderson localization [228, 229], strong signatures of localization have been reported recently in long-range interacting systems [202, 221, 222], questioning their utility

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Results

Conclusion