Exciton diffusion length in complex quantum systems: the effects of disorder and environmental fluctuations on symmetry-enhanced supertransfer

Abstract

Symmetric couplings among aggregates of n chromophores increase the transfer rate of excitons by a factor n 2 , a quantum-mechanical phenomenon called 'supertransfer'. In this work, we demonstrate how supertransfer effects induced by geometrical symmetries can enhance the exciton diffusion length by a factor n along cylindrically symmetric structures, consisting of arrays of rings of chromophores, and along spiral arrays. We analyse both closed-system dynamics and open quantum dynamics, modelled by combining a random bosonic bath with static disorder. In the closed-system case, we use the symmetries of the system within a short-time approximation to obtain a closed analytical expression for the diffusion length that explicitly reveals the supertransfer contribution. When subject to disorder, we show that supertransfer can enhance excitonic diffusion lengths for small disorders and characterize the crossover from coherent to incoherent motion. Owing to the quasi-one-dimensional nature of the model, disorder ultimately localizes the excitons, diminishing but not destroying the effects of supertransfer. When dephasing effects are included, we study the scaling of diffusion with both time and number of chromophores and observe that the transition from a coherent, ballistic regime to an incoherent, random-walk regime occurs at the same point as the change from supertransfer to classical scaling.

The feasibility of coherent energy transfer in microtubules

“…However, as the interdimer spacing of Trps is uninterrupted (figure 4), it is feasible that such an arrangement could effectively transfer energy along the protofilament length via a combination of coherent tunnelling and incoherent relaxation/excitation. Additionally, the unique cylindrical lattice symmetries found [36], induced by geometrical symmetries, can enhance the exciton diffusion length along cylindrically symmetric structures [37], similar to the helical arrangement of tubulin, and its chromophores, in microtubules.…”

Superradiance at the localization-delocalization crossover in tubular chlorosomes

“…The localization length of the system has been shown to limit the number of monomers contributing to the superradiance [23]. These results should also apply to supertransfer, a coined term describing non-radiative excitonic transfer of a superradiant patch [24][25][26]. Supertransfer has been ascribed to play a crucial role in the efficiency enhancement of light-harvesting systems, and in the chlorosome in particular [27,28].…”

Dynamics of coherence, localization and excitation transfer in disordered nanorings

“…As an example, for a tight-binding ring in the presence of uniform and coherent coupling γ to a single dissipative channel, only the superradiant state has a non-zero decay width Γ = N γ, being N the total number of chromophores in the ring [62]. If the exciton is required to be transferred along this channel, the presence of superradiance enhances dramatically the transfer rate as compared to the decay width of an isolated site, a phenomena called supertransfer [63][64][65][66], a corollary companion of superradiance. Superradiance in cyclic aggregates and its robustness to static disorder has been extensively studied [13,24,62,67,68].…”