Gestsson, Hallmann; (2025) Non-perturbative energy transfer rates and filtered photon correlations for excitonic systems. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Photosynthetic bacteria use light-harvesting antenna complexes to absorb and funnel excitation energy that then drives metabolic processes. Ensemble experiments have established that the photoexcitation dynamics exhibit signatures of coherences maintained for timescales comparable to their energy transfer process. Theoretical studies indicate that non-perturbative approaches are obligatory for a detailed understanding of the energy transfer process, and to rationalise experimental observations. Several questions remain open such as: how can we characterise the energy transfer kinetics for dynamics involving coherences and non-Markovian processes; what experiments can probe quantum processes during energy transfer in single complexes that avoids the ambiguity of ensemble averaging? This thesis addresses these two important questions by deploying the non-perturbative hierarchical equations of motion (HEOM) approach to investigate both generalised transfer rates in natural excitonic systems, and a theoretical investigation of quantum optical signatures of non- trivial quantum effects under conditions of biological relevance. A detailed derivation of the HEOM and explanation of our efficient implementation is given, which enables us to analyse large bacteriochlorophyll complexes. We then consider the influence of vibronic mechanisms in the energy transfer process for the Fenna-Matthews-Olson complex and the light-harvesting complex 2, applying projection operator techniques to perform a non-perturbative investigation of the excitonic kinetics. It is found that perturbative techniques are not appropriate, as a qualitative and quantitative disagreement with HEOM is observed. Next, we determine signatures of coherent energy transfer, exciton delocalisation, and steady-state coherence within the second-order cross correlation function for an acceptor-donor system. Then we present our dynamical expansion of frequency-resolved correlation functions that enables a simple and efficient numerical implementation, such that we may consider them for antenna complexes evolving in a non-perturbative manner. Finally, we give our approach towards simulating exact dynamics of disordered ensemble observables and demonstrate its effectiveness by considering examples of disordered qubits and dimers.

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