Environmental design principles for efficient excitation energy transfer in dimer and trimer pigment-protein molecular aggregates and the relation to non-Markovianity

Abstract

Lately there has been an interest in studying the effects and mechanisms of environment-assisted quantum transport, especially in the context of excitation energy transfer (EET) in pigment-protein molecular aggregates. Since these systems can be seen as open quantum systems where the dynamics is within the non-Markovian regime, the effect of non-Markovianity on efficient EET as well as its role in preserving quantum coherence and correlations has also been investigated in recent works. In this study, we explore optimal environments for efficient EET between end sites in a number of dimer and trimer model pigment-protein molecular aggregates when the EET dynamics is modeled by the HEOM-method. For these optimal environmental parameters, we further quantify the non-Markovianity by the BLP-measure to elucidate its possible connection to efficient EET. We also quantify coherence in the pigment systems by means of the measure l1−norm of coherence to analyze its interplay with environmental effects when EET efficiency is maximal. Our aim is to investigate possible environmental design principles for achieving efficient EET in model pigmentprotein molecular aggregates and to determine whether non-Markovianity is a possible underlying resource in such systems. We find that the structure of the system Hamiltonian (i.e., the pigment Hamiltonian parameter space) and especially, the relationship between the site excitation energies, determines whether one of two specific environmental regimes is the most beneficial in promoting efficient EET in these model systems. In the first regime, optimal environmental conditions are such that the EET dynamics in the system is left as coherent as possible. In the second regime, the most advantageous role of the environment is to drive the system towards equilibrium as fast as possible. In reality, optimal environmental conditions may involve a combination of these two effects. We cannot establish a relation between efficient EET and non-Markovianity, i.e., non-Markovianity cannot be regarded as a resource in the systems investigated in this study.