Role of coherence in excitation transfer in photosynthetic bacteria chlorobium tepidum

Abstract

Under the in-situ light-harvesting by green sulfur bacteria Chlorobium tepidum, a photon from sun light is absorbed by pigments of thin chlorosome antenna due to its high absorption co-e cient. Subsequently, this excitation energy is then transferred with very high quantum e ciency ( 100%) to the reaction center core complex (RCC) via Fenna-Matthews-Olson (FMO) complex, where the photo-chemical reaction occurs. FMO complex is a trimer and each monomer comprises bacteriochlorophyll-a (BChla) molecules surrounded by protein molecules. Simple structure of FMO complex encourages the study of highly e cient excitation energy transfer (EET) in this biological system. Although the broad mechanism of light-harvesting by Chlorobium tepidum is known but the reason for it high quantum e ciency is still elusive, which can be used to improve the solar light-harvesting to meet our future renewable energy needs. Earlier theoretical model (i.e. Forster resonance energy transfer model) had shown EET as non-oscillatory incoherent process. But recent 2-D electronic spectroscopy (2DES) experiments on isolated FMO complex illustrate the EET as oscillatory process. These oscillation were explained as reminiscence of coherence. It has started the heated debate about the role of the coherence in the high quantum e ciency of photosynthetic bacteria. Despite the development various theoretical approaches after this experimental observation the explicit role of coherence is still elusive. To answer to this question, we use non-Markovian master equation approach and hierarchical equation of motion (HEOM) approach. We also have used the inhomogeneous protein environment around di erent BChla sites in the presence of active vibronic modes local to each BChla site which were largely missed in earlier approaches. We show that the coherence between di erent BChla sites in the FMO complex is an essential ingredient for excitation energy transfer between various sites. The coherence delocalizes the excitation energy, which results in the redistribution of excitation among all the BChla sites in the steady state. We further show that the system remains partially coherent at the steady state. Further to study the e ect of initial coherence created by interaction of coherent laser pulse with the isolated FMO complex, we make a comparative numerical study of the EET, in terms of non-Markovian evolution of an initial coherent superposition state and a mixed state. We theoretically show that the initial coherence plays a crucial role in enhancing the speed of EET in FMO complex. A femto-second coherent laser pulse is suitably chosen to create the initial coherent superposition state. Such an initial state relaxes much faster than a mixed state thereby speeding up the EET. In this analysis, we have taken into account the relative orientation of the transition dipole moments of the BChla sites and their relative excitation energies. Next, to analyze the e ect of newly discovered 8th BChla site we study the dynamics of EET for eight BChla site monomer of FMO complex. Even more impressively, in the presence of the 8th chromophore, the initial pure state relaxes much faster than in the 7-site monomer. Hence the inclusion of 8th chromophore additionally enhances the EET relaxation. Furthermore, to study the e ect of initial coherence on excitation transfer e ciency (ETE) we have added the reaction center site. We show that the initial coherence enhances not only the speed of energy transfer, but also the ETE in photosynthetic bacteria Chlorobium tepidum. We have considered the pigment of RCC in addition to the eight sites of the monomer of FMO complex to explicitly study the ETE from FMO to RCC. With the use of realistic bath spectrum and several dominant vibronic modes in the non-Markovian master equation, we have compared the ETE for an initial pure state and an initial mixed state. We observe that the initial pure state relaxes e ciently to increase the trapping at the RCC. We further illustrate that the the competitive role of coherences to block the back transfer of excitation from RCC pigment to FMO complex and hence to maximize the ETE. Next, we have employed the highly non-Markovian approach i.e. HEOM approach, to nd the e ect of the coherence in ETE in the photosynthetic bacteria Chlorobium tepidum with better accuracy. We have compared the ETE in 9-site system (i.e. one monomer connected to RCC) with 25-site system (three monomers i.e. a trimer connected RCC) with realistic initial pure state in the presence of in-homogeneous protein environment. We have observed the same amount of excitation transfer from FMO to RCC as has been observed in the relevant experiment by femtosecond absorption spectroscopy. Moreover, we nd that although the excitation gets transferred almost independently in the adjacent monomers of FMO complex, full FMO complex needs to considered to be connected to the RCC pigment for better estimate of the ETE.