We develop a method to simulate the excitonic dynamics of realistic photosynthetic light harvesting systems including non-Markovian coupling to phonon degrees of freedom, under excitation by N-photon Fock state pulses. This method combines the input-output and the hierarchical equations of motion (HEOM) formalisms into a double hierarchy of density matrix equations. We show analytically that, under weak field excitation relevant to natural photosynthesis conditions, an N-photon Fock state input and a corresponding coherent state input give rise to equal density matrices in the excited manifold. However, an N-photon Fock state input induces no off-diagonal coherence between the ground and excited subspaces, in contrast with the coherences created by a coherent state input. We derive expressions for the probability to absorb a single Fock state photon, with or without the influence of phonons. For short pulses (or equivalently, wide bandwidth pulses), we show that the absorption probability has a universal behavior that depends only upon a system-dependent effective energy spread parameter $\Delta$ and an exciton-light coupling constant $\Gamma$. This holds for a broad range of chromophore systems and for a variety of pulse shapes. We also analyze the absorption probability in the opposite long pulses (narrow bandwidth) regime. We then derive an expression for the long time emission rate in the presence of phonons and use it to study the difference between collective versus independent emission. Finally, we present a numerical simulation for the LHCII monomer (14-mer) system under single photon excitation that illustrates the use of the double hierarchy equations.

We investigate how collective behaviors of vibrations such as cooperativity and interference can enhance energy transfer in a nontrivial way, focusing on an example of a donor–bridge–acceptor trimeric chromophore system coupled to two vibrational degrees of freedom. Employing parameters selected to provide an overall uphill energy transfer from donor to acceptor, we use numerical calculations of dynamics in a coupled exciton–vibration basis, together with perturbation-based analytics and calculation of vibronic spectra, to identify clear spectral features of single- and multi-phonon vibrationally-assisted energy transfer (VAET) dynamics, where the latter include up to six-phonon contributions. We identify signatures of vibrational cooperation and interference that provide enhancement of energy transfer relative to that obtained from VAET with a single vibrational mode. We observe a phononic analogue of two-photon absorption, as well as a novel heteroexcitation mechanism in which a single phonon gives rise to simultaneous excitation of both the trimeric system and the vibrational degrees of freedom. The impacts of vibrations and of the one- and two-phonon VAET processes on the energy transfer are seen to be quite different in the weak and strong site–vibration coupling regimes. In the weak coupling regime, two-phonon processes dominate, whereas in the strong coupling regime up to six-phonon VAET processes can be induced. The VAET features are seen to be enhanced with increasing temperature and site–vibration coupling strength, and are reduced in the presence of dissipation. We analyze the dependence of these phenomena on the explicit form of the chromophore–vibration couplings, with comparison of VAET spectra for local and non-local couplings.

In this work we study the first step in photosynthesis for the limiting extreme case of a single photon interacting with photosystem II (PSII). We model our system using quantum trajectory theory, which allows us to consider not only the average evolution, but also the conditional evolution of the system given individual realizations of idealized measurements of photons that have been absorbed and subsequently emitted by fluorescence. The quantum nature of the single photon input requires a fully quantum model of both the input and output light fields. We show that PSII coupled to the field via three collective "bright states", whose orientation and distribution correlate strongly with its natural geometry. Measurements of the transmitted beam strongly affects the system state, since a (null) detection of the outgoing photon confirms that the system must be in the electronic (excited) ground state. Using numerical and analytical calculations we show that observing the null result transforms a state with a low excited state population O(10 −5 ) to a state with nearly all population contained in the excited states. This is solely a property of the single photon input, as we confirm by comparing this behavior with that for excitation by a coherent state possessing an average of one photon, using a smaller five site "pentamer" system. We further analytically predict and also numerically verify that the time-dependent variations in the observed rates of fluorescence reflect interference between eigenstates of the non-Hermitian Hamiltonian that are superposed in the absorption of the incident single photon, providing a new photon-counting witness of excitonic coherence in electronic energy transfer.

We study the interplay between two environmental influences on excited state energy transfer in photosynthetic light harvesting complexes, namely, vibrationally assisted energy transfer(VAET) and environment-assisted quantum transport (ENAQT), considering a dimeric chromophore donor-acceptor model as a prototype for larger systems. We demonstrate how the basic features of the excitonic energy transfer are influenced by these two environments, both separately and together, with the environment being fully quantum in the case of VAET and treated in the Haken-Strobl-Reineker classical limit in the case of ENAQT. Our results reveal that in the weak noise regime, the presence of a classical noise source is detrimental to the energy transfer that is resonantly assisted by the exciton-vibration interactions intrinsic to VAET. In the strong noise regime we reproduce all the features of ENAQT including the turnover into a Zeno regime where energy transfer is suppressed, and VAET is insignificant.