A Quantum trajectory picture of single photon absorption and energy transport in photosystem II

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.