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Register a new userSteady-State Analysis of Light-harvesting Energy Transfer Driven by Incoherent Light: From Dimers to Networks
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The question of how quantum coherence facilitates energy transfer has been intensively debated in the scientific community. Since natural and artificial light-harvesting units operate under the stationary condition, we address this question via a non-equilibrium steady-state analysis of a molecular dimer irradiated by incoherent sunlight and then generalize the key predictions to arbitrarily-complex exciton networks. The central result of the steady-state analysis is the coherence-flux-efficiency relation:$eta=csum_{i eq j}F_{ij}kappa_j=2csum_{i eq j}J_{ij}{rm Im}[{rho}_{ij}]kappa_j$ with $c$ the normalization constant. In this relation, the first equality indicates that energy transfer efficiency $eta$ is uniquely determined by the trapping flux, which is the product of flux $F$ and branching ratio $kappa$ for trapping at the reaction centers, and the second equality indicates that the energy transfer flux $F$ is equivalent to quantum coherence measured by the imaginary part of the off-diagonal density matrix, i.e., $F_{ij}=2J_{ij}{rm Im}[{rho}_{ij}]$. Consequently, maximal steady-state coherence gives rise to optimal efficiency. The coherence-flux-efficiency relation holds rigorously and generally for any exciton networks of arbitrary connectivity under the stationary condition and is not limited to incoherent radiation or incoherent pumping. For light-harvesting systems under incoherent light, non-equilibrium energy transfer flux (i.e. steady-state coherence) is driven by the breakdown of detailed balance and by the quantum interference of light-excitations and leads to the optimization of energy transfer efficiency. It should be noted that the steady-state coherence or, equivalently, efficiency is the combined result of light-induced transient coherence, inhomogeneous depletion, and system-bath correlation, and is thus not necessarily correlated with quantum beatings.
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We explore the properties of steady-state Fano coherences generated in a three-level V-system continuously pumped by polarized incoherent light in the absence of coherent driving. The ratio of the stationary coherences to excited-state populations $mathcal{C} = (1+frac{Delta^2}{gamma(r+gamma)} )^{-1}$ is maximized when the excited-state splitting $Delta$ is small compared to either the spontaneous decay rate $gamma$ or the incoherent pumping rate $r$. We demonstrate that an intriguing regime exists where the $mathcal{C}$ ratio displays a maximum as a function of the dephasing rate $gamma_d$. We attribute the surprising dephasing-induced enhancement of stationary Fano coherences to the environmental suppression of destructive interference of individual incoherent excitations generated at different times. We identify the imaginary Fano coherence with the non-equilibrium flux across a pair of qubits coupled to two independent thermal baths, unraveling a direct connection between the seemingly unrelated phenomena of incoherent driving of multilevel quantum systems and non-equilibrium quantum transport in qubit networks. The real part of the steady-state Fano coherence is found to be proportional to the deviation of excited-state populations from their values in thermodynamic equilibrium, making it possible to observe signatures of steady-state Fano coherences in excited-state populations. We put forward an experimental proposal for observing steady-state Fano coherences by detecting the total fluorescence signal emitted by Calcium atoms excited by polarized vs. isotropic incoherent light. Our analysis paves the way toward further theoretical and experimental studies of non-equilibrium coherent steady states in thermally driven atomic and molecular systems, and for the exploration of their potential role in biological processes.
Light harvesting processes are often computationally studied from a time-dependent viewpoint, in line with ultrafast coherent spectroscopy experiments. Yet, natural processes take place in the presence of incoherent light, which induces a stationary state. Such stationary states can be described using the eigenbasis of the molecular Hamiltonian, but for realistic systems a full diagonalization is prohibitively expensive. We propose three efficient computational approaches to obtaining the stationary state that circumvent system Hamiltonian diagonalization. The connection between the incoherent perturbations, decoherence, and Kraus operators is established.
We provide a unified theoretical approach to the quantum dynamics of absorption of single photons and subsequent excitonic energy transfer in photosynthetic light-harvesting complexes. Our analysis combines a continuous mode <n>-photon quantum optical master equation for the chromophoric system with the hierarchy of equations of motion describing excitonic dynamics in presence of non-Markovian coupling to vibrations of the chromophores and surrounding protein. We apply the approach to simulation of absorption of single-photon coherent states by pigment-protein complexes containing between one and seven chromophores, and compare with results obtained by excitation using a thermal radiation field. We show that the values of excitation probability obtained under single-photon absorption conditions can be consistently related to bulk absorption cross-sections. Analysis of the timescale and efficiency of single-photon absorption by light-harvesting systems within this full quantum description of pigment-protein dynamics coupled to a quantum radiation field reveals a non-trivial dependence of the excitation probability and the excited state dynamics induced by exciton-phonon coupling during and subsequent to the pulse, on the bandwidth of the incident photon pulse. For bandwidths equal to the spectral bandwidth of Chlorophyll a, our results yield an estimation of an average time of ~0.09 s for a single chlorophyll chromophore to absorb the energy equivalent of one (single-polarization) photon under irradiation by single-photon states at the intensity of sunlight.
The non-equilibrium stationary coherences that form in donor-acceptor systems are investigated to determine their relationship to the efficiency of energy transfer to a neighboring reaction center. It is found that the effects of asymmetry in the dimer are generally detrimental to the transfer of energy. Four types of systems are examined, arising from combinations of localized trapping, delocalized (Forster) trapping, eigenstate dephasing and site basis dephasing. In the cases of site basis dephasing the interplay between the energy gap of the excited dimer states and the environment is shown to give rise to a turnover effect in the efficiency under weak dimer coupling conditions. Furthermore, the nature of the coherences and associated flux are interpreted in terms of pathway interference effects. In addition, regardless of the cases considered, the ratio of the real part and the imaginary part of the coherences in the energy-eigenbasis tends to a constant value in the steady state limit.
Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. However, the theories employed have reached a high degree of sophistication and have become complex, making it difficult to gain insights into microscopic processes and biologically significant questions. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and criteria by which the necessity of the vibrational assistance is considered.
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