Quantum phase synchronization via exciton-vibrational energy dissipation sustains long-lived coherence in photosynthetic antennas

Long coherent lifetime in the excitation energy transfer was observed in photosynthetic pigment dimers. The long-lasting coherences are protected by quantum phase synchronization realized by exciton-vibrational coupling where resonant anti-symmetric collective modes were dissipated.
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Primary processes in photosynthetic systems include light absorption, excitation energy transfer between light-harvesting antennas, and ultimately to the reaction center for charge separation. The quantum efficiency of the primary process is almost close to 100%. Such a high efficiency of the primary process likely implies the optimal design of the spatial arrangement of pigments and the energy transfer paths driven by the principles of physics in nature. The energy transfer mechanism in photosynthetic light-harvesting systems has long been described by the mechanism of Förster resonance energy transfer, which is also called the classical energy transfer mechanism. It applies to the case where the donor-acceptor pigment molecules are far apart and have weak interactions, i.e. the donor molecule absorbs the photon energy, leaps to an excited state, and then transmits the excitation energy to the neighboring acceptor molecule in the form of energy resonance. For a large number of pigment molecules, the energy is transferred in a random walking pattern. The excited state of the pigment is completely localized and energy dissipation is inevitable:  the transfer time from the initial excitation site to the reaction center is too long and  there is a possibility of energy loss at each jump.

However, in actual light-harvesting systems, the interactions and couplings between pigments tend to be stronger. The pigments will share molecular orbitals and excitation of any one of the pigments will lead to delocalization, forming a superposition of the excited states of these pigments, that is, the coherent superposition state. The energy transfer between these coherent superposition states is called coherent energy transfer. Experiments have shown that the efficiency of coherent energy transfer processes is significantly higher than that of classical energy transfer mechanisms. These coherent states can be either constructive or destructive for the amplitude, depending on the phase of the individual states. If the phases do not remain synchronized, the coherence effect disappears. With the advent of ultrashort pulsed lasers, it is no longer difficult to prepare coherent states, as long as the laser spectrum is broad enough to cover the energy gap between energy levels. However, most of the excited systems are non-isolated, and the interaction with the ambient thermal reservoir leads to the disappearance of the phase relationship, i.e., the decoherence process. For electronically excited states, the time scale of the decoherence process is usually in the range of a few femtoseconds to tens of femtoseconds, which is much smaller than the hundreds of femtoseconds necessary for the energy transfer occurring  among photosynthetic pigments. Therefore, if the coherent energy transfer  is effective in the photosynthetic system, then the lifetime of the quantum coherences has to match with the energy transfer time. Therefore, questions remain open that how do photosynthetic systems maintain long-lived quantum coherent states in the fluctuating protein environmental noise? What is the physical mechanism behind it,  and how to verify such a mechanism  experimentally ? .

  The emergence of two-dimensional electronic spectroscopy (2DES) provides an opportunity for these purposes. 2DES is a nonlinear spectroscopy method with simultaneously both high temporal and spectral resolution. By probing the correlation between the excitation light and the probe light, it can track the spectral evolution caused by energy dissipation, energy transfer, and energy delocalization with femtosecond-scale time resolution, and becomes a powerful tool for probing electronic coherence, vibrational coherence, and electron-vibrational coherence within molecules.

  In this work,  long-lived quantum coherences and its quantum phase synchronization mechanism have investigated in the  recombinant allophycocyanin (rAPC).  Allophycocyanin is the core light-harvesting antenna of the phycobilisome complex in red algae and cyanobacteria. APC efficiently transmits light energy captured from the phycobilisome rods to the reaction center of the photosystem, with an overall quantum efficiency of more than 90%. In the rAPC trimer, the phycocyanobilin (PCB) pigments on different monomers form three pairs of identical dimers, about 20 Å away from each other. The electronic coupling strength of these dimers is 155 cm-1, and the energy splitting of the excitonic states is about 800 cm-1, which is an ideal photosynthetic antenna for studying the coherent excitonic states of the dimer.  

In 1665, Huygens found that no matter what the initial positions of the two pendulums were, after about 30 minutes, the two pendulums hung on a beam would always swing at the same frequency and in opposite phases, leading to zero combined force acting on the beam with minimal friction loss,  leading to prolongation of the double pendulum’s swinging time. Inspired by the Huygens double pendulum experiment, different international research groups have established dimer exciton systems to describe the quantum coherence in photosynthetic systems. Theoretical studies show that the dimer exciton system has an intrinsic mechanism to overcome the environmental noise fluctuation to achieve the quantum phase synchronization. Based on the dimeric theory with exciton-vibrational couplings, we reached an important conclusion that the symmetric and antisymmetric collective vibrational modes of the dimer realize quantum phase synchronization if the vibrational energy can be resonant or quasi-resonant with the exciton energy level splitting. This is realized by the fast energy dissipation of the antisymmetric collective vibrational modes  which are coupled to the fast dephasing excitonic levels, while symmetric collective vibrational modes of less energy dissipation remain. Consequently, the following experimentally testable corollaries can be obtained:

(1) The intensity of coherent vibrational modes resonant with the excitonic energy gaps in a dimer are only half as strong as those in the monomer due to the dissipation of antisymmetric collective vibrational modes.

(2) Vibrational modes resonant with excitonic energy gaps in a dimer do not participate in the dynamic Stokes shifts of the low-energy excitonic state, i.e., they do not participate in energy dissipation.

(3) The lifetime of the exciton-vibrational coherences in a dimer is extended compared to that of the monomer.

The above three theoretical predictions are confirmed by 2DES experiments in the rAPC trimer and the subunit (containing only one pigment). This work reveals that the quantum phase synchronization is a universal strategy for dimer excitons to resist environmental noise and protect long-lived quantum coherences through exciton-vibrational coupling. This principle is a great masterpiece from nature that applies quantum mechanics to optimize the energy-transfer paths, which is not only applicable to photosynthetic systems, but will also be applied to artificially designed quantum coherent systems.

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