Quantum Correlation and Synchronisation-Enhanced Energy Transfer in Driven-Dissipative Light-Harvesting Dimers

Quantum synchronisation has recently been proposed as a mechanism for electronic excitation energy transfer in light-harvesting complexes, yet its robustness in driven-dissipative settings remains under active investigation. Here, we revisit this mechanism in cryptophyte photosynthetic antennae using an exciton–vibrational dimer model. By comparing the full open quantum dynamics with semi-classical rate equations for electronic density-matrix elements and vibrational observables, we demonstrate that quantum correlations between electronic and vibrational degrees of freedom, beyond the semi-classical factorised limit, underpin the emergence of quantum synchronisation. Furthermore, we introduce an environment-assisted transfer mechanism arising as a nonlinear, non-Condon correction to the dipole–dipole interaction. This mechanism enables long-lived quantum coherence and continuous, synchronisation-enhanced energy transfer in a driven-dissipative regime, thereby suggesting new avenues for investigating photosynthetic energy-transfer dynamics.

💡 Research Summary

This paper revisits the hypothesis that quantum synchronization can facilitate excitation energy transfer in photosynthetic light‑harvesting complexes, focusing on cryptophyte antennae modeled as an exciton‑vibrational dimer. The authors construct a full open‑quantum‑system description: a two‑site electronic Hamiltonian with site energies ε₁, ε₂, dipole‑dipole coupling J, and two local vibrational modes of frequencies ω₁ and ω₂. Linear electron‑phonon couplings g₁, g₂ are derived from experimentally measured Huang‑Rhys factors. Dissipative processes are introduced via Lindblad operators: electronic dephasing at rate Γ_deph and vibrational relaxation at rate Γ_th. The resulting master equation yields eight coupled equations of motion for electronic populations (ρ₁₁, ρ₂₂), coherences (⟨σ⁺₁σ⁻₂⟩, ⟨σ⁺₂σ⁻₁⟩), and vibrational quadratures (⟨bₘ†+bₘ⟩, ⟨i(bₘ†−bₘ)⟩). Because the equations contain higher‑order correlations such as ⟨σ⁺₁σ⁻₂(bₘ†+bₘ)⟩, they cannot be solved analytically; the authors therefore integrate them numerically using the QuTiP package.

Two dynamical regimes are explored. In the absence of electronic dephasing (Γ_deph = 0) but with vibrational damping, the system develops strong electron‑phonon correlations. The two vibrational displacements become phase‑locked, which the authors quantify using a phase‑locking value (PLV) based on the instantaneous phase difference Δϕ(t) = ϕ₁(t) − ϕ₂(t). PLV values close to unity indicate robust quantum synchronization, and this synchronized motion coincides with sustained energy flow from donor to acceptor. When electronic dephasing is introduced (Γ_deph ≈ 10 THz), the synchronization appears only after the donor excitation has already decayed, rendering it irrelevant for transfer efficiency.

To overcome this limitation, the authors propose an environment‑assisted transfer mechanism that goes beyond the usual Condon approximation. They introduce a non‑Condon correction Γ_dip to the dipole‑dipole interaction, effectively making the coupling J a function of the instantaneous donor‑acceptor separation modulated by nuclear normal modes. When the donor is continuously driven by coherent light, this nonlinear term generates a steady‑state where electron‑phonon correlations persist, the vibrational modes remain phase‑locked, and the PLV stays high over hundreds of picoseconds. Consequently, the electronic population on the donor does not vanish quickly, allowing continuous energy transfer to the acceptor even under strong dephasing.

Parameter values are taken from spectroscopic data on PE545 antennae (Δε = 1042 cm⁻¹, J = 92 cm⁻¹, ω₁ = 1450 cm⁻¹, ω₂ = 1111 cm⁻¹, S₁ = 0.1013, S₂ = 0.0578, Γ_th = 1 THz, Γ_deph = 10 THz). Simulations without the non‑Condon term show rapid loss of coherence and PLV, whereas adding Γ_dip ≈ 0.5 THz maintains PLV ≈ 0.9 and retains ~10 % donor population for the duration of the simulation.

The study concludes that (i) quantum synchronization in photosynthetic dimers is fundamentally rooted in electron‑phonon quantum correlations, not captured by semiclassical factorised models; (ii) a non‑Condon, environment‑assisted dipole modulation can sustain these correlations in driven‑dissipative conditions, providing a viable pathway for long‑lived coherence and efficient energy transfer; and (iii) experimental verification could be pursued by tuning vibrational mode frequencies or the intensity of the driving field to probe the predicted non‑Condon effects. This work advances the quantitative understanding of how quantum synchronization and vibronic coupling may be harnessed in natural photosynthetic systems.