Entanglement and entangling power of the dynamics in light-harvesting complexes

We study the evolution of quantum entanglement during exciton energy transfer (EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a biological pigment-protein complex involved in the early steps of photosynthesis in sulphur bacteria. The influence of Markovian, as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct chromophores (site entanglement) and different excitonic eigenstates (mode entanglement) is studied for different injection mechanisms, including thermal and coherent laser excitation. Additionally, we study the entangling power of the FMO complex under natural operating conditions. While quantum information processing tends to favor maximal entanglement, near unit EET is achieved as the result of an intricate interplay between coherent and noisy processes where the initial part of the evolution displays intermediate values of both forms of entanglement.

💡 Research Summary

This paper presents a comprehensive quantum‑dynamical study of exciton energy transfer (EET) in the Fenna‑Matthews‑Olson (FMO) light‑harvesting complex, focusing on the generation, evolution, and functional role of quantum entanglement. The authors model the seven chromophoric sites of the FMO complex as a network of two‑level systems (qubits) coupled by dipolar interactions. The coherent part of the dynamics is described by a Hamiltonian containing site energies ωj and inter‑site couplings vj,l. Dissipative loss and pure dephasing are incorporated via Lindblad operators with rates Γj and γj, guaranteeing complete positivity of the dynamical map and allowing the use of logarithmic negativity as a reliable entanglement measure.

To explore the impact of environmental structure beyond the usual Markovian approximation, two non‑Markovian bath models are introduced. In the first “local‑bath” model each site couples linearly to a resonant harmonic mode of strength gj; each mode is damped into a zero‑temperature reservoir with rate κj. By varying the ratio g/κ (parameterised by a scaling factor f), the authors can continuously interpolate between a strongly damped, effectively Markovian regime (f≫1) and a regime with long environmental memory (f≪1). A second model (not detailed in the excerpt) treats the sites as coupled to a common structured bath, emphasizing the role of spectral density and correlation time.

Entanglement is quantified by the logarithmic negativity E(A|B)=log2‖ρΓA‖1. In the single‑excitation subspace this reduces to a compact expression involving the off‑diagonal coherences aij between sites i and j and the ground‑state population a00. The authors stress that non‑zero coherences are a prerequisite for any bipartite entanglement, but that entanglement is a stricter resource than mere coherence.

Numerical simulations reveal several key findings. In the purely Markovian limit, with optimal dephasing rates (as identified in earlier work), site‑site entanglement rises sharply within ~200 fs, reaches a modest peak, and then decays rapidly, while the transfer efficiency to the sink (site 8) approaches ~90 %. When the system is placed in the non‑Markovian regime (low f, i.e., strong system‑mode coupling and weak mode damping), the entanglement peak is higher and persists longer. Remarkably, the transfer efficiency also shows a non‑monotonic dependence on f, attaining its maximum around f≈1, where the environment provides enough memory to sustain coherence without trapping the excitation. This demonstrates the “environment‑assisted transport” concept: optimal transport does not correspond to either purely coherent or purely incoherent dynamics but to a balanced interplay.

The authors also examine entanglement across different bipartitions (e.g., (1…i)|(i+1…7)). Early in the dynamics, small partitions involving the initially excited site exhibit the strongest entanglement, reflecting the localized nature of the excitation. As time progresses, entanglement spreads more uniformly across the network, mirroring the physical diffusion of excitonic population.

Beyond passive dynamics, the paper introduces the notion of “entangling power” of the FMO evolution: the average amount of entanglement generated by the quantum map when acting on various initial states (thermal versus coherent laser excitation). Thermal (natural‑light) initial conditions produce modest entangling power, whereas coherent laser preparation yields a pronounced initial surge of entanglement that can be maintained by non‑Markovian baths. This analysis underscores that, unlike quantum information processing where maximal entanglement is the goal, biological EET operates optimally with intermediate entanglement combined with appropriate dephasing. Entanglement serves as a diagnostic of coherent pathways, but the functional advantage lies in the temporal overlap between the entangled window and the energy‑transfer pathway.

In conclusion, the study provides a quantitative link between environmental correlations, entanglement dynamics, and exciton transport efficiency in a prototypical photosynthetic complex. It shows that non‑Markovian noise can enhance both entanglement longevity and transfer yield, and that the “entangling power” of the natural dynamics is modest yet sufficient to support high‑efficiency energy transport. These insights suggest design principles for artificial light‑harvesting systems: engineered environments with tunable memory times could be exploited to balance coherence and noise, thereby achieving optimal performance without requiring maximal quantum correlations.