Signatures of coherent energy transfer and exciton delocalization in time-resolved optical cross correlations
Abstract
We investigate how optical second-order cross correlations witness the quantum features of a prototype donor-acceptor light-harvesting unit. By considering a pair of detuned two-level emitters electronically coupled and incoherently driven to a non-equilibrium steady-state, we gain insight into how electronic quantum properties such as exciton eigenstate delocalization, coherent energy transfer and steady-state electronic coherence, are manifested in the joint probability of emission or optical second-order cross correlation. Specifically, we show that the frequency associated with oscillations present in time-resolved second-order cross correlation functions quantifies not only the time scale of coherent energy transfer but also the degree of delocalization of the exciton eigenstates. Furthermore, we show that time-resolved cross correlations directly witness steady-state electronic coherence. Our work strengthens the idea that measurements of the intensity quantum cross correlations can provide distinctive signatures of the quantum behavior of biophysical emitters.
Summary
This paper investigates how time-resolved optical second-order cross correlations can reveal quantum features in a donor-acceptor light-harvesting unit. The authors model the unit as a pair of detuned, electronically coupled two-level emitters incoherently driven to a non-equilibrium steady-state. The primary research question is how exciton delocalization, coherent energy transfer, and steady-state electronic coherence manifest in the joint probability of photon emission, as captured by the time-resolved second-order cross correlation function. The authors employ a quantum master equation approach within the Born-Markov approximation to describe the system's dynamics, including radiative decay and incoherent pumping. They derive semi-analytical expressions for the time-resolved cross correlation function and relate its features to the system's quantum properties. They analyze how the frequency of oscillations in the cross correlation function relates to the timescale of coherent energy transfer and the degree of exciton delocalization. They also define a figure of merit for the time asymmetry of the cross correlations and demonstrate its correlation with steady-state electronic coherence. The key finding is that time-resolved cross correlations can serve as a distinctive signature of quantum behavior in biophysical emitters. The oscillation frequency in the cross correlation reveals the time scale of coherent energy transfer and the degree of exciton delocalization. The time asymmetry in the cross correlation directly witnesses steady-state electronic coherence. These results are significant because they offer a potential experimental probe to identify and quantify quantum features in light-harvesting complexes, which are crucial for understanding photosynthetic efficiency.
Key Insights
- •The frequency of oscillations (ω) in the time-resolved second-order cross correlation function is directly related to the exciton energy gap (∆E) and the degree of exciton delocalization, especially under imbalanced pumping conditions (γo ≠ 0). Specifically, ω = ∆E * sqrt{1 - (γo/∆E)^2 * sin^2(2θ)/2} + O((γo/∆E)^4), where θ is the mixing angle quantifying delocalization.
- •For completely delocalized excitons (θ = π/4), population oscillations are suppressed and exponentially damped when γo ≥ ∆E.
- •The time asymmetry of the second-order cross correlation function is positively correlated with the steady-state electronic coherence, quantified by the introduced asymmetry parameter A = γ * integral[0,inf] dτ |g^(2)_12(τ) - g^(2)_21(τ)|.
- •Under balanced pumping (γo = 0), the second-order cross correlation function is symmetric and simplifies to g^(2)_12(τ) = 1 - exp(-γe|τ|) * sin^2(2θ) * sin^2(∆Eτ/2). This shows a clear dependence of the oscillation amplitude on the mixing angle θ.
- •The authors demonstrate that the cross-correlation function provides a stronger witness to the collective behavior within the dimer compared to individual emitter auto-correlations, as it is less restricted by the timescale of emitter repopulation.
- •The analysis assumes a Born-Markov master equation, implying weak coupling to the environment and neglecting memory effects. The paper also focuses on a simple heterodimer model, which may not fully capture the complexity of real light-harvesting complexes.
- •The study considers weak incoherent pumping to simulate physiological conditions, but the results might differ under strong or coherent driving.
Practical Implications
- •This research suggests that time-resolved measurements of intensity cross correlations can be used to experimentally probe and quantify quantum features like exciton delocalization and steady-state coherence in light-harvesting complexes.
- •Biophysicists and chemists studying photosynthesis can use these findings to design and interpret experiments aimed at understanding the role of quantum coherence in energy transfer processes.
- •The analysis can be extended to more complex models of light-harvesting systems to investigate the robustness of these signatures in more realistic scenarios. Future research could explore the impact of non-Markovian environments and structured phonon modes on the observed cross correlations.
- •Engineers working on artificial light-harvesting systems can potentially use the insights from this work to optimize the design of these systems for efficient energy transfer by manipulating the degree of exciton delocalization and coherence.
- •The theoretical framework developed in this paper can be applied to other quantum emitter systems, such as quantum dots or superconducting qubits, to investigate the role of quantum coherence in their optical properties.