Signatures of coherent energy transfer and exciton delocalization in time-resolved optical cross correlations

TL;DR

The study investigates whether time-resolved optical second-order cross correlations can reveal quantum features in a donor-acceptor heterodimer modeled as two detuned, electronically coupled two-level emitters with incoherent pumping. By deriving a Lindblad master equation and semi-analytical expressions for steady-state populations and coherences, the authors show that the cross correlations exhibit oscillations at the exciton gap $ΔE$, with amplitude set by exciton delocalization through the mixing angle $θ$, and that pumping imbalance induces time asymmetry linked to steady-state coherence. The frequency shift of the correlations directly encodes exciton delocalization, while the symmetry or asymmetry of the correlations provides a witness for steady-state coherence, offering a practical spectroscopic probe of quantum effects in biomolecular emitters. The results remain relevant under realistic environmental conditions and connect coherent energy transfer, exciton delocalization, and steady-state coherence to measurable photon statistics.

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.

Figures (7)

• Figure 1: Level structure of the site basis states. One-way arrows indicate incoherent pathways between the site states of the system that arise due to radiative decay and incoherent pumping of the electronic states.
• Figure 2: Participation ratio as a function of the mixing angle. The inset shows the mixing angle as a function of the ratio $2V/\delta$, as determined by Eq. (\ref{['eq:mixing_angle']}). For $\theta = 0$ the excitons will be completely localized to a single site and for $\theta = \pm\frac{\pi}{4}$ the excitons will be completely delocalized across both sites.
• Figure 3: steady-state populations in the site basis as a function of the electronic coupling strength $V$ scaled by the transition frequency $\nu_1$. Here we have set $\delta = \gamma_e = 0.25$, $P_2 = 0$ and $\frac{P_1}{2\gamma} = \frac{1}{3}$. For uncoupled emitters we have the steady-state populations to be completely determined by the radiative rates. As the coupling strength increases, the second site becomes populated leading to non-zero electronic coherence in the steady-state (see Eq. (\ref{['eq:SteadyStateCoherence']})). In the strong coupling limit, i.e. $V\rightarrow\infty$, site populations reach the same value thereby leading to a vanishing steady-state coherence.
• Figure 4: Graph of $\omega/\Delta E$ as a function of $\gamma_o/\Delta E$ as determined by Eq. (\ref{['Eq:MainFreq']}). The dashed line corresponds to the case $\theta=\frac{\pi}{4}$ whilst the solid line corresponds to $\theta = \frac{\pi}{8}$. The dotted line is the limit of $\omega$ when $\gamma_o$ tends towards infinity and is determined as $\frac{\delta}{\Delta E}$.
• Figure 5: The figure shows $\omega$ scaled by the exciton energy gap as a function of the mixing angle $\theta$. The lines represent the deviation of $\omega$ away from $\Delta E$ as a function of $\theta$ for several values of $\frac{\gamma_o}{\Delta E}$, as indicated by the legend.