Optical signatures of coherence in molecular dimers

TL;DR

The paper tackles how to detect quantum coherence between two strongly vibronically coupled molecular emitters by introducing a polaron-frame master equation and mode-resolved, direction-specific photon measurements. By analyzing emission intensity and two-photon coincidences across different dimer geometries, it shows that cooperative signatures can be revealed via projective measurements even for orthogonal dipoles, and that coherent oscillations can arise in intermediate configurations when dipole coupling is nonzero. Temperature, disorder, and finite detector resolution are shown to modulate the visibility and lifetimes of these signatures, with robustness observed under realistic experimental conditions. The findings provide a practical framework for probing coherent dynamics in molecular dimers and guide future experiments on vibronic coherence in light-harvesting–like systems.

Abstract

We calculate experimentally measurable signatures of quantum correlations in a coupled molecular dimer that strongly interacts with its vibrational environment. We investigate intensity and mode-resolved photon coincidences for different relative orientations of such dimers, and observe spatio-temporal correlations for various configurations. We find that projective measurements can produce cooperative signatures even when emitters are arranged orthogonal to each other. To model effects of vibrational environments that are present in realistic experimental situations, we use the polaron framework. Further, we also account for the effects of finite instrument response, varying temperature, and presence of static disorder. We analyse the effect of disorder in both dimer orientation and measurement direction and find that photon coincidences remain well-resolvable using state-of-the-art detectors. This work enhances our understanding of cooperative emission from two coupled emitters and offers direction for future experiments on probing their coherent dynamics.

Figures (11)

• Figure 1: (a) Sketch of a photon coincidence measurement setup. The zoomed-in image shows a level scheme for a H-dimer (dipoles aligned parallel to each other resulting in a positive dipole interaction). The rate of incoherent sunlight pumping is given as $\gamma_{\text{photon}}$ and the rate of leakage into the dark state as $\gamma_{\text{phonon}}$. The bright and dark states are shown as $|B \rangle$ and $| D \rangle$ respectively. (b) This panel illustrates a photon detection direction which is associated with a certain mode $\boldsymbol{q}(\theta, \phi)$. Each such mode $\boldsymbol{q}$ of an emitted photon is associated with two polarisation directions $\boldsymbol{\lambda}_{1}$ and $\boldsymbol{\lambda}_{2}$.
• Figure 2: Illustration of decay pathways under mode-selective photon detection in optical modes $\boldsymbol{q}$ and $\boldsymbol{q}^{\prime}$. Blue arrows indicate transitions involving specific intermediate states $|\psi_{\boldsymbol{q}}^{(e)}\rangle$ and $|\psi_{\boldsymbol{q}^{\prime}}^{(g)}\rangle$, onto which the system is projected after photon emission. Unrealized decay channels are shown as red dashed arrows. These sets of intermediate states depend on the relative orientation of dimer dipoles and are equivalent only if the dipoles are identical. Panels (b) and (c) show energy level diagrams for transitions from the doubly excited state to the single-excitation manifold, and from there to the ground state, under detection of specific $\boldsymbol{q}$- and $\boldsymbol{q}^{\prime}$-modes. In contrast to (a), these are shown from the reduced system's perspective in the space of electronic states. Panel (d) shows emission intensity over time for different dipole orientations. Insets highlight level structures for H- and J-dimer configurations, marked by blue and red circles, respectively.
• Figure 3: (a) Two-photon coincidences for different dimer configurations with pumping rate $\gamma_{p} = \gamma$. (b and c) Photon coincidence for H- and J-dimers plotted for different reorganisation energies of the phonon bath.
• Figure 4: (a) Unnormalised second-order correlation $G^{(2)}(\infty, 0)$ and (b) normalised $g^{(2)}(\infty, 0)$ at zero time delay for an orthogonal dimer plotted as a function of the azimuthal angle $\phi$ (blue) and the spherical angle $\theta$ (red) in a polar plot. All angles are in radians. (c) Photon coincidence $g^{(2)}(\infty, \tau)$ plotted as a function of time-delay for different detection directions as indicated by the detector colour in the inset.
• Figure 5: Photon coincidence $g^{(2)}(\infty, \tau)$ for a $45\degree$ dimer. (a) Dependence on detection direction. The inset highlights coherent oscillations around $\tau \approx 0$, occurring at a frequency set by the renormalized dipole coupling $J_{1,2}^{\prime}$ (gray curve; see Appendix \ref{['sec:polaron_brme']}). (b) Dependence on vibrational reorganization energy $\lambda$. Increasing $\lambda$ leads to faster dephasing of coherent oscillations and a narrowing of the $g^{(2)}$ envelope around zero delay, reflecting a reduced electronic coherence lifetime. The dipole-dipole coupling strength of $7.8$ meV and $36.11$ meV in (b) correspond to dimer separation of $2$ nm and $1.2$ nm, respectively.