MQED-QD: An Open-Source Package for Quantum Dynamics Simulation in Complex Dielectric Environments

Abstract

Simulating the dynamics of molecular excitons in complex nanophotonic environments requires integrating rigorous electromagnetic simulations with accurate treatments of open quantum system dynamics. In this work, we develop MQED-QD (Macroscopic Quantum Electrodynamics for Quantum Dynamics), a robust computational package for simulating exciton dynamics in arbitrary dielectric and plasmonic environments. Based on the MQED framework, the package offers a unified workflow for constructing the dyadic Green's functions from classical electromagnetic solvers, parametrizing quantum master equations, and propagating the time evolution to determine the molecular subsystem's dynamical properties. To demonstrate the package's capabilities, we simulate exciton transport within a one-dimensional molecular chain near a silver nanostructure, including benchmarking against planar surfaces and exploring the influence of silver nanorods. Our results reveal that surface plasmon polaritons on nanorods dramatically enhance long-range dipole-dipole interactions, accelerating exciton delocalization and yielding higher participation ratios compared to planar geometries. By elucidating accurate molecular exciton dynamics in conjunction with nanophotonics and plasmonics, MQED-QD provides a powerful, open-source package that facilitates the rational design of nanoscale architectures.

Figures (6)

• Figure 1: The workflow of the MQED-QD package to investigate exciton transport in the presence of dielectric environments.
• Figure 2: The calibration of dipole moment intensity in BEM. (a)Geometry used for calibration: a $z-$oriented donor dipole located at $z=2$ nm above a planar silver surface. Electric fields are sampled at a set of observation (“acceptor”) points along $x$ at $z=3$ nm. Points within a minimum separation $d$ from the donor are excluded from the least-squares fit to reduce near-source numerical artifacts in MNPBEM. (b) Reconstruction accuracy (eq \ref{['Eq:accuracy']}) of the dyadic Green’s function as a function of the minimum donor–observation separation $d$ for three wavelengths ($\lambda=300, 665,\text{and}\ 1000$ nm)
• Figure 3: Exciton dynamics in molecular aggregates above silver surface with various heights. (a) Schematic illustration of molecular aggregates with 100 $z-$oriented emitters (H-aggregate) above an infinite silver planar surface. $h$ denotes the height of the aggregates. A single exciton is initialized at the emitter at $x=0$. $\mathbf{r}_{\alpha}$ indicates the response emitter position. Panel (b) shows the DDI ratio as a function of intermolecular separation ($\Delta{x}$) for different heights. The vertical red dashed line indicates the nearest-neighbor (NN) separation ($\Delta{x}=3~\text{nm}$) and the vertical green dashed line indicates the next nearest-neighbor separation ($\Delta{x}=6~\text{nm}$). Time evolution of the MSD (in panel c) and the PR (in panel d) as obtained by the Fresnel approach (dashed lines) and the BEM simulation (solid lines) for $h=2,5,8~\text{nm}$ (blue, orange, red). The two results are identical, which further demonstrates the accuracy of the reconstructed dyadic Green's function through the BEM simulations. Interestingly, we observe that, while the MSD is overall reduced as $h$ decreases, the PR can be enhanced for $h=2$ nm.
• Figure 4: Convergence of the electric field and Purcell factor above a silver nanorod. (a) Schematic illustration of the simulation setup where an oscillating dipole is located in the middle of the nanorod at height $h=8~\text{nm}$ and orientated in the $z$ direction. The length of the nanorod is $1000~\text{nm}$ and the radius is $10~\text{nm}$. (b) The Purcell factor of the dipole above the nanorod converges with the mesh size $N_\mathrm{mesh}$ (the maximum side length of a triangular boundary element in the BEM simulation). At a closed observation point at $\Delta x=3~\text{nm}$, The real part (c) and imaginary part (d) of $E_z$ also converge as the mesh size increases.
• Figure 5: Quantum dynamics of $N_\mathrm{M}=30$ molecular chain above a silver nanorod (radius $10~\mathrm{nm}$, length $1000~\mathrm{nm}$) with intermolecular separation $\Delta{x}=8~\mathrm{nm}$ and height $h=8~\mathrm{nm}$. (a) Mean-square displacement (MSD) as a function of time. (b) Participation ratio (PR) as a function of time. Solid blue: planar silver surface. Solid green: silver nanorod. Dashed curves show results obtained with a nearest-neighbor (NN) truncation of the intermolecular couplings for the corresponding geometry.