Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantum-Electrodynamical Time-Dependent Density Functional Theory Description of Molecules Interacting with Light

Yetmgeta Aklilu, Tiany Yang, Cody Covington, Kalman Varga

TL;DR

This work develops a real-time quantum electrodynamical TDDFT framework in the velocity gauge based on the Pauli–Fierz Hamiltonian to model light–matter coupling in a single-mode cavity. Using a tensor-product KS representation and a dipole-approximate single-mode description, it demonstrates that a delta-kick excitation on one molecule can induce coherent dynamics in a distant, initially unexcited molecule via the shared quantized field, with strong dependence on molecular orientation and species. The key contribution is a first-principles, nonperturbative approach that reveals photon-mediated energy transfer and synchronization across diverse molecular dimers, providing mechanistic insight into cavity-controlled energy transport and nonlocal excitation control. The results establish a scalable framework that can be extended to multimode cavities, larger assemblies, and dissipative environments, with potential applications in cavity-enabled chemistry and ultrafast quantum control.

Abstract

We study light-mediated interactions between spatially separated molecules using real-time quantum electrodynamical time-dependent density functional theory based on the Pauli-Fierz Hamiltonian. An ultrashort delta-kick excitation selectively perturbs a single molecule, while a second, distant molecule remains initially unexcited. In free space, the excitation stays localized and no response is observed in the second molecule. In contrast, when both molecules are coupled to the same cavity mode, the initial excitation induces coherent dynamics in the distant molecule through the shared quantized electromagnetic field.

Quantum-Electrodynamical Time-Dependent Density Functional Theory Description of Molecules Interacting with Light

TL;DR

This work develops a real-time quantum electrodynamical TDDFT framework in the velocity gauge based on the Pauli–Fierz Hamiltonian to model light–matter coupling in a single-mode cavity. Using a tensor-product KS representation and a dipole-approximate single-mode description, it demonstrates that a delta-kick excitation on one molecule can induce coherent dynamics in a distant, initially unexcited molecule via the shared quantized field, with strong dependence on molecular orientation and species. The key contribution is a first-principles, nonperturbative approach that reveals photon-mediated energy transfer and synchronization across diverse molecular dimers, providing mechanistic insight into cavity-controlled energy transport and nonlocal excitation control. The results establish a scalable framework that can be extended to multimode cavities, larger assemblies, and dissipative environments, with potential applications in cavity-enabled chemistry and ultrafast quantum control.

Abstract

We study light-mediated interactions between spatially separated molecules using real-time quantum electrodynamical time-dependent density functional theory based on the Pauli-Fierz Hamiltonian. An ultrashort delta-kick excitation selectively perturbs a single molecule, while a second, distant molecule remains initially unexcited. In free space, the excitation stays localized and no response is observed in the second molecule. In contrast, when both molecules are coupled to the same cavity mode, the initial excitation induces coherent dynamics in the distant molecule through the shared quantized electromagnetic field.
Paper Structure (17 sections, 35 equations, 14 figures)

This paper contains 17 sections, 35 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Formalism
  3. Pauli--Fierz Hamiltonian in Velocity Gauge
  4. Single--Mode Truncation in Velocity Gauge
  5. Single--Mode PF--KS Hamiltonian
  6. Dipole (Long--Wavelength) Approximation
  7. Dipole-Approximate Single--Mode PF--KS Hamiltonian
  8. Tensor-Product KS Ansatz
  9. Physical quantities
  10. Time propagation
  11. Results
  12. Nitrobenzene in cavity coupled to light
  13. Two formaldehyde molecules coupled by light
  14. Two HF molecules coupled by light
  15. Two CO molecules coupled by light
  16. ...and 2 more sections

Figures (14)

  • Figure 1: Temporal dynamics of nitrobenzene's dipole moment. Solid line: cavity-coupled molecule; dashed line: uncoupled molecule in vacuum (magnified by 100 for clarity). $\lambda=0.005$ a.u. and $\omega=$ 0.289 a.u. is used in the calculations.
  • Figure 2: Snapshots of the charge density difference between the excited state and the ground state. Left panel: molecule in vacuum; right panel: molecule in an optical cavity. All parameters are identical to those used in Fig. \ref{['fig:nitro_dp']}. The three shades of magenta represents values of -0.00002,-0.00001,0.00002 electrons/$\Delta x^3$ ranging from the lightest to the darkest.
  • Figure 3: Formaldehyde dimer configuration: cavity frequency $\omega$ = 0.289, light-matter coupling strength $\lambda$ = 0.005. The light polarization vector is aligned along the O-C bond direction of each molecule, with the O-C axes positioned perpendicular to the z-axis that connects the two carbon centers.
  • Figure 4: Temporal evolution of dipole moment changes relative to ground state values for the formaldehyde dimer.
  • Figure 5: Temporal evolution of (a) photon occupation number P$_1$ of the $\vert 1 \langle$ space, (b) dipole moment, (c) photon coordinate and (d) energies of the formaldehyde dimer. The solid black line shows the dynamics of the left, kicked molecule, the dashed red line represents the right initially unperturbed system.
  • ...and 9 more figures