Quantum Dynamics of an Interacting Electron Gas in a Nanosphere

Plasmonic nanostructures provide a suitable environment for light-matter interaction on the nanoscale. The plasmonic excitation in the nanostructure generates hot electrons, with applications in chemistry, photovoltaics and... [ view full abstract ]

Plasmonic nanostructures provide a suitable environment for light-matter interaction on the nanoscale. The plasmonic excitation in the nanostructure generates hot electrons, with applications in chemistry, photovoltaics and photodetection devices. With the size of the nanoparticle becoming smaller and smaller, quantum effects will become increasingly important and the accuracy of classical models to describe the microscopic electronic structure is questionable. In this work, we study the optically generated many-particle dynamics using the density matrix formalism providing a quantum picture of the optical response of a metal nanosphere.

To describe the physical mechanism behind the short-lived non-equilibrium distribution, we use a microscopic density matrix theory. Our model describes a small nanosphere with discrete electronic states and analytic wave functions. The Hamiltonian takes into account both the Coulomb interaction between electrons and the interaction with an external electric field in dipole approximation. We analyse the linear optical response by exciting the partially filled few-electron system from the ground state with a weak short pulse. Specifically, we consider the case of 9 states, i.e., we take into account the lowest three s and p-shell states, filled with 5 electrons.

We calculate the total induced macroscopic polarisation from the light-induced coherences between states in the density matrix. The resulting spectra display discrete resonances which, for the non-interacting case, are dipole-allowed transitions between an empty and a filled electron state.

When the electron-electron interaction is included, the spectrum is blue-shifted and the discrete resonances cannot be associated with transitions between eigenstates of the interacting multi-level system, unlike in the non-interacting case. Studying the light-induced coherences between states in the frequency domain reveals that the Coulomb interaction mixes the response of the individual states, indicating the formation of a collective oscillation.

In conclusion, we calculated the optically-induced electron dynamics in a fully-interacting few-electron system by determining its effective dielectric susceptibility. We showed that the Coulomb interaction is an essential factor in shifting the spectrum and obtaining a collective response of the interacting electron-system. Our work paves the way towards the microscopic description for the formation of plasmons.