Quantum dissipation and decoherence of collective excitations in metallic nanoparticles

The excitation of a nanoparticle by a laser pulse creates a collective mode of the electrons, the so-called surface plasmon. It decays because of surface effects and electron-electron interactions, creating particle-hole excitations (Landau damping). The thermal equilibrium of the electronic system is reached after about hundred femtoseconds, and only on a much larger time scale, the electron-phonon interactions permit the relaxation of the electronic energy to the ionic lattice. Throughout this work we treat the metallic nanoparticle in the jellium approximation where the ionic structure is replaced by a continuous and homogeneous positive charge. Such an approximation allows to decompose the electronic Hamiltonian into a part associated with the electronic center of mass, a part describing the relative coordinates (treated here in the mean-field approximation), and finally a coupling between the two subsystems. The external laser field puts the center of mass into a coherent superposition of its ground and first excited state and thus creates a surface plasmon. The coupling between the center of mass and the relative coordinates causes decoherence and dissipation of this collective excitation. We have developed a theoretical formalism well adapted to the study of this dissipation, which is the reduced-density-matrix formalism. Within the Markovian approximation, one is then able to solve analytically or numerically the corresponding equations. There are mainly two parameters which govern the surface plasmon dynamics: the decay rate of the plasmon, and the resonance frequency. An experimentally accessible quantity is the photoabsorption cross section of the metallic cluster, where the surface plasmon excitation appears as a broad resonance spectrum. The width of the plasmon resonance peak is a quantity that one can determine in different manners. A numerical approach consists of the resolution of the time-dependent Kohn-Sham equations in the local density approximation. This yields the absorption spectrum for a ...