Rodolfo Jalabert

1. CHARGE AND SPIN DIPOLE RESONANCES IN METALLIC NANOPARTICULES : collective versus single-particle excitations Rodolfo Jalabert D. Weinmann P.-A. Hervieux G. Manfredi Y. Yin R. Molina (Madrid) G. Weick (Berlin) C. Seoánez (Madrid) G.-L. Ingold (Augsburg)

2. MIE THEORY On the color of gold colloids - 1908 λ >> 2a in a metal: resonance pour surface plasmon

3. ABSORPTION AND SCATTERING BY SMALL PARTICLES Lycurgus cup, 4th century AD

4. Plasmon resonance in free clusters (visible) Bréchignac et al, PRL 1993 Photo-absorption cross section of 12C nucleus

5. Interaction with the local environment BIOLOGY d-electrons matrix Single-nanoparticle sensors Feldmann et al, Nano Lett. 2007 PLASMONICS Plasmon-based miniaturized optical elements

6. COLLECTIVE AND RELATIVE COORDINATES relative coordinates:mean field center of mass: harmonic oscillator One-particle potential: uniform jellium background with a Coulomb tail plasmon coupling:dipole field

7. Drude, τ‾1 confinement, a<τvF SIZE-OSCILLATIONS OF THE LINEWIDTH Kawabata & Kubo, 1966 Na Nonmonotonic behavior !! Time-Dependent Local Density Approximation R.A. Molina et al., PRB 2002, EPJD 2003

8. Doremus, J. Chem. Phys. 1965 SEMICLASSICAL APPROACH particle and hole angular-momentum-restricted DOS Semiclassics in the radial problem: TDLDA calculations? Experiments? Half-width for noble metals? Temperature? G. Weick et al., PRB 2005 & 2006

9. TDLDA SPILL-OUT INDUCED RED-SHIFT Bréchignac et al, PRL 1993 Lamb shift ? Jellium model ? Spill-out from from semiclassics Temperature ? TDLDA G. Weick et al., PRB 2006

10. (ps) ps (eV) ps ps ps TIME RESOLVED EXPERIMENTS, POMP-PROBE Differential transmission correlated electrons collective modes nonthermal regime energy transfer to the matrix e-phonons scattering relaxation to the lattice cooling of the distribution e-e & e-surface scattering, thermal distribution Slowdown of relaxation at the resonance ! Bigot et al., Chem. Phys., 2000

11. ANOMALY CLOSE TO THE RESONANCE G. Weick et al., EPL 2007

12. S(E) E MATRIX RPA DESCRIPTION OF THE PLASMON HF + Residual interaction : α, β, γ, and δ : single-particle HF states Separable residual interaction : Plasmon

13. PLASMON AS A COLLECTIVE EXCITATION C. Yannouleas, R.A. Broglia, Ann. Phys. (N.Y.) 217, 105 (1992) RPA eigenenergies : C. Seoánez et al., EPJ D 2007 restricted subspace additional subspace Plasmon= superposition of low-energy e-h coupled to high-energy e-h

14. REDUCED DENSITY MATRIX FOR THE PLASMON excitation: laser field system: plasmon, center of mass, collective coordinate Rabi frequency bath: high-energy e-h, relative coordinates density matrix of the electron gas coupling: dipole field reduced density matrix (center of mass system) equation of motion for

15. BLOCH EQUATIONS FOR THE PLASMON free evolution coupling (perturbation) correlation function of the bath: Markovian approximation justified populations coherence

16. COHERENCE EFFECTS FOR THE PLASMON G. Weick et al., EPJ D 2007

17. SPIN DIPOLE EXCITATION dipole absorption cross-section

18. LOCAL DENSITY APPROXIMATION Hartree = 0 kinetic: exchange-correlation: Spin-dipole frequency:

19. SPIN DIPOLE FREQUENCY Spill-out correction: TDLDA Non uniform ground-state density Equilibrium under external field:

20. S(E) E IS THE SPIN DIPOLE A COLLECTIVE EXCITATION ? ~ΔE1 Hartree-Fock HF + residual interaction the spin-dipole is an e-h excitation

21. COUPLED MODES IN OPEN-SHELL CLUSTERS charge dipole excitation SD SP

22. CONCLUSIONS Plasmons in nanoparticles: many-body dynamics, quantum coherence, dissipation classical and quantum descriptions, collective excitation mesoscopic effects: size-oscillations of the half-width electronic dynamics in pump-and-probe experiments PERSPECTIVES Driven nanoparticles: quantum coherence effects, sidebands in the absorption Plasmonics: plasmon interaction and transfer between nano-objects Spin effects: spin-dipole excitation, coupling of charge and spin Magnetic nanoparticles: fast dynamics of the magnetization, collective excitations