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

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

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

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

Single-nanoparticle sensors d-electronsmatrix Feldmann et al, Nano Lett Plasmon-based miniaturized optical elements PLASMONICS PLASMONICS BIOLOGY BIOLOGY Interaction with the local environment

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

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

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

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

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

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

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

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

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

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

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

dipole absorption cross-section SPIN DIPOLE EXCITATION

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

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

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

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

CONCLUSIONS CONCLUSIONS PERSPECTIVES 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 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