Rodolfo Jalabert LA RESONANCE PLASMON DANS LES NANOPARTICULES METALLIQUES : un degré de liberté quantique couplé aux excitations électron-trou Rodolfo Jalabert expérimentateurs à Strasbourg: R. Molina (Madrid) G. Weick (Berlin) C. Seoánez (Madrid) G.-L. Ingold (Augsburg) D. Weinmann (Strasbourg) J.-Y. Bigot E. Beaurepaire V. Halté M. Vomir P.-A. Hervieux G. Manfredi Y. Yin

PLASMONS POUR TOUS ET PARTOUT Plasmons au début du XXème Plasmons dans les années 90 Plasmons pour les artisans de l’antiquité Plasmons pour les biologistes Plasmons pour les physiciens nucléaires Les autres plasmons Plasmons pour les ingénieurs (plasmonique) Plasmons pour la physique mésoscopique Plasmons et optique femto-seconde Plasmons comme excitations collectives Optique quantique avec les plasmons Plasmons et spins Conclusion et prospectives

Plasmons au début du XXème

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

Plasmons dans les années 90

PLASMON RESONANCE IN FREE CLUSTERS (visible) Photo-absorption cross section of Li clusters, small red-shift with increasing cluste size Bréchignac et al, PRL 1993

Plasmons pour les artisans de l’antiquité

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

Plasmons pour les biologistes

INTERACTION WITH THE LOCAL ENVIRONMENT d-electrons matrix Single-nanoparticle sensors Feldmann et al, Nano Letters 2007 Strong local dipole field Biological markers, tracking of individual receptors in neurons Dahan et al, Science 2003

Plasmons pour les physiciens nucléaires

GIANT DIPOLE RESONANCE Photo-absorption cross section of 12C nucleus

Les autres plasmons

BULK AND SURFACE PLASMONS Landau damping bulk plasmon, 3DEG Plasmon band, semiconductor multilayer surface plasmon 2D plasmon, 2DEG electron-hole excitations

Plasmonique = plasmons + optique

PLASMON PROPAGATION IN MICROSTRUCTURES Surface plasmon subwavelength optics Ebbesen et al, Nature 2003 Plasmon-based miniaturized optical elements

Plasmons pour la physique mésoscopique cohérence quantique interaction él-él dans un système confiné régime semi-classique a > λF évolution temporelle des systèmes finis décohérence et dissipation des états collectifs

SIZE-OSCILLATIONS OF THE LINEWIDTH Drude, τ‾1 confinement, a < τ vF Kawabata & Kubo, 1966 Doremus, J. Chem. Phys. 1965 Na Nonmonotonic behavior !! gamma^osc: rough estimation (curve: from numerical integration) in addition of gamma^0 Time-Dependent Local Density Approximation R.A. Molina et al., PRB 2002, EPJD 2003

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

SEMICLASSICAL APPROACH particle and hole angular-momentum-restricted DOS : in agreement with TDLDA calculations Experiments ? gamma^osc: rough estimation (curve: from numerical integration) in addition of gamma^0 Half-width for noble metals ? Temperature ? G. Weick et al., PRB 2005 & 2006

SPILL-OUT INDUCED RED-SHIFT TDLDA Bréchignac et al, PRL 1993 Lamb shift ? Jellium model ? \tilde omega_M: “zero-order approximation” Spill-out from from semiclassics Temperature ? TDLDA G. Weick et al., PRB 2006

Plasmons et optique femto-seconde Femto = la bonne échelle pour la dynamique électronique

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

ANOMALY CLOSE TO THE RESONANCE Emphasize the importance & relevance of this result G. Weick et al., EPL 2007

Description quantique du plasmon Plasmons comme excitations collectives Description quantique du plasmon

DISCRETE (MATRIX) RPA Hartree-Fock + Residual interaction : (symmetrized) Coulomb matrix element α, β, γ, and δ : single-particle (Hartree-Fock) states Separable residual interaction : Emphasize the importance & relevance of this result Diagonalization in the one-particle-hole basis (RPA) :

PLASMON AS A COLLECTIVE EXCITATION Landau damping γ and Lamb shift δ RPA eigenenergies : C. Seoánez et al., EPJ D 2007 TDLDA E S(E) Plasmon = superposition of low-energy e-h coupled to high-energy e-h Plasmon Emphasize the importance & relevance of this result Landau damping γ and Lamb shift δ

Optique quantique avec les plasmons

Rabi frequency system: plasmon, excitation: bath: high-energy e-h, REDUCED DENSITY MATRIX FOR THE PLASMON system: plasmon, center of mass, collective coordinate excitation: laser field Rabi frequency bath: high-energy e-h, relative coordinates density matrix of the electron gas H_cm: not a perfect harmonic oscillator (damping) H_cm: in one direction (z) Density matrix -> time-evolution, coherences, thermalization (Quantum Optics) But here: we restrict ourselves to the populations coupling: dipole field reduced density matrix (center of mass system) equation of motion for

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

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

Plasmons et spins

SPIN DIPOLE EXCITATION exchange-correlation Hartree = 0 exchange-correlation (local) kinetic: (Thomas-Fermi)

LOCAL APPROXIMATION FOR XC exchange correlation equilibrium charge TDLDA Spin-dipole frequency:

IS THE SPIN DIPOLE A COLLECTIVE EXCITATION ? HF + residual interaction S(E) ~ΔE1 Hartree-Fock HF + residual interaction \tilde omega_M: “zero-order approximation” the spin-dipole is an e-h excitation

Conclusion et prospectives

CONCLUSIONS PERSPECTIVES Plasmons in nanoparticles: many-body dynamics, quantum coherence, dissipation classical and quantum descriptions, collective excitation center of mass and relative coordinates mesoscopic effects: size-oscillations of the half-width coherence effects: time-dependence of the reduced DM 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