Rodolfo Jalabert LA RESONANCE PLASMON DANS LES

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1 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

2 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

3 Plasmons au début du XXème

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

5 Plasmons dans les années 90

6 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

7 Plasmons pour les artisans de l’antiquité

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

9 Plasmons pour les biologistes

10 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

11 Plasmons pour les physiciens nucléaires

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

13 Les autres plasmons

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

15 Plasmonique = plasmons + optique

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

17 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

18 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

19 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

20 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

21 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

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

23 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

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

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

26 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) :

27 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

28 Optique quantique avec les plasmons

29 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

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

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

32 Plasmons et spins

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

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

35 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

36 Conclusion et prospectives

37 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