Rodolfo Jalabert

LA RESONANCE PLASMON DANS LES NANOPARTICULES METALLIQUES : un degré de liberté quantique couplé

aux excitations électron-trou

R. Molina (Madrid)G. Weick (Berlin)C. Seoánez (Madrid)G.-L. Ingold (Augsburg)D. Weinmann (Strasbourg)

J.-Y. BigotE. BeaurepaireV. HaltéM. Vomir

P.-A. HervieuxG. ManfrediY. Yin

expérimentateurs à Strasbourg:

• 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 POUR TOUS ET PARTOUT

• Plasmons au début du XXème

in a metal:

MIE THEORY On the color of gold colloids -

1908

λ >> 2a

resonance pour surface plasmon

• Plasmons dans les années 90

Bréchignac et al, PRL 1993

Photo-absorption cross section of Li clusters,small red-shift with increasing cluste size

PLASMON RESONANCE IN FREE CLUSTERS

(visible)

• Plasmons pour les artisans de l’antiquité

Lycurgus cup, 4th century AD

Chartres cathedral

ABSORPTION AND SCATTERING BY SMALL PARTICLES

• Plasmons pour les biologistes

INTERACTION WITH THE LOCAL ENVIRONMENT

Single-nanoparticle sensors

d-electrons matrix

Feldmann et al, Nano Letters 2007

Biological markers,tracking of individual receptors in neurons

Strong local dipole field

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

bulk plasmon, 3DEG

2D plasmon, 2DEG

electron-hole excitations

Plasmon band, semiconductor multilayer

surface plasmon

Landau damping

= plasmons + optique

• Plasmonique

Plasmon-based miniaturized optical elements

Surface plasmon subwavelength optics

PLASMON PROPAGATION IN MICROSTRUCTURES

Ebbesen et al, Nature 2003

• 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

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

Drude, τ‾1

confinement, a < τ vF

Doremus, J. Chem. Phys. 1965

One-particle potential: uniform

jellium background with a

Coulomb tail

COLLECTIVE AND RELATIVE COORDINATES

center of mass: harmonic oscillator

plasmon

relative coordinates: mean field

coupling: dipole field

particle and hole angular-momentum-restricted DOS :

G. Weick et al., PRB 2005 & 2006

in agreement with TDLDA calculations

SEMICLASSICAL APPROACH

Temperature ?

Experiments ?

Half-width for noble metals ?

TDLDA

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

• Plasmons et optique femto-seconde

Femto = la bonne échelle pour la dynamique électronique

Differential transmission

Bigot et al., Chem. Phys., 2000

(ps)

(eV)

pscorrelated electrons

collective modesnonthermal regime

e-e & e-surface scattering,

thermal distribution

e-phonons scatteringrelaxation to the lattice

cooling of the distribution

energy transfer to the matrix

TIME RESOLVED EXPERIMENTS, POMP-PROBE

pspspsSlowdown of

relaxation at the resonance !

ANOMALY CLOSE TO THE RESONANCE

G. Weick et al., EPL 2007

• Plasmons comme excitations

collectivesDescription quantique du

plasmon

DISCRETE (MATRIX) RPA

Hartree-Fock + Residual interaction :

α, β, γ, and δ : single-particle (Hartree-Fock) states

(symmetrized) Coulomb matrix element

Separable residual interaction :

Diagonalization in the one-particle-hole basis (RPA) :

PLASMON AS A COLLECTIVE EXCITATION

RPA eigenenergies :

C. Seoánez et al., EPJ D 2007

Plasmon = superposition of low-energy e-h coupled to

high-energy e-h

Landau damping γ and Lamb shift δ

Plasmon

E

S(E)TDLDA

• Optique quantique avec les plasmons

reduced density matrix (center of mass system)

REDUCED DENSITY MATRIX FOR THE PLASMON

Rabi frequency

system: plasmon, center of mass,

collective coordinate

bath: high-energy e-h,relative coordinates

coupling: dipole field

excitation: laser field

density matrix of the electron gas

equation of motion for

Markovian approximation justified

BLOCH EQUATIONS FOR THE PLASMON

free evolution coupling (perturbation)

correlation function of the bath:

populations

coherence

COHERENCE EFFECTS FOR THE PLASMON

G. Weick et al., EPJ D 2007

• Plasmons et spins

kinetic: (Thomas-Fermi)

SPIN DIPOLE EXCITATION

exchange-correlation(local)

Hartree = 0

exchange correlation

Spin-dipole frequency:

equilibrium charge

LOCAL APPROXIMATION FOR XC

TDLDA

IS THE SPIN DIPOLE A COLLECTIVE EXCITATION ?

E

S(E)

Hartree-Fock

HF + residual interaction

~ΔE

1

the spin-dipole is an e-h excitation

• Conclusion et prospectives

CONCLUSIONS

PERSPECTIVES

Driven nanoparticles: quantum coherence effects, sidebands in the

absorptionPlasmonics: plasmon interaction and transfer between nano-objectsSpin effects: spin-dipole excitation, coupling of charge and spinMagnetic nanoparticles:

fast dynamics of the magnetization, collective excitations

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