Strong coupling between a metallicnanoparticle and a single molecule

Andi Trügler and Ulrich Hohenester

Institut für Physik, Univ. Grazhttp://physik.uni-graz.at/~uxh

Novotny group

Cavity QED

Atoms

Artificial atoms

Strong coupling

K. Hennessy et al., Nature 445, 896 (2007).

d ~ 1 / (10 fs) … but also g large (enhancement of r and nr)

Strong MNP - molecule coupling?

P. Anger et al., Phys. Rev. Lett. 96, 113002 (2006).

- Quantum theory of surface plasmons1

- Open system dynamics for coupled MNP-molecule system- Results for spherical MNP and single molecule

Goal of this work

Strong MNP – molecule coupling ?

Agenda

1J. C. Ashley, T. L. Ferrell, and R. H. Ritchie, Phys. Rev. B 10, 554 (1974).

Quantum mechanical MNP description

Implicit dynamics

Explicit dynamics

Problem: Quantization of EM fields in presence of absorbing media ?

Linear response: Fluctuation – dissipation theorem,microscopic dynamics hidden in () or G

Nonlinear response ?

Use Drude model to describe electron dynamics in MNPs

Advantage: Quantization of surface plasmons (nonlinear response OK)

Is Drude description appropriate for Au or Ag ?

Drude description

Hot electron lifetimes Dielectric function

Drudeab initio

I. G. Gurtubay et al., Phys. Rev. B 69, 245106 (2004). Johnson and Christy, Phys. Rev. B 6, 4370 (1972).

Free electrons, dielectric background 0 , plasmon damping ( )

Surface plasmons

Eigenmodes

Free electrons moving in dielectric background … eigenmode expansion1

1U. Hohenester and J. Krenn, Phys. Rev. B 72, 195429 (2004).

Quantization

Electron current density described in terms of velocity potential ( r )2

2J. C. Ashley, T. L. Ferrell, and R. H. Ritchie, Phys. Rev. B 10, 554 (1974).

Surface plasmons

Free electrons moving in dielectric background … eigenmode expansion1

1U. Hohenester and J. Krenn, Phys. Rev. B 72, 195429 (2004).

Eigenmodes

Interaction Hamiltonian

Coupling between molecule dipole and surface plasmons

Quantum mechanical description

Hamilton operator

Molecule, quantized surface plasmons, interaction, light – matter coupling

Master equation

Lindblad form1 for environement coupling (plasmon damping, photons)1Walls and Milburn, Quantum Optics (Springer, Berlin, 1995).

Fluoresence spectra computed through quantum – regression theorem

dipolequadrupole

PlasmonMolecule0

1

2

2´

hvexc

Simulation setup

Molecule excitation to auxiliary state 2

Internal relaxation to opticallyactive state 1

Plasmon – mediated relaxation

Novotny group

Molecule-MNP coupling

z

Diameter … 20 nmTransition energy … 2.3 eV

Weak coupling

For weak coupling (small molecule dipole) we can compare with Mie theory

Molecule-MNP coupling

Strong coupling

Molecule dipole moment for rhodamin 6G (15 Debye)

Strong coupling ?Not for dipole, but only for higher modes !

Fluorescence spectra

PlasmonMolecule

Dipole mode driven by broadenedhybrid plasmon - molecule mode

Hybrid plasmon - molecule mode

d=3.5 nm

d=2 nm

Fluorescence decay

Polaritons

Hybrid MNP – molecule modes

Eigenstates of master equation provide polariton modes with complex energies

Anticrossing … strong coupling

- Quantum theory of surface plasmons- Open system dynamics for coupled MNP-molecule system- Strong coupling between MNP and molecule is possible

Summary

- Different particle shapes and coupled MNPs- Förster – type energy transfer- Superradiance of many molecules ?

Outlook