Strong coupling between a metallic nanoparticle and a single molecule Andi Trügler and Ulrich Hohenester Institut für Physik, Univ. Graz 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, (2006).

- Quantum theory of surface plasmons 1 - Open system dynamics for coupled MNP-molecule system - Results for spherical MNP and single molecule Goal of this work Strong MNP – molecule coupling ? Agenda 1 J. 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 lifetimesDielectric function Drude ab initio I. G. Gurtubay et al., Phys. Rev. B 69, (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 expansion 1 1 U. Hohenester and J. Krenn, Phys. Rev. B 72, (2004). Quantization Electron current density described in terms of velocity potential  ( r ) 2 2 J. C. Ashley, T. L. Ferrell, and R. H. Ritchie, Phys. Rev. B 10, 554 (1974).

Surface plasmons Free electrons moving in dielectric background … eigenmode expansion 1 1 U. Hohenester and J. Krenn, Phys. Rev. B 72, (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 form 1 for environement coupling (plasmon damping, photons) 1 Walls and Milburn, Quantum Optics (Springer, Berlin, 1995). Fluoresence spectra computed through quantum – regression theorem

dipole quadrupole PlasmonMolecule ´ hv exc Simulation setup Molecule excitation to auxiliary state 2 Internal relaxation to optically active state 1 Plasmon – mediated relaxation Novotny group

Molecule-MNP coupling z Diameter … 20 nm Transition 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 broadened hybrid 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