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Strong coupling between a metallic nanoparticle and a single molecule

Novotny group. Strong coupling between a metallic nanoparticle and a single molecule. Andi Trügler and Ulrich Hohenester Institut für Physik, Univ. Graz http://physik.uni-graz.at/~uxh. K. Hennessy et al., Nature 445 , 896 (2007). Atoms. Strong coupling. Cavity QED. Artificial atoms.

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Strong coupling between a metallic nanoparticle and a single molecule

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  1. Novotny group Strong coupling between a metallic nanoparticle and a single molecule Andi Trügler and Ulrich Hohenester Institut für Physik, Univ. Graz http://physik.uni-graz.at/~uxh

  2. K. Hennessy et al., Nature 445, 896 (2007). Atoms Strong coupling Cavity QED Artificial atoms

  3. gd ~ 1 / (10 fs)… but also g large (enhancement of gr and gnr) P. Anger et al., Phys. Rev. Lett. 96, 113002 (2006). Strong MNP - molecule coupling?

  4. Goal of this work Strong MNP – molecule coupling ? Agenda • - Quantum theory of surface plasmons1 • Open system dynamics for coupled MNP-molecule system • Results for spherical MNP and single molecule 1J. C. Ashley, T. L. Ferrell, and R. H. Ritchie, Phys. Rev. B 10, 554 (1974).

  5. Implicit dynamics Problem: Quantization of EM fields in presence of absorbing media ? Linear response: Fluctuation – dissipation theorem, microscopic dynamics hidden in e(w) or Gw Nonlinear response ? Explicit dynamics 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 ? Quantum mechanical MNP description

  6. Hot electron lifetimes Dielectric function I. G. Gurtubay et al., Phys. Rev. B 69, 245106 (2004). Johnson and Christy, Phys. Rev. B 6, 4370 (1972). Drude ab initio Free electrons, dielectric background e0 , plasmon damping g( w ) Drude description

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

  8. Eigenmodes Free electrons moving in dielectric background … eigenmode expansion1 1U. Hohenester and J. Krenn, Phys. Rev. B 72, 195429 (2004). Interaction Hamiltonian Coupling between molecule dipole and surface plasmons Surface plasmons

  9. 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 Quantum mechanical description

  10. Molecule excitation to auxiliary state 2 Internal relaxation to optically active state 1 Novotny group 2 1 quadrupole dipole hvexc 2´ 0 Molecule Plasmon Simulation setup Plasmon – mediated relaxation

  11. z Weak coupling For weak coupling (small molecule dipole) we can compare with Mie theory Diameter … 20 nm Transition energy … 2.3 eV Molecule-MNP coupling

  12. Strong coupling Molecule dipole moment for rhodamin 6G (15 Debye) Strong coupling ? Not for dipole, but only for higher modes ! Molecule-MNP coupling

  13. Hybrid plasmon - molecule mode Molecule Plasmon Fluorescence spectra Dipole mode driven by broadened hybrid plasmon - molecule mode

  14. d=2 nm d=3.5 nm Fluorescence decay

  15. Hybrid MNP – molecule modes Eigenstates of master equation provide polariton modes with complex energies Polaritons Anticrossing … strong coupling

  16. Summary • - Quantum theory of surface plasmons • Open system dynamics for coupled MNP-molecule system • Strong coupling between MNP and molecule is possible Outlook • - Different particle shapes and coupled MNPs • - Förster – type energy transfer • Superradiance of many molecules ?

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