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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
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?
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).
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
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
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
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
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
Molecule excitation to auxiliary state 2
Internal relaxation to optically
active state 1
Novotny group
2
1
quadrupole
dipole
hvexc
2´
0
Molecule
Plasmon
Plasmon – mediated relaxation
Simulation setup
Weak coupling
For weak coupling (small molecule dipole) we can compare with Mie theory
Diameter
… 20 nm
Transition energy … 2.3 eV
z
Molecule-MNP coupling
Strong coupling
Molecule dipole moment for rhodamin 6G (15 Debye)
Strong coupling ?
Not for dipole, but only for higher modes !
Molecule-MNP coupling
Hybrid plasmon - molecule mode
Molecule
Dipole mode driven by broadened
hybrid plasmon - molecule mode
Plasmon
Fluorescence spectra
d=2 nm
d=3.5 nm
Fluorescence decay
Hybrid MNP – molecule modes
Eigenstates of master equation provide polariton modes with complex energies
Anticrossing … strong coupling
Polaritons
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 ?