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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. - PowerPoint PPT Presentation
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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
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