Strong coupling and molecular plasmonics
Javier Aizpurua
http://cfm.ehu.es/nanophotonics
Center for Materials Physics, CSIC-UPV/EHU and Donostia International Physics Center - DIPC Donostia-San Sebastián, Basque Country
AMOLF Nanophotonics School June 17-21, 2019, Science Park, Amsterdam, The Netherlands Organic molecules & light
Excited molecule (=exciton on molecule) Photon
Photon Adding mirrors to this interaction
The photon can come back!
Optical cavities to enhance light-matter interaction
Optical mirrors Dielectric resonator
Veff
Q ∼ 1/κ
Photonic crystals Plasmonic cavity
Veff
Q∼1/κ Coupling of plasmons and molecular excitations
Plasmon-Exciton Coupling Plasmon-Vibration Coupling
Absorption, Scattering, IR Absorption, Fluorescence Veff Raman Scattering
Extreme plasmonic cavities
Top-down Bottom-up STM ultra high-vacuum Wet Chemistry Low temperature Self-assembled monolayers (Hefei, China) (Cambridge, UK) “More interacting system” One cannot distinguish whether we have a photon or an excited molecule. The eigenstates are “hybrid” states, part molecule and part photon: “polaritons”
Strong coupling! Experiments: organic molecules
Organic molecules: Microcavity: D. G. Lidzey et al., Nature 395, 53 (1998) • Large dipole moments • High densities collective enhancement • Rabi splitting can be >1 eV (~30% of transition energy) • Room temperature!
Surface plasmons: J. Bellessa et al., Single molecule with gap plasmon: Phys. Rev. Lett. 93, 036404 (2004) Chikkaraddy et al., Nature 535, 127 (2016)
from lecture by V. Shalaev Plasmonic cavities as optical resonators
λ V
Ultra-compact (V∼sub-nm),
Ultrafast (1/γa∼ fs), Room Temperature (g∼eV) Effective mode volume V/ volume mode Effective
Chikkarady et al. Nature 7, 535 (2016) Plasmonic Nanocavities and Quantum Emiters:
QEs: quantum dots, diamond vacancies, dye molecules, J-aggregates, TMDs…
Shegai, Pelton, Sandhogar, Bozhevolnyi, Lukin, Sanvitto, Liedl, Acuña, Raschke, Mikkelsen, Hecht, Baumberg… Strong Coupling Classical treatment A molecule as an harmonic oscillator
Molecule (or other emitter)
In frequency domain The nanoresonator
Scattering
hν + E + + - - - Extinction
Absorption
We assume that the nanophotonic resonance is a simple Lorentzian
Or equivalently The plasmonic cavity
For a small metallic particle or radius R surrounded by vacuum
giving
Or equivalently
Other plasmonic resonators follow similar expressions A key plasmonic nanoresonator: the plasmonic cavity
Sphere - plane Sphere - sphere
dipole – mirror dipole near-field interaction dipole – dipole near-field interaction
High field enhancement in the gap due to resonant near-field coupling
• local light sources • enhanced Raman signals (detection of single molecule Raman signals) • nonlinear effects Dipolar sphere-sphere near-field interaction
Scattered field: 3 ε i −1 Polarizability of spheres: α = 4πa i i E ∝α E ε i + 2 sca eff in
Effective polarizability of interacting dipoles (dipole approximation):
α1 α1 2a 2a
z r z Ein r Ein
α 2 α 2
αα 21 αα 21 αα 21 ++ 3 αα 21 −+ 3 α = πr α = 2πr eff αα eff αα 1− 21 1− 21 4π r 62 16π r 62
Resonance shift effects – two resonant particles
2 10 ω p ε ε −== 7.5 2 metal spheres: 21 1 2 ε′ (drude term) ω + iγω 5 γ = 2.0 2.5 ω 0.2 0.40.6 0.8 1 1.2 1.4 -2.5 α -5 ε ′′ 1 2a -7.5 -10 z = 0 z E r z = 0.3a in αeff (a.u.)80
60 z = 3a α 2 40 z αα 21 20 αα 21 ++ 3 α = πr eff αα ω 1− 21 0.2 0.4 0.6 0.8 1 1.2 1.4 π 62 4 r Arg()αeff ()rad 3 2.5
2 dipolar approximation predicts 1.5 • resonance shifts 1 ωω p
∝α 0.5 • field enhancement ( E sca eff) Ein ω 0.2 0.4 0.6 0.8 1 1.21.4
Modes energy shift due to coupling
Sphere Coupled dimer Sphere + ω1 _ + + a a + _ _ + l=2 _ l=1 + _
+ Prodan et al, Science 302, 419 (2003) _ l Nordlander et al, ωωlp= Nanoletters 4, 899 (2004) 21l + − ω1 Schmeits and Dambly, Phys. Rev. B 44, 12706 (1991) Coupled modes in a metallic dimer
Schmeits and Dambly, Phys. Rev. B 44, 12706 (1991) The gap plasmon: a distorted dipole
-Q Q - - + + Isolated rod: dipole - + - - + + ~ L
-Q Q -Q Q Weak coupling: - - + + - + + - + -- + two dipoles - - + + S - - + + ~ L ~ L
-Q Q -Q Q - - Strong coupling: ++ - + + - + -- + distorted dipoles - - ++ S - + + < L < L Spectral complexity: higher-order modes Gold spherical dimers (a=60nm) Closely located spheres
- + - + - + - + Romero, et al. • The dipole peak redshifts when closer Optics Express • New multipolar peaks appear. 14, 9988 (2006) Gap antenna: localization and field-enhancement Hot-sites
Single antenna Gap-antenna Plasmonic cavity-molecule coupling
Molecule cavity
It is useful to write these equations using the notation
g defined to be the same as in the quantum formulation!!!
One obtains: Plasmonic cavity-molecule coupling
Molecule cavity
Briefly back to the time domain
This is equivalent to an harmonic oscillator system
k1 kg k2 m1 m2 Dynamics of two coupled mechanical oscillators Dynamics of two coupled mechanical oscillators Tuning of the frequency of the mechanical resonator frequency
Losses
Resonant k1 k1 Without external illumination
Molecule cavity
≈Eigenvalue problem ( )( ) = 0 Without external illumination
Molecule cavity
≈Eigenvalue problem Eigenvalues
Molecule cavity
Energy of the modes
Losses Zero detuning Molecule cavity Energy of the modes Losses
Two different situations
Square root is imaginary Weak coupling Energy of the modes does not change, only the losses (decay) are modified Regimes of light-matter coupling Weak coupling regime Modified EM mode density modify radiative decay
Zero detuning Molecule cavity Energy of the modes Losses
Two different situations
Square root is imaginary Weak coupling Energy of the modes does not change, only the losses (decay) are modified
Square root is real Strong coupling Two new modes at new energies -> polaritons Regimes of light-matter coupling Strong coupling regime Interaction faster than decay Hybrid light-matter states (polaritons / dressed states) vacuum Rabi oscillations (coherent energy exchange)
Zero detuning Molecule cavity Energy of the modes Losses
Two different situations
Square root is imaginary Weak coupling Energy of the modes does not change, only the losses (decay) are modified
Square root is real Strong coupling Two new modes at new energies -> polaritons
Note: The equation is the mathematical condition to obtain splitting of the modes. However, for practical purposes, it might be better to impose that the splitting/coupling is sufficiently larger than the sum of the losses (see Törmä and Barnes, Rep. Prog. Phys. 78 013901 (2015))
Strong coupling in frequency: anticrossing
Plasmon population
The energies never cross Notice also the evolution of the linewidth J. Bellesa et al, PRB 80, 033303 (2009) Strong coupling in time: Rabi Oscillations
Energy at zero detuning
P. Vasa et al, Nature Photonics 7, 128–132 (2013)
The oscillations can be seen as the beating between the two different frequencies
The Rabi frequency is thus Progressive emergence of strong coupling Extinction 1100
) nm ) g=0.025 g=0.05 g=0.1 g=0.15 (
κ κ κ κ wavelength
900 Cavity
1100
) nm ) g=0.2 g=0.25 g=0.3 g=0.35 (
κ κ κ κ wavelength
900 Cavity
1100
) nm ) g=0.4 g=0.5 g=0.75 g=1 (
κ κ κ κ wavelength
900
Cavity 900 1100 900 1100 900 1100 900 1100 Excitation wavelength(nm) Excitation wavelength(nm) Excitation wavelength(nm) Excitation wavelength(nm) Time domain is (can be) the key to identify Strong Coupling Regimes of light-matter coupling Weak coupling regime Modified EM mode density modify radiative decay
Weak coupling regime: Purcell Factor
The cavity acts as a new decay channel for the emitter
Molecule Cavity
Decay of the molecule into the cavity
Decomposing the molecular losses into spontaneous decay and other losses
Purcell Factor
The Purcell Factor does not depend on the emitter ( and has the same dependence) Weak coupling regime: Fano resonances ‘A’ complex
Lamb shift Purcell Factor Weak coupling regime: Fano resonances
Lamb shift Purcell Factor Example of application of this classical description: Controlling single molecule coupling in a plasmonic cavity
Experiment Theory
Dnorm
Y. Zhang et al. Nature Communications. 8, 15225 (2017) Strong Coupling Quantum treatment Hamiltonian Plasmon Molecule Plasmon Molecule Coupling illumination illumination
Coupling between one (or more) localized single cavity mode and a single photon emitter
The losses are introduced via Lindblad operators and the density matrix
Density Matrix Master Equation
Incoherent Losses Strong coupling Focusing on the coupling and ignoring losses
Looking for eigenvalues and eigenvectors of this lossless Hamiltonian
In matrix form Strong coupling Considering n=1
And making the (non-rigorous) transformation
We recover
Estimation of the parameters in the Hamiltonian for the single plasmonic resonator
With effective volume
So that
The volume can be calculated in a similar manner as for dielectric cavities, but • Different contributions of electric and magnetic energy • (R. Esteban et al., New J. of Physics 16, 013052, 2014) • Need to subtract the radiative radiation (A. F. Koenderink, Optics Letter 35, 4208, 2010)
Estimation of coupling strengths for a typical single plasmonic resonance Laser-molecule coupling
Cavity-molecule coupling
Molecule Cavity
The key why we use plasmons Laser-cavity coupling Quantum versus classical
The Jaynes-Cummings Ladder
Uncoupled Coupled system Uncoupled molecule cavity
Ground State
The state-dependent splitting introduces: • Non-Linearities • Non -classical correlations Acknowledgements
-Rubén Esteban
- Francisco J. García Vidal Annex: Some thoughts
There is significant discussion in the literature about when it is justified to model the plasmon as a single mode as presented here.
This approach assumes that a single Lorentzian-like mode dominates the response. This can be valid to a large degree for well chosen systems, but not always.
Approaches to overcome this limitations include • Quasi-normal modes (groups of Hughes, Lalanne, Giessen… ) • Formulations based on the Green’s function (for example, H. T. Dung et al., PRA 68, 043816 (2003), P. Yao et al., PRB 80, 195106, (2009))
Applications of quantum treatments Undertanding Luminescence
No emission from upper polariton Emission from upper polariton Elastic Inelastic
G. Zengin et al., Sci. Rep. 3, 3074 (2013) D. Melnikau et al., J. Phys. Chem. Lett. 7, 354 (2016) J. Bellessa et al., PRL. 93, 036404 (2004)
Applications of quantum treatments Undertanding Luminescence
No emission from upper polariton Theoretical Analysis Elastic Inelastic Standard Jaynes-Cummings
More sophisticated treatments
G. Zengin et al., Sci. Rep. 3, 3074 (2013) T. Neuman and J. Aizpurua, Optica 5, 1247 (2018) J. Bellessa et al., PRL. 93, 036404 (2004)
Applications of quantum treatments Changing chemistry reaction rates
Strong coupling with electronic states Strong coupling with vibrations
J. Galego et al., PRL 119, 136001 (2017) A. Thomas et al, Angew. Chem. Int. Ed. 55, 11462 (2016) Applications of quantum treatments
Energy transfer Complex dynamics Need to consider vibrational and electronic states
X. Zhong et al., Angew. Chem. 128, 6310 (2016)
B. Xiang et al., PNAS. 115, 4845 (2018) J. Feist and F. J. García Vidal PRL 114, 196402 (2015) Annex: Some history
For a historical discussion of many contributions, see the reviews by
Torma and Barnett (Rep. Prog. Phys. 78 (2015) 013901 (34pp)) and
Liberato (Kockum, A. F., Miranowicz, A., De Liberato, S., Savasta, S., & Nori, F. Ultrastrong coupling between light and matter. Nature Reviews Physics, 1(1), 19, (2019)
In the following, some papers that are (or seem to be) important on the topic, with some figures that look relevant.
Y. Kaluzny, P. Goy, M. Gross, J. M. Raimond, & S. Haroche “Observation of self-induced Rabi oscillations in two-level atoms excited inside a resonant cavity: The ringing regime of superradiance.” Physical Review Letters 51, 1175 (1983) R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity," Phys. Rev. Lett. 68, 1132 (1992). M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, & H. J. Carmichael. “Normal- mode splitting and linewidth averaging for two-state atoms in an optical cavity.” Physical Review Letters, 63, 240 (1989) Y. Zhu, D. J. Gauthier, S. E., Morin, Q. Wu, H. J. Carmichael & T. W. Mossberg “Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations.” Physical Review Letters, 64, 2499 (1990) C. Weisbuch, M. Nishioka, A. Ishikawa, & Y. Arakawa. “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity.” Physical Review Letters, 69, 3314 (1992) R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini & M. Ilegems “Measurement of cavity-polariton dispersion curve from angle-resolved photoluminescence experiments.” Physical Review Letters, 73, 2043. (1994) R. Houdré, R . P. Stanley, U. Oesterle, M. Ilegems, & C. Weisbuch, “Room- temperature cavity polaritons in a semiconductor microcavity”. Physical Review B, 49, 16761 (1994). D. G. Lidzey, D. D. C. Bradley, M. S. Skolnick, T. Virgili, S. Walker & D. M. Whittaker. “Strong exciton–photon coupling in an organic semiconductor microcavity”. Nature, 395, 53 (1998) P. A . Hobson, W. L. Barnes, D. G. Lidzey, G. A. Gehring, D. M. Whittaker, M. S. Skolnick & S. Walker. “Strong exciton–photon coupling in a low-Q all-metal mirror microcavity”. Applied Physics Letters, 81, 3519 (2002). A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, ... & R. J. Schoelkopf. “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics.” Nature, 431, 162 (2004) J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke and A. Forchel “Strong coupling in a single quantum dot- semiconductor microcavity System” Nature 432 197 (2004) T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin and D. G. Deppe “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity” Nature 432, 200 (2004) K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoğlu “Quantum nature of a strongly coupled single quantum dot–cavity system” Nature 445, 896 (2007) A review
G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch and A. Scherer “Vacuum Rabi splitting in semiconductors” Nature Phys. 2, 81 (2006) I. Pockrand, A. Brillante and D. Möbius “Exciton–surface plasmon coupling: an experimental investigation”J. Chem. Phys. 77 6289 (1982 ) J. Bellessa, C. Bonnand, J. C. Plenet and J. Mugnier “Strong coupling between surface plasmons and excitons in an organic semiconductor” Phys. Rev. Lett. 93, 036404 (2004) Y. Sugawara, T. A. Kelf, J. J. Baumberg, M. E. Abdelsalam and P. N. Bartlett “Strong coupling between localized plasmons and organic excitons in metal nanovoids” Phys. Rev. Lett. 97 266808 (2006) A review
P. Törmä and W. L. Barnes “Strong coupling between surface plasmon polaritons and emitters: a review.” Reports on Progress in Physics 78, 013901 (2015) G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, & T. Shegai. “Realizing strong light- matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions”. Physical Review Letters, 114, 157401 (2015)