MOLECULAR POLARITONICS 2019:Theoretical and Numerical Approaches

Miraflores de la Sierra, Madrid, July 7-11, 2019Organizers: Claudiu Genes and Johannes Feist

Introduction / overview / perspective of the field

Molecular Polaritonics: Introduction

Laser:

Many coherent photonsAlternative:

Make single photon “strong” by confining it in space

Nanophotonics

Plasmonics

Cavity-modified material properties

Use light (vacuum field) to modify material properties?

Confine light in space to get strong few-photon interaction with interesting materials

Materials Science

Chemistry

Cavity QED

Quantum Optics

Weak coupling

Strong light–matter coupling

H =

ω0 − iγ

2g

g ω0 − iκ2

Simple model

excited emitter coupling

photon

Weak Strong Rabi splittingStrong coupling • Vacuum Rabi oscillations (coherent energy exchange)

• Interaction faster than decay

• Hybrid light-matter states(polaritons / dressed states)

• Absorption and emission• EM environment → modify

radiative decay (Purcell effect)

Strong coupling with organic molecules

Silvermirror

4TBPPZn inpolystyrene

Siliconnitride

Silicondioxide

Glasssubstrate

DB

R

Microcavity: D. G. Lidzey et al., Nature 395, 53 (1998)

from lecture by V. Shalaev

Surface plasmons: J. Bellessa et al., Phys. Rev. Lett. 93, 036404 (2004)

2000 2500

θ=59˚

θ=63˚

θ=51˚

θ=55˚

θ=49˚

Re

fle

cto

me

try (

a.u

.)

Energy (meV)

Few molecules with gap plasmon:Chikkaraddy et al., Nature 535, 127 (2016)

750800700600500

Wavelength (nm)

0

+–

p

Scatt

erin

g in

ten

sity

a b c

Nan

op

art

icle

nu

mb

er

Organic molecules:

• Large dipole moments

• High densities

• Rabi splitting can be >1 eV

(large fraction of transition energy)

• Room temperature!

ΩR ∝√ρµ

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Many vs single organic molecules

Problems

• Experimentally very challenging

• Extremely strong field confinement necessary (mode volume ~50 nm3) à large losses

• “Messy” system (molecules close to metal: quenching, chemical modification, etc.)

Promises

• Single molecule!

• ~all states/properties affected

• Quantum nature (more) evident

• Generates non-linearities (photon blockade)

Single (or few) molecules

Problems

• Many effects “classical” (Maxwell’s eqs)

• No few-photon nonlinearity

• Small polariton density of states compared to “dark” states

• delocalized à single-molecule effects small

Promises

• ”Easy” to reach strong coupling

• Modifications of electronic properties

• Tunable chemistry

• Could integrate in devices

Many molecules / macroscopic

Room temperature:

Many vs single organic molecules

Problems

• Requires good cavities while minimizing the mode volume

• Requires cryogenic conditions

• Reactivity is bad for experiments

Promises

• Coherent control of quantum states

• Coherent quantum light-matter interface

• Generates non-linearities (photon blockade)

• Integrated into quantum networks

Cryogenic single molecule

Localized surface plasmon resonancesGalego et al., Nature Commun. 7, 13841 (2016)

What is a cavity?

Nanowires

Surface plasmon polaritonsTörmä & Barnes,

Rep. Prog. Phys. 78, 13901 (2015)

bMetal mirror

Metal mirror

Fabry-Perot / planar cavitiesSanvitto & Kéna-Cohen,

Nat. Mater. 15, 1061 (2016)

Plasmonic nanoparticle arrayRamezani et al., Optica 4, 31 (2017)

“Cavity” in this context: any material system

… that confines or enhances light / EM modes

Almost never a single

cavity mode!

Proper quantized

description?

Macroscopic QED?

Photonic CrystalGalego, PhD thesis (2019)

Quantized approaches to plasmonic “cavities”

Weak and strong coupling

regimes in plasmonic QED T. Hümmer et al., Phys. Rev. B 87, 115419 (2013)

(a)

(b)

Quantum Emitters Near a Metal

Nanoparticle: Strong Coupling and

Quenching A. Delga et al, Phys. Rev. Lett. 112, 253601 (2014)ω (eV)(c)

ω (

eV

)

1

2.8

3

3.2

3.4

3.6 50

ω0 (eV)

ω (

eV

)

100

2.8 3 3.2 3.4 3.6

2.8

3

3.2

3.4

3.6

ω0 (eV)

200

2.8 3 3.2 3.4 3.6

100

101

102

103

104

a.u.

Transformation Optics Approach to

Plasmon-Exciton Strong Coupling in

Nanocavities R.-Q. Li et al., Phys. Rev. Lett. 117, 107401 (2016)

(b)(a)

Hybrid cavities

Hybrid cavities to manipulate

quenching and strong couplingB. Gurlek et al., ACS Phot. 5, 456 (2018)

Explicit quantization of quasinormal

modesS. Franke et al., Phys. Rev. Lett. 122, 213901 (2019)

Cavity Quantum Electrodynamics with

Frequency-Dependent ReflectorsO. Černotík et al., Phys. Rev. Lett. 122, 243601 (2019)

(b)

(c)

(a)

Two-level emitters?

This is not a molecule!

Real molecules:

• Many nuclear (vibrational) DOFs

• Large exciton-phonon coupling

• Fast nuclear dynamics

b d

0

1Absorbance

(0,1′)

(0,0

′)

(0′,1)

(0′,0

)

Emission

550 650 750

Wavelength (nm)

The complex nature of molecules

S0

S1

S2Vibrational relaxation

Fluorescence

Phosphorescence

Absorption

Intersystem

crossing

Internal

conversion

QuenchingNonradiative

relaxation

Rovibrational

energy levels

T1

Coupling to electronic transitions

S0

S1

S2Vibrational relaxation

Fluorescence

Phosphorescence

Absorption

Intersystem

crossing

Internal

conversion

QuenchingNonradiative

relaxation

Rovibrational

energy levels

T1

Coupling at optical frequencies

• Experimentally: chemistry, charge/exciton transport, polariton condensation, etc.

• Theory: role of vibrations, Tavis-Cummings-Holstein model, polaritonic potential energy surfaces, polariton cross-talk, etc...

Coupling to electronic transitions - experiments

Modify photochemical reaction rates

J. A. Hutchison et al., Angew. Chemie 124, 1624 (2012)

Polariton-mediated energy transferD. M. Coles et al., Nat. Mater. 13, 712 (2014)

Spatially separated donor and acceptorX. Zhong et al., Angew. Chem. Int.Ed. 56, 9034 (2017)

Polariton lasingS. Kéna-Cohen and S. Forrest, Nat. Phot. 4, 402 (2010)

Ag

Ag

J-aggregatesin gelatinematrix

NK-2707 J-aggregate

TDBC J-aggregate

Coupling to electronic transitions - experiments

Trion-Polariton Formation in

Single-Walled Carbon Nanotube

Microcavities

C. Möhl et al, ACS Phot., 5, 2074 (2018)

Effect of strong coupling on photo-

degradation of the semiconducting

polymer P3HT

V. N. Peters et al, Optica, 6, 318 (2019)

Turning a molecule into a coherent

two-level quantum system

D. Wang et al, Nat. Phys. 15, 483 (2019)

Ultrafast dynamics of everything

ARTICLE

Quantum electrodynamics at room temperaturecoupling a single vibrating molecule with aplasmonic nanocavityOluwafemi S. Ojambati1, Rohit Chikkaraddy1, William D. Deacon1, Matthew Horton1, Dean Kos1,

Vladimir A. Turek1, Ulrich F. Keyser 1 & Jeremy J. Baumberg 1

https://doi.org/10.1038/s41467-019-08611-5 OPEN

b d

c

Norm

. in

tensity

0

1Absorbance

(0,1′)

(0,0

′)

(0′,1)

(0′,0

)

Emission

550 650 750

Wavelength (nm)

DNAo

Au NP

Au mirror

dg

!

Ω0.5

0

1.5

1

2

101 101100102

Time (s)

0.5

0

1

Time (s)

5

10

0

Coin

cid

ence

Raw g2 (0) =

1.28 ± 0.22

g2 (! =

0)

g2 (! =

0)

Raw g2 (0) =

0.61 ± 0.18

5

10

0 12.5 25–12.5–25

Time delay ! (ns)

0 12.5 25–12.5–25

Time delay ! (ns)

0

Coin

cid

ence

a

b c"p = 520 nm "p = 590 nm

Start-stop

counter

• Short-pulse driving

• short plasmon lifetime

• ΩR ≈ ωv

Ultrafast electronic, photonic & phononic dynamics!

Both in system and in absorption and emission.

Coupling to electronic transitions – intersystem crossing

S0

S1

S2Vibrational relaxation

Fluorescence

Phosphorescence

Absorption

Intersystem

crossing

Internal

conversion

QuenchingNonradiative

relaxation

Rovibrational

energy levels

T1

Coupling at optical frequencies

• Modifications of the intersystem crossing dynamics

Intersystem crossing – experimental progress

Increased reverse intersystem crossing

Crossing from triplet to singlet increased by reducing gapK. Stranius et al., Nat. Commun. 9, 2273 (2018)

Inverting singlet and tripletE. Eizner et al., arXiv:1903.09251 (2019)

Suppression of photo-oxidation of organic chromophores

Significantly increased lifetime against photobleaching under strong couplingB. Munkhbat et al., Science Advances 4, eaas9552 (2018).

𝐶(𝑡) 𝐶(0)⁄Ω𝑅 = 2√(𝜔+ −𝜔0)(𝜔0 −𝜔−) 𝜔±𝜔0 𝐶(𝑡) 𝐶(0) ≈ [Ω𝑅(𝑡) Ω𝑅(0)⁄ ]2⁄ Ω𝑅~√𝑁 𝑉⁄ = √𝐶 𝑁𝑉

700

CS1

T1

HO·HO ·2

HO2

H O2 2

RROS:3O2

1O2

ET

3O2

O2

CT

S0

exc

ISC

0

UP

LP

500 600 700

Wavelength (nm)

Scattering (

a.u

.)

Hybrid

AgNPJ-agg

A

B

J-agg

Bleached J-agg

O2

b

kT

avg (

s–

1)

10,000

8000

6000

4000

2000

∆ETP (meV)

300 400350

Inside

OutsideP

+

P–

∆ETP

kRISC

kNRkP

T1

h!R

c

Ag 300 nm

ErB in PVA

130 nm

Ag 20 nm

Glass

Intersystem crossing – experimental progress

Manipulating matter with strong coupling: harvesting

triplet excitons in organic exciton microcavities

D. Polak et al., arXiv:1806.09990 (2018).

Coupling to electronic transitions – theoretical approaches

Quantum optics/condensed matter approaches

Cavity polaritons in microcavities

containing disordered organic

semiconductorsV. M. Agranovich, M. Litinskaya and D. G. Lidzey, Phys. Rev. B 67, 085311 (2003)

Polariton states & polariton-

polariton scattering in disordered

organic microcavitiesP. Michetti and G. C. La Rocca, Phys. Rev. B 71, 115320 (2005); Phys. Rev. B 82, 115327 (2010)

K

E

q

k,k

i

ERLP

Pump

Theory of Strong Coupling between

Quantum Emitters and Propagating

Surface PlasmonsA. González-Tudela et al, Phys. Rev. Lett. 110, 126801 (2013).

Coupling to electronic transitions – theoretical approaches

10−4 10−3 10−2 10−1 1ΩR (eV)

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

σe(eV)

40 regular

60 regular

40 random

60 random

0.4 0.7 1

0.01

0.02

0.03

γp γd~di

~Ec(~r)

Extraordinary exciton conductance J. Feist, F. J. Garcia-Vidal, Phys. Rev. Lett. 114, 196402 (2015)

Cavity enhanced transport of excitonsJ. Schachenmayer, C. Genes, E. Tignone and G. Pupillo , Phys. Rev. Lett. 114, 196403 (2015)

Quantum optics/condensed matter approaches

Cavity-controlled chemistry in

molecular ensemblesF. Herrera and F. C. Spano, Phys. Rev. Lett 116, 238301 (2016)

Dark vibronic polaritons and the

spectroscopy of organic microcavitiesF. Herrera and F. C. Spano, Phys. Rev. Lett 118, 223601 (2017)

Coupling to electronic transitions – theoretical approaches

Quantum optics/condensed matter approaches

Quantum Langevin approach to

quantum optics with moleculesM. Reitz, C. Sommer and C. Genes, Phys. Rev. Lett122, 203602 (2019)

Vibrational dressing of polaritonsM. A. Zeb et al., ACS Photonics 5, 249 (2018).

Long-distance energy transferDonorAcceptor

Silver mirror

Polymer spacer

Cavitymode

Silver mirror

Polymer spacer

Phonon

Phonon

Upper polariton

Middlepolariton

Lower polariton

Long-distance operator for energy

transferF. J. Garcia-Vidal, J. Feist, Science 357, 1357 (2017)(perspective on Zhong, Angew. Chem. 56, 9034)

Quantitative explanation:R. Sáez-Blázquez, J. Feist, A.I. Fernández-Domínguez, F.J. García-Vidal, Phys. Rev. B 97, 241407(R) (2018)

Coupling to electronic transitions – theoretical approaches

Tensor network simulations of non-

markovian dynamics in organic

polaritonsJ. Del Pino et al, Phys. Rev Lett. 121, 227401 (2018)

Quantum optics approaches – numerical tensor matrix simulations

Efficient non-markovian quantum

dynamics using time-evolving matrix

product operatorsA. Strathearn et al, Nat. Comms. 9, 3322 (2018)

Quantum optics approaches

Coupling to electronic transitions – theoretical approaches

Ab initio / electronic-structure-based approaches

Nonadiabatic dynamics in cavitiesM. Kowalewski et al, J. Chem. Phys. 144, 054309 (2016).

Quantum light-induced conical

intersectionsA. Csehi et al., arXiv:1902.03640

Quantum-electrodynamical DFTI. V. Tokatly, Phys. Rev. Lett. 110, 233001 (2013)M. Ruggenthaler et al., Phys. Rev. A 90, 012508 (2014)

Polaritonic potential energy surfacesJ. Galego et al., Phys. Rev. X 5, 041022 (2015)

Coupling to electronic transitions – theoretical approaches

Ab initio / electronic-structure-based approaches

Cavity Born-Oppenheimer

approximationJ. Flick et al., PNAS 114, 3026 (2017)J. Flick et al.; JCTC 13, 1616 (2017)

Cavity-Correlated Electron-Nuclear

Dynamics & Variational TheoryJ. Flick and P. Narang, Phys. Rev. Lett. 121, 113002 (2018).N. Rivera et al., Phys. Rev. Lett. 122, 193603 (2019).

Coupling to electronic transitions – theoretical approaches

Molecular dynamics / quantum chemistry etc

Multiscale QM/MM molecular dynamics

H. L. Luk et al., JCTC 13, 4324 (2017)Collective Jahn-Teller Interactions

through Light-Matter Coupling in a

Cavity (MCTDH)

O. Vendrell, Phys. Rev. Lett. 121, 253001 (2018)

Revealing the Presence of Potential

Crossings in Diatomics Induced by

Quantum Cavity Radiation

J. F. Triana and J. L. Sanz-Vicario, Phys. Rev. Lett. 122, 063603 (2019)

Coherent Light Harvesting

G. Groenhof, J. J. Toppari, J. Phys. Chem. Lett. 9, 4848 (2018)

The complex nature of molecules

S0

S1

S2Vibrational relaxation

Fluorescence

Phosphorescence

Absorption

Intersystem

crossing

Internal

conversion

QuenchingNonradiative

relaxation

Rovibrational

energy levels

T1

Coupling at infrared frequencies

• All within electronic ground state – thermally driven effects

• “Optomechanical” (nuclear motion coupled to light)

• Modification of ground-state chemical reactions

Strong coupling to vibrations – experimental progress

Coherent coupling of molecular

resonators with a microcavity modeA. Shalabney et al, Nat Comms. 6, 6981 (2015)

Vibrational strong couplingJ. P. Long and B. S. Simpkins, ACS Phot. 2, 130 (2015)

Changing ground-state chemistryA. Thomas et al., Angew. Chem. Int. Ed. 55, 6202 (2016);Science, 363, 6427 (2019)

Strong coupling to vibrations – experimental progress

Cavity catalysis by cooperative

vibrational strong coupling of reactant

and solvent moleculesJ. Lather et al, Ang. Chemie (2019)

Voltage-controlled switching of

strong light–matter interactions

using liquid crystalsM. Hertzog et al, Chem. Eur. J., 23, 18166 (2017)

Nonlinear Spectroscopy of Vibrational

PolaritonsB. Xiang et al., PNAS 115, 4845 (2018)

t2

t1

t3

Pro

be IR

Pul

se

Pro

be IR

Pul

se

Pump

IR P

ulse

s

Pump

IR P

ulse

s

2D IR

Sig

nal

2D IR

Sig

nal

W(CO)W(CO)6 6 / Cavity/ Cavity

SystemSystem

θ Microscopic Physical Picture Microscopic Physical Picture

Incident Incident

IR BeamIR Beam

Dielectric

Mirrors

B

A

C D

Wa

ve

nu

mb

er

(cm

-1)

Tilting Angle (deg)

0

2

4

6

8

1010

0 5 1010 1515 2020

21002100

20502050

20002000

19501950

19001900

Molecule/Cavity Coupling: Molecule/Cavity Coupling:

Polaritons FormedPolaritons Formed

Cavity Cavity

ModeMode

UP

LP

1

0

VibrationalVibrational

ModeMode19401940

19601960

19801980

20002000

20202020

20402040

Strong coupling to vibrations – theory

Theory for Nonlinear Spectroscopy of

Vibrational PolaritonsR. F. Ribeiro et al, J. Phys. Chem. Lett. 9 3766, (2019)

Quantum theory of collective strong

coupling of molecular vibrations with a

microcavity modeJ. del Pino et al., New J. Phys. 17, 053040 (2015)

∣ ⟩ 4

4 1 4

γ

γ

γ γ 1 4

N

∞

N

∞

Cavity Casimir-Polder forces & self-

induced electrostatic catalysisJ. Galego et al., Phys. Rev. X 9, 021057 (2019)C. Climent et al., Angew. Chem. Int. Ed. 58, 8698 (2019).

(a) (b)(c)

Theoretical challenges ahead…

Proper modelling of light-matter interaction in non-trivial cavities (plasmonic structures,

hybrid cavities, frequency dependent mirrors etc)

Huge playing field!

• Identify interesting effects that can be controlled/manipulated/enhanced via strong coupling

• Which chemical reactions can be affected, and how? (ground state, solvent effects…)

• Room-temperature quantum optics?

• Connection to ultrafast laser physics?

Efficient/reliable simulations for many particles (including many vibrations, dissipative

coupling to bulks or solvent etc)