We propose a cavity QED approach to describe light-matter interaction of an infrared cavity field with an anharmonic vibration of a single nonpolar molecule. Starting from a generic Morse oscillator potential with quantized nuclear motion, we derive a multilevel quantum Rabi model to study vibrational polaritons beyond the rotating-wave approximation. We analyze the spectrum of vibrational polaritons in detail and compare it with available experiments. For high excitation energies, the system exhibits a dense manifold of polariton level crossings and avoided crossings as the light-matter coupling strength and cavity frequency are tuned. We also analyze polariton eigenstates in nuclear coordinate space. We show that the bond length of a vibrational polariton at a given energy is never greater than the bond length of a Morse oscillator with the same energy. This type of polariton bond strengthening occurs at the expense of the creation of virtual infrared cavity photons and may have implications in chemical reactivity of polariton states.
REFERENCES
1.
H. J.
Kimble
, “The quantum internet
,” Nature
453
(7198
), 1023
(2008
).2.
J. L.
O’Brien
, A.
Furusawa
, and J.
Vučković
, “Photonic quantum technologies
,” Nat. Photonics
3
(12
), 687
–695
(2009
).3.
H.
Mabuchi
and A. C.
Doherty
, “Cavity quantum electrodynamics: Coherence in context
,” Science
298
(5597
), 1372
–1377
(2002
).4.
A.
Blais
, R.-S.
Huang
, A.
Wallraff
, S. M.
Girvin
, and R. J.
Schoelkopf
, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation
,” Phys. Rev. A
69
, 062320
(2004
).5.
R.
Miller
et al, “Trapped atoms in cavity QED: Coupling quantized light and matter
,” J. Phys. B: At., Mol. Opt. Phys.
38
(9
), S551
(2005
).6.
T. W.
Ebbesen
, “Hybrid light-matter states in a molecular and material science perspective
,” Acc. Chem. Res.
49
, 2403
–2412
(2016
).7.
A.
Canaguier-Durand
, E.
Devaux
, J.
George
, Y.
Pang
, J. A.
Hutchison
, T.
schwartz
, C.
Genet
, N.
Wilhelms
, J.-M.
Lehn
, and T. W.
Ebbesen
, “Thermodynamics of molecules strongly coupled to the vacuum field
,” Angew. Chem., Int. Ed.
52
(40
), 10533
–10536
(2013
).8.
J. P.
Long
and B. S.
Simpkins
, “Coherent coupling between a molecular vibration and Fabry–Perot optical cavity to give hybridized states in the strong coupling limit
,” ACS Photonics
2
(1
), 130
–136
(2015
).9.
B. S.
Simpkins
, K. P.
Fears
, W. J.
Dressick
, B. T.
Spann
, A. D.
Dunkelberger
, and J. C.
Owrutsky
, “Spanning strong to weak normal mode coupling between vibrational and Fabry–Pérot cavity modes through tuning of vibrational absorption strength
,” ACS Photonics
2
(10
), 1460
–1467
(2015
).10.
A.
Shalabney
, J.
George
, H.
Hiura
, and J. A.
Hutchison
, C.
Genet
, P.
Hellwig
, and T. W.
Ebbesen
, “Enhanced Raman scattering from vibro-polariton hybrid states
,” Angew. Chem., Int. Ed.
54
(27
), 7971
–7975
(2015
).11.
A.
Shalabney
, J.
George
, J.
Hutchison
, G.
Pupillo
, C.
Genet
, and T. W.
Ebbesen
, “Coherent coupling of molecular resonators with a microcavity mode
,” Nat. Commun.
6
, 5981
(2015
).12.
R.
Chikkaraddy
, B.
de Nijs
, F.
Benz
, S. J.
Barrow
, O. A.
Scherman
, E.
Rosta
, A.
Demetriadou
, P.
Fox
, O.
Hess
, and J. J.
Baumberg
, “Single-molecule strong coupling at room temperature in plasmonic nanocavities
,” Nature
535
(7610
), 127
–130
(2016
).13.
F.
Benz
, M. K.
Schmidt
, A.
Dreismann
, R.
Chikkaraddy
, Y.
Zhang
, A.
Demetriadou
, C.
Carnegie
, H.
Ohadi
, B.
de Nijs
, R.
Esteban
, J.
Aizpurua
, and J. J.
Baumberg
, “Single-molecule optomechanics in picocavities
,” Science
354
(6313
), 726
–729
(2016
).14.
J.
George
, T.
Chervy
, A.
Shalabney
, E.
Devaux
, H.
Hiura
, C.
Genet
, and T. W.
Ebbesen
, “Multiple Rabi splittings under ultrastrong vibrational coupling
,” Phys. Rev. Lett.
117
(15
), 153601
(2016
).15.
R. M. A.
Vergauwe
, J.
George
, T.
Chervy
, J. A.
Hutchison
, A.
Shalabney
, V. Y.
Torbeev
, and T. W.
Ebbesen
, “Quantum strong coupling with protein vibrational modes
,” J. Phys. Chem. Lett.
7
(20
), 4159
–4164
(2016
).16.
A.
Thomas
, J.
George
, A.
Shalabney
, M.
Dryzhakov
, J.
Sreejith
, J. M.
Varma
, T.
Chervy
, X.
Zhong
, E.
Devaux
, C.
Genet
, and J. A.
Hutchison
, and T. W.
Ebbesen
, “Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field
,” Angew. Chem., Int. Ed.
55
(38
), 11462
–11466
(2016
).17.
M.
Hertzog
, P.
Rudquist
, J. A.
Hutchison
, J.
George
, T. W.
Ebbesen
, and K.
Börjesson
, “Voltage-controlled switching of strong light-matter interactions using liquid crystals
,” Chem. - Eur. J.
23
(72
), 18166
–18170
(2017
).18.
D.
Wang
, H.
Kelkar
, D.
Martin-Cano
, T.
Utikal
, S.
Götzinger
, and V.
Sandoghdar
, “Coherent coupling of a single molecule to a scanning Fabry-Perot microcavity
,” Phys. Rev. X
7
(2
), 021014
(2017
).19.
V. F.
Crum
, S. R.
Casey
, and J. R.
Sparks
, “Photon-mediated hybridization of molecular vibrational states
,” Phys. Chem. Chem. Phys.
20
(2
), 850
–857
(2018
).20.
T.
Chervy
, A.
Thomas
, E.
Akiki
, R. M. A.
Vergauwe
, A.
Shalabney
, J.
George
, E.
Devaux
, J. A.
Hutchison
, C.
Genet
, and T. W.
Ebbesen
, “Vibro-polaritonic IR emission in the strong coupling regime
,” ACS Photonics
5
(1
), 217
–224
(2018
).21.
M.
Du
, R. F.
Ribeiro
, and J.
Yuen-Zhou
, “Remote control of chemistry in optical cavities
,” Chem
5
(5
), 1167
–1181
(2019
).22.
H.
Hiura
, A.
Shalabney
, and J.
George
, “Cavity catalysis ? accelerating reactions under vibrational strong coupling ?
,” chemRxiv
(to be published).23.
A.
Thomas
, L.
Lethuillier-Karl
, K.
Nagarajan
, R. M. A.
Vergauwe
, J.
George
, T.
Chervy
, A.
Shalabney
, E.
Devaux
, C.
Genet
, J.
Moran
, and T. W.
Ebbesen
, “Tilting a ground-state reactivity landscape by vibrational strong coupling
,” Science
363
(6427
), 615
–619
(2019
).24.
R. J.
Gordon
, L.
Zhu
, and T.
Seideman
, “Coherent control of chemical reactions
,” Acc. Chem. Res.
32
(12
), 1007
–1016
(1999
).25.
J.
del Pino
, J.
Feist
, and F. J.
Garcia-Vidal
, “Signatures of vibrational strong coupling in Raman scattering
,” J. Phys. Chem. C
119
(52
), 29132
–29137
(2015
).26.
A. D.
Dunkelberger
, B. T.
Spann
, K. P.
Fears
, B. S.
Simpkins
, and J. C.
Owrutsky
, “Modified relaxation dynamics and coherent energy exchange in coupled vibration-cavity polaritons
,” Nat. Commun.
7
, 1
–10
(2016
).27.
A. D.
Dunkelberger
, R. B.
Davidson
II, W.
Ahn
, B. S.
Simpkins
, and J. C.
Owrutsky
, “Ultrafast transmission modulation and recovery via vibrational strong coupling
,” J. Phys. Chem. A
122
(4
), 965
–971
(2018
).28.
J.
Feist
, J.
Galego
, and F. J.
Garcia-Vidal
, “Polaritonic chemistry with organic molecules
,” ACS Photonics
5
(1
), 205
–216
(2018
).29.
R. F.
Ribeiro
, L. A.
Martínez-Martínez
, M.
Du
, J.
Campos-Gonzalez-Angulo
, and J.
Yuen-Zhou
, “Polariton chemistry: Controlling molecular dynamics with optical cavities
,” Chem. Sci.
9
(30
), 6325
–6339
(2018
).30.
M.
Hertzog
, M.
Wang
, J.
Mony
, and K.
Börjesson
, “Strong light–matter interactions: A new direction within chemistry
,” Chem. Soc. Rev.
48
(3
), 937
–961
(2019
).31.
A. F.
Kockum
, A.
Miranowicz
, S.
De Liberato
, S.
Savasta
, and F.
Nori
, “Ultrastrong coupling between light and matter
,” Nat. Rev. Phys.
1
, 19
–40
(2019
).32.
F.
Herrera
and F. C.
Spano
, “Cavity-controlled chemistry in molecular ensembles
,” Phys. Rev. Lett.
116
, 238301
(2016
).33.
J.
del Pino
, J.
Feist
, and F. J.
Garcia-Vidal
, Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode
, New J. Phys.
17
, 053040
(2015
).34.
M.
Muallem
, A.
Palatnik
, G. D.
Nessim
, and Y. R.
Tischler
, “Strong light-matter coupling and hybridization of molecular vibrations in a low-loss infrared microcavity
,” J. Phys. Chem. Lett.
7
(11
), 2002
–2008
(2016
).35.
P.
Saurabh
and S.
Mukamel
, “Two-dimensional infrared spectroscopy of vibrational polaritons of molecules in an optical cavity
,” J. Chem. Phys.
144
(12
) (2016
).36.
H.
Ling Luk
, J.
Feist
, J.
Jussi Toppari
, and G.
Groenhof
, “Multiscale molecular dynamics simulations of polaritonic chemistry
,” J. Chem. Theory Comput.
13
(9
), 4324
–4335
(2017
).37.
L. A.
Martínez-Martínez
, R. F.
Ribeiro
, J.
Campos-González-Angulo
, and J.
Yuen-Zhou
, “Can ultrastrong coupling change ground-state chemical reactions?
,” ACS Photonics
5
(1
), 167
–176
(2018
).38.
B.
Xiang
, W.
Xiong
, B. S.
Simpkins
, J. C.
Owrutsky
, R. F.
Ribeiro
, A. D.
Dunkelberger
, and J.
Yuen-Zhou
, “Theory for nonlinear spectroscopy of vibrational polaritons
,” J. Phys. Chem. Lett.
9
(13
), 3766
–3771
(2018
).39.
J.
Flick
, M.
Ruggenthaler
, H.
Appel
, and A.
Rubio
, “Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry
,” Proc. Natl. Acad. Sci. U. S. A.
114
(12
), 3026
–3034
(2017
).40.
J.
Flick
, H.
Appel
, M.
Ruggenthaler
, and A.
Rubio
, “Cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon systems
,” J. Chem. Theory Comput.
13
(4
), 1616
–1625
(2017
).41.
B.
Xiang
, R. F.
Ribeiro
, A. D.
Dunkelberger
, J.
Wang
, Y.
Li
, B. S.
Simpkins
, J. C.
Owrutsky
, J.
Yuen-Zhou
, and W.
Xiong
, “Two-dimensional infrared spectroscopy of vibrational polaritons
,” Proc. Natl Acad. Sci.
115
(19
), 4845
–4850
(2018
).42.
P. M.
Morse
, “Diatomic molecules according to the wave mechanics. II. Vibrational levels
,” Phys. Rev.
34
(1
), 57
–64
(1929
).43.
V. S.
Vasan
and R. J.
Cross
, “Matrix elements for Morse oscillators
,” J. Chem. Phys.
78
(6
), 3869
–3871
(1983
).44.
J. C.
Light
and T.
Carrington
, Jr., Discrete-Variable Representations and Their Utilization
(John Wiley & Sons
, 2007
), pp. 263
–310
.45.
D. T.
Colbert
and W. H.
Miller
, “A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method
,” J. Chem. Phys.
96
(3
), 1982
–1991
(1992
).46.
I. P.
Hamilton
and J. C.
Light
, “On distributed Gaussian bases for simple model multidimensional vibrational problems
,” J. Chem. Phys.
84
(1
), 306
–317
(1986
).47.
W.
Demtröder
, Molecular Physics: Theoretical Principles and Experimental Methods
(John Wiley & Sons
, 2008
).48.
P.
Jakob
and B. N. J.
Persson
, “Infrared spectroscopy of overtones and combination bands
,” J. Chem. Phys.
109
(19
), 8641
–8651
(1998
).49.
G.
Marcus
, A.
Zigler
, and L.
Friedland
, “Molecular vibrational ladder climbing using a sub-nanosecond chirped laser pulse
,” Europhys. Lett.
74
(1
), 43
–48
(2006
).50.
D. P.
Craig
and T.
Thirunamachandran
, Molecular Quantum Electrodynamics: An Introduction to Radiation-Molecule Interactions
(Courier Corporation
, 1998
).51.
D. L.
Andrews
, G. A.
Jones
, A.
Salam
, and R. G.
Woolley
, “Perspective: Quantum Hamiltonians for optical interactions
,” J. Chem. Phys.
148
(4
), 040901
(2018
).52.
S. Y.
Buhmann
, Dispersion Forces I: Macroscopic Quantum Electrodynamics and Ground-State Casimir, Casimir–Polder and van der Waals Forces
, Springer Tracts in Modern Physics (Springer Berlin Heidelberg
, 2013
).53.
V.
Rokaj
, D. M.
Welakuh
, M.
Ruggenthaler
, and A.
Rubio
, “Light–matter interaction in the long-wavelength limit: No ground-state without dipole self-energy
,” J. Phys. B: At., Mol. Opt. Phys.
51
(3
), 034005
(2018
).54.
A. I.
Burshtein
and S. I.
Temkin
, Spectroscopy of Molecular Rotation in Gases and Liquids
(Cambridge University Press
, 2005
).55.
L.
Novotny
and B.
Hecht
, Principles of Nano-Optics
(Cambridge University Press
, 2012
).56.
T.
Werlang
, A. V.
Dodonov
, E. I.
Duzzioni
, and C. J.
Villas-Bôas
, “Rabi model beyond the rotating-wave approximation: Generation of photons from vacuum through decoherence
,” Phys. Rev. A
78
, 053805
(2008
).57.
D.
Braak
, “Integrability of the Rabi model
,” Phys. Rev. Lett.
107
, 100401
(2011
).58.
F. A.
Wolf
, F.
Vallone
, G.
Romero
, M.
Kollar
, E.
Solano
, and D.
Braak
, “Dynamical correlation functions and the quantum Rabi model
,” Phys. Rev. A
87
, 023835
(2013
).59.
E. T.
Jaynes
and F. W.
Cummings
, “Comparison of quantum and semiclassical radiation theories with application to the beam maser
,” Proc. IEEE
51
(1
), 89
–109
(1963
).60.
O.
Kühn
, J.
Manz
, and Y.
Zhao
, “Ultrafast IR laser control of photodissociation: Single- vs. multi-pulse schemes
,” Phys. Chem. Chem. Phys.
1
, 3103
–3110
(1999
).61.
Q.-H.
Chen
, C.
Wang
, S.
He
, T.
Liu
, and K.-L.
Wang
, “Exact solvability of the quantum Rabi model using Bogoliubov operators
,” Phys. Rev. A
86
, 023822
(2012
).62.
V. V.
Albert
, “Quantum Rabi model for N-state atoms
,” Phys. Rev. Lett.
108
, 180401
(2012
).63.
J.
Casanova
, G.
Romero
, I.
Lizuain
, J. J.
García-Ripoll
, and E.
Solano
, “Deep strong coupling regime of the Jaynes-Cummings model
,” Phys. Rev. Lett.
105
, 263603
(2010
).64.
P.
Forn-Díaz
, L.
Lamata
, E.
Rico
, J.
Kono
, and E.
Solano
, “Ultrastrong coupling regimes of light-matter interaction
,” Rev. Mod. Phys.
91
, 025005
(2019
).65.
H.
Carmichael
, Statistical Mehods in Quantum Optics 1: Master Equations and Fokker-Planck Equations
(Springer Berlin
, Heidelberg
, 1999
).66.
J. F.
Triana
, D.
Peláez
, and J. L.
Sanz-Vicario
, “Entangled photonic-nuclear molecular dynamics of LiF in quantum optical cavities
,” J. Phys. Chem. A
122
(8
), 2266
–2278
(2018
).67.
H. P.
Breuer
and F.
Petruccione
, The Theory of Open Quantum Systems
(Oxford University Press
, 2002
).68.
A.
Strashko
and J.
Keeling
, “Raman scattering with strongly coupled vibron-polaritons
,” Phys. Rev. A
94
, 023843
(2016
).69.
M.
Litinskaya
, P.
Reineker
, and V. M.
Agranovich
. Fast polariton relaxation in strongly coupled organic microcavities
. J. Lumin.
110
, 364
–372
(2004
).70.
B. M.
Garraway
, “The Dicke model in quantum optics: Dicke model revisited
,” Philos. Trans. R. Soc., A
369
(1939
), 1137
–1155
(2011
).71.
P.
Kirton
, M. M.
Roses
, J.
Keeling
, and E. G.
Dalla Torre
, “Introduction to the Dicke model: From equilibrium to nonequilibrium, and vice versa
,” Adv. Quantum Tech.
2
(1-2
), 1800043
(2019
).72.
M.
Litinskaya
and P.
Reineker
, “Loss of coherence of exciton polaritons in inhomogeneous organic microcavities
,” Phys. Rev. B
74
, 165320
(2006
).73.
F.
Herrera
and F. C.
Spano
, “Absorption and photoluminescence in organic cavity QED
,” Phys. Rev. A
95
, 053867
(2017
).74.
F.
Herrera
and F. C.
Spano
, “Theory of nanoscale organic cavities: The essential role of vibration-photon dressed states
,” ACS Photonics
5
, 65
–79
(2018
).© 2019 Author(s).
2019
Author(s)
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