By employing the numerically accurate multiple Davydov Ansatz (mDA) formalism in combination with the thermo-field dynamics (TFD) representation of quantum mechanics, we systematically explore the influence of three parameters—temperature, photonic-mode detuning, and qubit–phonon coupling—on population dynamics and absorption spectra of the Holstein–Tavis–Cummings (HTC) model. It is found that elevated qubit–phonon couplings and/or temperatures have a similar impact on all dynamic observables: they suppress the amplitudes of Rabi oscillations in photonic populations as well as broaden the peaks and decrease their intensities in the absorption spectra. Our results unequivocally demonstrate that the HTC dynamics is very sensitive to the concerted variation of the three aforementioned parameters, and this finding can be used for fine-tuning polaritonic transport. The developed mDA-TFD methodology can be efficiently applied for modeling, predicting, optimizing, and comprehensively understanding dynamic and spectroscopic responses of actual molecular systems in microcavities.
REFERENCES
1.
J.
Galego
, F. J.
Garcia-Vidal
, and J.
Feist
, “Cavity-induced modifications of molecular structure in the strong-coupling regime
,” Phys. Rev. X
5
, 041022
(2015
).2.
R.
Bhuyan
, J.
Mony
, O.
Kotov
, G. W.
Castellanos
, J. G.
Rivas
, T.O.
Shegai
, and K.
Bäorjesson
, “The rise and current status of polaritonic photochemistry and photophysics
,” Chem. Rev.
123
, 10877
–10919
(2023
).3.
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
, 6325
–6339
(2018
).4.
F. J.
Garcia-Vidal
, C.
Ciuti
, and T. W.
Ebbesen
, “Manipulating matter by strong coupling to vacuum fields
,” Science
373
, eabd0336
(2021
).5.
A.
Mandal
, M. A. D.
Taylor
, B. M.
Weight
, E. R.
Koessler
, X.
Li
, and P.
Huo
, “Theoretical advances in polariton chemistry and molecular cavity quantum electrodynamics
,” Chem. Rev.
123
, 9786
–9879
(2023
).6.
B. M.
Weight
, X.
Li
, and Y.
Zhang
, “Theory and modeling of light-matter interactions in chemistry: Current and future
,” Phys. Chem. Chem. Phys.
25
, 31554
(2023
).7.
I. S.
Ulusoy
and O.
Vendrell
, “Dynamics and spectroscopy of molecular ensembles in a lossy microcavity
,” J. Chem. Phys.
153
, 044108
(2020
).8.
F. C.
Spano
, “Exciton–phonon polaritons in organic microcavities: Testing a simple ansatz for treating a large number of chromophores
,” J. Chem. Phys.
152
, 204113
(2020
).9.
J.
Fregoni
, S.
Corni
, M.
Persico
, and G.
Granucci
, “Photochemistry in the strong coupling regime: A trajectory surface hopping scheme
,” J. Comput. Chem.
41
, 2033
–2044
(2020
).10.
X.
Li
, A.
Mandal
, and P.
Huo
, “Cavity frequency-dependent theory for vibrational polariton chemistry
,” Nat. Commun.
12
, 1315
(2021
).11.
B.
Gu
and S.
Mukamel
, “Optical-cavity manipulation of conical intersections and singlet fission in pentacene dimers
,” J. Phys. Chem. Lett.
12
, 2052
–2056
(2021
).12.
T. E.
Li
, A.
Nitzan
, and J. E.
Subotnik
, “Collective vibrational strong coupling effects on molecular vibrational relaxation and energy transfer: Numerical insights via cavity molecular dynamics simulations
,” Angew. Chem., Int. Ed.
60
, 15533
–15540
(2021
).13.
J. B.
Pérez-Sánchez
, A.
Koner
, N. P.
Stern
, and J.
Yuen-Zhou
, “Simulating molecular polaritons in the collective regime using few-molecule models
,” Proc. Natl. Acad. Sci. U. S. A.
120
, e2219223120
(2023
).14.
R. H.
Dicke
, “Coherence in spontaneous radiation processes
,” Phys. Rev.
93
, 99
(1954
).15.
C.
Emary
and T.
Brandes
, “Quantum chaos triggered by precursors of a quantum phase transition: The dicke model
,” Phys. Rev. Lett.
90
, 044101
(2003
).16.
J.
Larson
and T.
Mavrogordatos
, The Jaynes-Cummings model and its descendants (IOP Publishing
, Bristol
, 2021
).17.
J. A.
Ćwik
, S.
Reja
, P. B.
Littlewood
, and J.
Keeling
, “Polariton condensation with saturable molecules dressed by vibrational modes
,” Europhys. Lett.
105
, 47009
(2014
).18.
F. C.
Spano
, “Optical microcavities enhance the exciton coherence length and eliminate vibronic coupling in J-aggregates
,” J. Chem. Phys.
142
, 184707
(2015
).19.
F.
Herrera
and F. C.
Spano
, “Cavity-controlled chemistry in molecular ensembles
,” Phys. Rev. Lett.
116
, 238301
(2016
).20.
F.
Herrera
and F. C.
Spano
, “Dark vibronic polaritons and the spectroscopy of organic microcavities
,” Phys. Rev. Lett.
118
, 223601
(2017
).21.
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
).22.
F.
Herrera
and F. C.
Spano
, “Absorption and photoluminescence in organic cavity QED
,” Phys. Rev. A
95
, 053867
(2017
).23.
N.
Wu
, J.
Feist
, and F. J.
Garcia-Vidal
, “When polarons meet polaritons: Exciton-vibration interactions in organic molecules strongly coupled to confined light fields
,” Phys. Rev. B
94
, 195409
(2016
).24.
M. A.
Zeb
, P. G.
Kirton
, and J.
Keeling
, “Exact states and spectra of vibrationally dressed polaritons
,” ACS Photonics
5
, 249
–257
(2018
).25.
G.
Gaddemane
, W. G.
Vandenberghe
, M. L.
Van de Put
, S.
Chen
, S.
Tiwari
, E.
Chen
, and M. V.
Fischetti
, “Theoretical studies of electronic transport in monolayer and bilayer phosphorene: A critical overview
,” Phys. Rev. B
98
, 115416
(2018
).26.
J. A.
Ćwik
, P.
Kirton
, S.
De Liberato
, and J.
Keeling
, “Excitonic spectral features in strongly coupled organic polaritons
,” Phys. Rev. A
93
, 033840
(2016
).27.
Q.
Zhang
and K.
Zhang
, “Collective effects of organic molecules based on the Holstein–Tavis–Cummings model
,” J. Phys. B: At. Mol. Opt. Phys.
54
, 145101
(2021
).28.
M.
Schröter
, S. D.
Ivanov
, J.
Schulze
, S. P.
Polyutov
, Y.
Yan
, T.
Pullerits
, and O.
Kühn
, “Exciton–vibrational coupling in the dynamics and spectroscopy of frenkel excitons in molecular aggregates
,” Phys. Rep.
567
, 1
–78
(2015
).29.
M. F.
Gelin
, L.
Chen
, and W.
Domcke
, “Equation-of-Motion methods for the calculation of femtosecond time-resolved 4-wave-mixing and N-wave-mixing signals
,” Chem. Rev.
122
, 17339
–17396
(2022
).30.
H.-D.
Meyer
, U.
Manthe
, and L. S.
Cederbaum
, “The multi-configurational time-dependent Hartree approach
,” Chem. Phys. Lett.
165
, 73
–78
(1990
).31.
M. H.
Beck
, A.
Jäckle
, G. A.
Worth
, and H.-D.
Meyer
, “The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wavepackets
,” Phys. Rep.
324
, 1
–105
(2000
).32.
G. A.
Worth
, H.-D.
Meyer
, H.
Köppel
, L.
Cederbaum
, and I.
Burghardt
, “Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics
,” Int. Rev. Phys. Chem.
27
, 569
–606
(2008
).33.
H.-D.
Meyer
, “Studying molecular quantum dynamics with the multiconfiguration time-dependent Hartree method
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 351
–374
(2012
).34.
U.
Manthe
, “Wavepacket dynamics and the multi-configurational time-dependent Hartree approach
,” J. Phys.: Condens. Matter
29
, 253001
(2017
).35.
H.
Wang
and M.
Thoss
, “Multilayer formulation of the multiconfiguration time-dependent Hartree theory
,” J. Chem. Phys.
119
, 1289
–1299
(2003
).36.
U.
Manthe
, “A multilayer multiconfigurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces
,” J. Chem. Phys.
128
, 164116
(2008
).37.
O.
Vendrell
and H.-D.
Meyer
, “Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine
,” J. Chem. Phys.
134
, 044135
(2011
).38.
H.
Wang
, “Multilayer multiconfiguration time-dependent Hartree theory
,” J. Phys. Chem. A
119
, 7951
–7965
(2015
).39.
H.
Wang
and H.-D.
Meyer
, “Importance of appropriately regularizing the ML-MCTDH equations of motion
,” J. Phys. Chem. A
125
, 3077
–3087
(2021
).40.
W.
Hackbusch
, Tensor Spaces and Numerical Tensor Calculus
(Springer
, Berlin
, 2012
).41.
I. V.
Oseledets
, “Tensor-train decomposition
,” SIAM J. Sci. Comput.
33
, 2295
–2317
(2011
).42.
J.
Haegeman
, T. J.
Osborne
, and F.
Verstraete
, “Post-matrix product state methods: To tangent space and beyond
,” Phys. Rev. B
88
, 075133
(2013
).43.
V.
Murg
, F.
Verstraete
, R.
Schneider
, P. R.
Nagy
, and O.
Legeza
, “Tree tensor network state with variable tensor order: An efficient multireference method for strongly correlated systems
,” J. Chem. Theory Comput.
11
, 1027
–1036
(2015
).44.
B.
Kloss
, Y. B.
Lev
, and D.
Reichman
, “Time-dependent variational principle in matrix-product state manifolds: Pitfalls and potential
,” Phys. Rev. B
97
, 024307
(2018
).45.
R.
Borrelli
and M. F.
Gelin
, “Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach
,” J. Chem. Phys.
145
, 224101
(2016
).46.
C.
Lubich
, I. V.
Oseledets
, and B.
Vandereycken
, “Time integration of tensor trains
,” SIAM J. Numer. Anal.
53
, 917
–941
(2015
).47.
Y.
Kurashige
, “Matrix product state formulation of the multiconfiguration time-dependent Hartree theory
,” J. Chem. Phys.
149
, 194114
(2018
).48.
Y.
Zhao
, K.
Sun
, L.
Chen
, and M.
Gelin
, “The hierarchy of Davydov’s ansätze and its applications
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
12
, e1589
(2022
).49.
Y.
Zhao
, “The hierarchy of Davydov’s ansätze: From guesswork to numerically “exact” many-body wave functions
,” J. Chem. Phys.
158
, 080901
(2023
).50.
K.
Sun
, M. F.
Gelin
, and Y.
Zhao
, “Accurate simulation of spectroscopic signatures of cavity-assisted, conical-intersection-controlled singlet fission processes
,” J. Phys. Chem. Lett.
13
, 4280
–4288
(2022
).51.
K.
Sun
, M. F.
Gelin
, and Y.
Zhao
, “Engineering cavity singlet fission in rubrene
,” J. Phys. Chem. Lett.
13
, 4090
–4097
(2022
).52.
C.
Zhang
, M.
Yu
, Y.
Yan
, L.
Chen
, Z.
Lü
, and Y.
Zhao
, “Emission spectral non-markovianity in qubit–cavity systems in the ultrastrong coupling regime
,” J. Chem. Phys.
157
, 214116
(2022
).53.
K.
Sun
, K.
Shen
, M. F.
Gelin
, and Y.
Zhao
, “Exciton dynamics and time-resolved fluorescence in nanocavity-integrated monolayers of transition-metal dichalcogenides
,” J. Phys. Chem. Lett.
14
, 221
–229
(2023
).54.
K.
Sun
, C.
Dou
, M. F.
Gelin
, and Y.
Zhao
, “Dynamics of disordered Tavis–Cummings and Holstein–Tavis–Cummings models
,” J. Chem. Phys.
156
, 024102
(2022
).55.
Y.
Takahashi
and H.
Umezawa
, “Thermo field dynamics
,” Int. J. Mod. Phys. B
10
, 1755
–1805
(1996
).56.
M.
Suzuki
, “Density matrix formalism, double-space and thermo field dynamics in non-equilibrium dissipative systems
,” Int. J. Mod. Phys. B
05
, 1821
–1842
(1991
).57.
D.
Kosov
and A.
Vdovin
, “The TFD treatment of the quasiparticle-phonon interaction at finite temperature
,” Mod. Phys. Lett. A
09
, 1735
–1743
(1994
).58.
R.
Borrelli
and M. F.
Gelin
, “Finite temperature quantum dynamics of complex systems: Integrating thermo-field theories and tensor-train methods
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
11
, e1539
(2021
).59.
L.
Chen
and Y.
Zhao
, “Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach
,” J. Chem. Phys.
147
, 214102
(2017
).60.
L.
Chen
, R.
Borrelli
, D. V.
Shalashilin
, Y.
Zhao
, and M. F.
Gelin
, “Simulation of time- and frequency-resolved four-wave-mixing signals at finite temperatures: A thermo-field dynamics approach
,” J. Chem. Theory Comput.
17
, 4359
–4373
(2021
).61.
K.
Shen
, K.
Sun
, M. F.
Gelin
, and Y.
Zhao
, “Finite-temperature hole-magnon dynamics in an antiferromagnet
,” J. Phys. Chem. Lett.
15
, 447
–453
(2024
).62.
M. F.
Gelin
and R.
Borrelli
, “Thermal Schrödinger equation: Efficient tool for simulation of many-body quantum dynamics at finite temperature
,” Ann. Phys.
529
, 1700200
(2017
).63.
L. A.
Martínez-Martínez
, E.
Eizner
, S.
Kéna-Cohen
, and J.
Yuen-Zhou
, “Triplet harvesting in the polaritonic regime: A variational polaron approach
,” J. Chem. Phys.
151
, 054106
(2019
).64.
N.
Zhou
, L.
Chen
, Z.
Huang
, K.
Sun
, Y.
Tanimura
, and Y.
Zhao
, “Fast, accurate simulation of polaron dynamics and multidimensional spectroscopy by multiple davydov Trial states
,” J. Phys. Chem. A
120
, 1562
(2016
).65.
Y.
Zhao
, D.
Brown
, and K.
Lindenberg
, “Variational energy band theory for polarons: Mapping polaron structure with the Merrifield method
,” J. Chem. Phys.
106
, 5622
(1997
).66.
C.
Sommer
, M.
Reitz
, F.
Mineo
, and C.
Genes
, “Molecular polaritonics in dense mesoscopic disordered ensembles
,” Phys. Rev. Res.
3
, 033141
(2021
).67.
T.
Gera
and K. L.
Sebastian
, “Effects of disorder on polaritonic and dark states in a cavity using the disordered Tavis–Cummings model
,” J. Chem. Phys.
156
, 194304
(2022
).68.
M.
Wersäll
, B.
Munkhbat
, D. G.
Baranov
, F.
Herrera
, J.
Cao
, T. J.
Antosiewicz
, and T.
Shegai
, “Correlative dark-field and photoluminescence spectroscopy of individual plasmon–molecule hybrid nanostructures in a strong coupling regime
,” ACS Photonics
6
, 2570
–2576
(2019
).69.
J.
del Pino
, F. A. Y. N.
Schröder
, A. W.
Chin
, J.
Feist
, and F. J.
Garcia-Vidal
, “Tensor network simulation of polaron-polaritons in organic microcavities
,” Phys. Rev. B
98
, 165416
(2018
).70.
M. F.
Gelin
, L.
Chen
, R.
Borrelli
, and E.
Thyrhaug
, “Generalized Huang-Rhys factors for molecular aggregates
,” Chem. Phys.
528
, 110495
(2020
).71.
M. F.
Gelin
, R.
Borrelli
, and W.
Domcke
, “Origin of unexpectedly simple oscillatory responses in the excited-state dynamics of disordered molecular aggregates
,” J. Phys. Chem. Lett.
10
, 2806
–2810
(2019
).72.
M. F.
Gelin
and R.
Borrelli
, “Thermo-field dynamics approach to photo-induced electronic transitions driven by incoherent thermal radiation
,” J. Chem. Theory Comput.
19
, 6402
–6413
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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