# Organic charged polaritons in the ultrastrong coupling regime

Mao Wang  Department of Chemistry and Molecular Biology, University of
Gothenburg, 412 96 Gothenburg, Sweden  Suman Mallick  Department of Chemistry
and Molecular Biology, University of Gothenburg, 412 96 Gothenburg, Sweden
Anton Frisk Kockum  Department of Microtechnology and Nanoscience, Chalmers
University of Technology, 412 96 Gothenburg, Sweden  Karl Börjesson
<EMAIL_ADDRESS>Department of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Gothenburg, Sweden

(August 27, 2024)

###### Abstract

We embedded an all-hydrocarbon-based carbocation in a metallic microcavity
that was tuned to resonance with an electronic transition of the carbocation.
The measured Rabi splitting was 41 % of the excitation energy, putting the
system well into the ultrastrong coupling regime. Importantly, due to the
intrinsic charge on the carbocation, the polaritons that form carry a
significant charge fraction (0.55 $e_{0}$) and a large charge-to-mass ratio
($\sim\,$2400 $e_{0}/m_{0}$). Moreover, the ground state of the ultrastrongly
coupled system is calculated to carry about one percent of one elementary
charge, implying a potentially enhanced charge transport across the molecules.
These unique properties of our system, together with its convenient
preparation, provide a practical platform to study charged polaritons in the
ultrastrong coupling regime.

## Introduction.

Exciton-polaritons are hybrid light-matter quasiparticles formed when the
electronic excitation in “matter” is strongly coupled to a resonant
electromagnetic field. To reach the strong coupling regime, the coupling
strength (i.e., half the Rabi splitting $\hbar\Omega$), which quantifies the
light-matter coupling strength, must be larger than the overall dissipation of
the system. When the coupling strength is further increased and approaches a
significant fraction ($\gtrsim$ 10 %) of the bare energy of the excitation
($E_{x}$), the system enters the so-called ultrastrong coupling (USC) regime
Kockum  _et al._ (2019); Ciuti  _et al._ (2005); Forn-Díaz  _et al._ (2019).
In this regime, not only the excited state of the system, but also the ground
state acquires photonic and excitonic contributions Kockum  _et al._ (2019);
Ciuti  _et al._ (2005); Forn-Díaz  _et al._ (2019); Ashhab and Nori (2010).
This change is due to the anti-resonant contribution in the interaction, which
is usually ignored in standard strongly coupled systems, and leads to a
renormalization of the electromagnetic field Yu  _et al._ (2021); Ye  _et al._
(2021); Wang  _et al._ (2021). Theoretical investigations show that the
virtual photons in the ground state can be released by nonadiabatic
manipulation of the coupling strength Günter  _et al._ (2009); De Liberato
_et al._ (2007); Beaudoin  _et al._ (2011); De Liberato  _et al._ (2009);
Takashima  _et al._ (2008); Werlang  _et al._ (2008); Carusotto  _et al._
(2012); Garziano  _et al._ (2013); Shapiro  _et al._ (2015). The new hybrid
ground state may have modified attributes including ground-state chemical
reactivity Herrera and Spano (2016), ground-state electroluminescence Cirio
_et al._ (2016), and electrical conductivity and optoelectrical properties
Gambino  _et al._ (2014); Askenazi  _et al._ (2014).

The USC regime has been reached in several systems, including inorganic
quantum well intersubband microcavities Anappara  _et al._ (2009),
superconducting circuits Niemczyk  _et al._ (2010), organic molecules in
metallic microcavities Schwartz  _et al._ (2011), plasmonic nanoparticles
Mueller  _et al._ (2020), etc. (a detailed list of systems can be found in
Ref. Kockum  _et al._ (2019)). Most of these systems demand precise
fabrication or cryogenic conditions, which is challenging. More diverse and
readily prepared systems are therefore needed in order to explore the new
phenomena predicted in the USC regime and to move towards practical
applications Sanvitto and Kéna-Cohen (2016).

In this Letter, we show how trions can be used to reach USC in a system that
only requires relatively simple preparation. Trions are excitons containing an
extra hole or electron. When trions are strongly coupled to cavity photons,
the newly formed polaritons are expected to carry a fraction of a net charge
Rapaport  _et al._ (2000, 2001). Trions therefore enable direct manipulation
of the polariton behavior with external electrical or magnetic fields.
Furthermore, charged polaritons have a strong interaction among each other
because of Coulomb interaction and therefore constitute a promising platform
to observe nonlinear phenomena Daskalakis  _et al._ (2014).

Trions are generally unstable and can easily decompose into an exciton and a
free charge at room temperature. Charged polaritons were therefore first
achieved in inorganic quantum wells inside a microcavity at liquid-helium
temperatures Rapaport  _et al._ (2000, 2001). Later they were realized by
strongly coupling trions in electrically doped semiconducting single-walled
carbon nanotubes to cavity photons Möhl  _et al._ (2018). However, the energy
of trions in both inorganic quantum wells and nanotubes lie close to that of
the neutral exciton. The formed charged polaritons are therefore always
strongly admixed with the neutral exciton, making it challenging to study
their intrinsic properties. For molecular systems, charged polaritons were
recently reported by strongly coupling the electronic transition of hole-doped
organic semiconductors in planar microcavities Cheng  _et al._ (2018);
Krainova  _et al._ (2020). The coupled transition arises from electronic
excitation from the lower-lying orbitals to the partially vacant highest
occupied molecular orbital of the hole-doped molecules. This method
establishes a path to achieve charged polaritons in molecules and open the
possibility to electrically tune polariton properties in organic
semiconductors, although the doping ratio was not unity (30 wt%), and the
highest possible collective coupling strength was therefore not achieved.

Here we demonstrate room-temperature stable charged polaritons in the USC
regime by strongly coupling the electronic transition of a carbocation to the
optical field in a metallic Fabry-Pérot cavity. The carbocation carries an
intrinsic net charge without extrinsic doping and can be regarded as a “100 %
doped” system. The obtained Rabi splitting can reach as high as $\sim\,$0.50
eV, amounting to 41 % of the corresponding exciton energy (1.22 eV), which
puts the system well into the USC regime. The charge-to-mass ratio of the
lower polaritonic state is estimated to be three orders of magnitude higher
than that of an electron. More importantly, the ground state of the system
carries a net charge of $0.01\,\mathrm{e_{0}}$ attributed to the effect of the
USC. These unique properties of our system, together with its simple
preparation, provide a practical platform to study charged polaritons in the
USC regime.

## Photophysics of the carbocation.

Figure 1:  (a) Conventional doping using an electron transfer reaction from a
donor to an acceptor molecule. (b) Protonation using trifluoroacetic acid
(TFA) followed by water elimination leading to the
tris(10-mesitylanthr-9-yl)methyl cation (TAntM).

In conventional chemical doping [Fig. 1(a)], an electron-transfer reaction
occurs between the donor and acceptor molecules. In our system [Fig. 1(b)],
the TAntM cation [tris(10-mesitylanthr-9-yl)methyl cation] was obtained by a
two-step reaction: a proton transfer from trifluoroacetic acid (TFA) followed
by an H2O elimination reaction Nishiuchi  _et al._ (2018). This two-step
reaction is irreversible as H2O is evaporated and the formed carbocation is,
therefore, more stable than charged molecules formed by an electron-transfer
reaction in the conventional doping method. Moreover, the formed carbocation,
which usually is a chemically highly unstable species, is protected from
nucleophilic attacks by the steric hindrance of the three surrounding bulky
mesityl-substituted anthryl groups. These two effects result in unusually high
stability for such an exotic molecule, allowing it to be handled under ambient
conditions and solution processed into films.

Figure 2:  (a) Top view of the crystal structure of TAntM showing the
120-degree binding angle of the central carbon. (b) Relative charge density
map calculated by density functional theory showing atoms with partially
positive charge as green and partially negative charge as red. (c) Absorption
and emission of TAntM in TFA solution and the absorption of a spin coated film
of TAntM.

The positive charge on TAntM is central to its photophysical properties.
Firstly, the single-crystal X-ray structure of the molecule shows that the
central carbon forms in-plane bonds having binding angles of $120^{\circ}$ to
the three bulky mesityl-substituted anthracene moieties Nishiuchi  _et al._
(2018). Thus, the central carbon is confirmed to be sp2-hybridized [Fig.
2(a)]. Based on the electrostatic potential surface of the molecule calculated
using density functional theory [Fig. 2(b)], the central carbon carries a
fraction of a positive charge. In addition, other carbons in the molecule have
a fractional positive charge (although smaller in comparison). These carbons
can all be predicted from resonance structures of the Lewis structure in Fig.
1(b). The positive charge can therefore be considered somewhat delocalized
over a considerable part of the molecule, increasing the chemical stability.

The characteristic feature of the absorption spectrum of the carbocation is an
intense, broad band in the near-infrared regime [$\lambda_{\rm
max}=990\,\mathrm{nm}$; Fig. 2(c)], with a peak molar absorption of
$\sim\;$$3.7\cdot 10^{4}\,\mathrm{M^{-1}cm^{-1}}$. This absorption band was
assigned to the lowest-energy electronic transition ($S_{1}\leftarrow S_{0}$),
due to its mirror-image relationship to the emission spectrum. Further, time-
dependent density-functional-theory calculations have previously predicted
this transition to be, to a high degree, the result of a transition from the
degenerate highest occupied molecular orbitals (HOMO and HOMO-1) to the lowest
unoccupied molecular orbital (LUMO) Nishiuchi  _et al._ (2018). The LUMO of
the molecule contains the empty $p$ orbital of the positive central carbon,
while the HOMOs were located on the surrounding anthracene moieties.

It is interesting to linger on the reason for the very low energy transition
of the molecule, considering the small size of the aromatic network. The
energy of the LUMO orbital is as low as $-5.81\,\mathrm{eV}$, a value
comparable to the energy of the HOMO of many organic chromophores Nishiuchi
_et al._ (2018). The reason for this low energy should be the empty $p$
orbital on the central carbon and the reason why a molecule having such a high
electron affinity can be stable at all should be the bulkiness of the
anthracene units. The anthracene bulk physically protects the $p$ orbital of
the central carbon, resulting in increased stability kinetically, and provides
an energetic penalty for the central carbon to adopt a tetrahedral geometry
resulting in increased stability thermodynamically. This class of dye, having
an empty carbon $p$ orbital, contains a positive charge on the LUMO and may
furthermore even represent a direction towards closed-shell organic dyes
having electronic transitions approaching vibrational energies. In summary,
the molecular exciton formed can be regarded as a positive trion: one exciton
bound to a positive charge. When this trion is strongly coupled to a cavity
photon, the polaritons formed will therefore carry a fraction of the net
charge.

Thin films of the carbocation were readily prepared by the spin-coating
method. The envelope of absorption of the films was retained from the one in
solution [Fig. 2(c)], suggesting that intermolecular interactions are weak.
This point is important in the following discussion of the photophysics within
the strong coupling regime, since it shows that each excited molecule can be
regarded as an individual exciton. The peak absorption coefficient $\alpha$ of
the film is $1.05\cdot 10^{5}\,\mathrm{cm^{-1}}$. Based on the absorption
cross-section $\sigma=6.14\cdot 10^{-17}\,\mathrm{cm^{2}}$ derived from the
molar absorption coefficient in solution, the charge density of the cation
film is on the order of $10^{21}\,\mathrm{cm^{-3}}$, one order of magnitude
higher than the density ($10^{20}\,\mathrm{cm^{-3}}$) in a previous report
using extrinsic doping by co-evaporation of matrix and dopant molecules Cheng
_et al._ (2018). As the coupling strength is proportional to the square root
of the exciton density Hertzog  _et al._ (2019), this high concentration
indicates that the carbocation can be expected to achieve a much larger
coupling strength and has the potential to reach the USC regime.

## The ultrastrong coupling regime.

Figure 3:  (a) The cavity structure: 22 nm Au / TAntM film / 22 nm Au. (b) The
absorption of a carbocation film (blue dashed line) outside and inside the
cavity (orange solid line). (c) The angular dispersion of the transmission
spectra of a carbocation cavity. The purple solid lines are polaritonic
branches obtained by fitting with the full Hopfield Hamiltonian, and the
dashed white and orange lines are the exciton ($E_{x}$) and cavity ($E_{\rm
cav}$) energies, respectively.

To explore the (ultra-)strong coupling regime, a metallic Fabry-Perot cavity
containing a carbocation film was fabricated. The active film was readily
prepared by the spin-coating method (details in the Methods section in the
Supplemental Material Sup ). The cavity structure is shown in Fig. 3(a). The
active layer did not contain any polymer matrix, which otherwise is commonly
used in the field. It therefore allowed the highest concentration possible and
thus the largest collective light-matter coupling strength achievable using
this molecule. A typical absorption spectrum of the cavity is shown in Fig.
3(b). The single absorption band of the bare film centered at 1.22 eV is
replaced by two polaritonic branches centered at 1.02 and 1.52 eV.

On resonance, the energy difference between the two polaritonic branches is
about 0.5 eV, amounting to 41 % of the bare exciton energy (1.22 eV). This
implies that the system is in the USC regime. In this regime, the rotating-
wave approximation is not valid and the system should be treated using the
full Hopfield Hamiltonian $H_{\rm Hop}$, where the anti-resonant and
diamagnetic terms should be included (see Ref. Kockum  _et al._ (2019) for
details).

The polaritonic energies $E$ are described analytically by the eigenvalues of
$H_{\rm Hop}$, which can be obtained by solving the quadratic equation Gambino
_et al._ (2014)

$\left(E_{\rm
cav}^{2}-E^{2}\right)\left(E_{x}^{2}-E^{2}\right)=\left(\hbar\Omega\right)^{2}E_{\rm
cav}^{2},$ (1)

where $E_{x}$ and $E_{\rm cav}$ are the energies of the bare exciton and
cavity, respectively. Figure 3(c) displays the angle-resolved transmission (TE
mode). The polaritons show an angular dispersive behavior and a clear
anticrossing feature is observed close to the exciton energy of the
carbocation. By fitting the angular data to the results from the full Hopfield
Hamiltonian, the obtained Rabi splitting is 0.50 eV, which leads to a
normalized coupling strength $\eta=\hbar\Omega/2E_{x}$ of 0.2. Thus, it
confirms that the system is well into the USC regime. Notably, in the resonant
case, the full treatment leads to an asymmetric anti-crossing in which the
polaritonic energies follow Gambino  _et al._ (2014); Kéna-Cohen  _et al._
(2013)

$E_{\rm
UP/LP}=\sqrt{E_{x}^{2}+\left(\frac{\hbar\Omega}{2}\right)^{2}}\pm\frac{\hbar\Omega}{2},$
(2)

due to a combined effect of the anti-resonant and diamagnetic terms. The
energy of the lower polariton lies closer to the exciton energy at resonance
($E_{x}=E_{\rm cav}$) and become more matter-like compared to the case for the
strong coupling regime [Fig. 3(c)]. This anomalous effect is proportional to
the normalized coupling strength $\eta$ and becomes significant in the USC
regime Ciuti  _et al._ (2005).

Figure 4:  (a) Polariton energy as a function of cavity energy. The continuous
line is the simulated polariton dispersion, using the parameters obtained from
the fit of the angular dispersive transmission spectrum with Eq. (1). The
shaded region indicates the polariton gap. (b) The photon (exciton) ratio in
the lower polariton (upper panel) and in the ground state (lower panel).

Another important feature of the USC regime is the appearance of a band gap of
forbidden polariton energies, where no solution to Eq. (1) will fall Gambino
_et al._ (2014); Todorov  _et al._ (2010); Jouy  _et al._ (2011); Delteil  _et
al._ (2012). The forbidden frequencies correspond to destructive interference
between the electromagnetic field radiated by the electronic oscillations and
the bare microcavity photon field. As shown in Fig. 4(a), the continuous lines
represent the polaritonic branches obtained from the solution of Eq. (1). A
polaritonic gap $E_{g}$ of 130 meV is formed between the asymptotic lines of
the upper and lower polaritonic dispersions
[$E_{g}=\left(\hbar\Omega\right)^{2}/2E_{x}$]. The relative size of the gap
($E_{g}/E_{x}$) is proportional to $\eta^{2}$ and therefore only becomes
significant in the USC regime. It can therefore also be regarded as a
signature of the USC regime Jouy  _et al._ (2011) and has been observed
previously Gambino  _et al._ (2014); Todorov  _et al._ (2010); Jouy  _et al._
(2011); Delteil  _et al._ (2012).

## Charged polariton and ground-state modifications.

Polaritons that are composed of charged excitons are expected to carry a net
electric charge that is equal to the electron charge $e_{0}$ times the
relative fraction of the charged exciton in the polariton mode. For example,
the effective charge of the lower polariton is $e_{\rm
eff,LP}=e_{0}\left|\alpha_{\rm LP,ex}\right|^{2}$, where $\left|\alpha_{\rm
LP,ex}\right|^{2}$ is the exciton fraction of the lower polariton. This
effective value represents the probability of finding an electron bound to the
polariton. The charge-to-mass ratio $e/m$ is a key parameter for the transport
behavior of charged species under an electrical field. The polariton effective
mass is the weighted harmonic mean of the mass of its exciton and photon
components,

$\frac{1}{m_{\rm eff,LP}}=\frac{\left|\alpha_{\rm LP,ex}\right|^{2}}{m_{\rm
ex}}+\frac{\left|\alpha_{\rm LP,ph}\right|^{2}}{m_{\rm ph}}$ (3)

where $m_{\rm ex}$ and $m_{\rm ph}$ are the effective exciton and cavity-
photon mass, respectively. As $m_{\rm ph}\ll m_{\rm ex}$, the effective
polariton mass therefore mainly depends on the mass of the cavity photon,
which is on the order of $10^{-4}$ times the bare electron mass $m_{0}$ Deng
_et al._ (2010). Due to this low effective mass, the charged polaritons
therefore possess a much larger charge-to-mass ratio than typical charge
carriers in organic semiconductors, enabling a potentially highly efficient
charge transport.

In a previous report on a charged inorganic polariton Rapaport  _et al._
(2001), the charge-to-mass ratio of polaritons was shown to be orders of
magnitude larger than that of the free electron, and the enclosed theoretical
calculations indicated a significantly higher drift velocity for the charged
polaritons. Similar enhanced effects for charge transport was also discussed
for trion-polaritons in semiconducting carbon nanotubes (CNTs) Möhl  _et al._
(2018). The resulting charge-to-mass ratio in CNTs was about 200 times higher
than that of an electron or hole. In our system, the net charge of the
polariton is higher than that in inorganic or CNT systems, since the
polaritonic states have no contribution from any neutral excitons. At zero
probing angle ($k_{\parallel}=0$), $e_{\rm eff,LP}$ is about
$0.55\,\mathrm{e_{0}}$ and the effective charge-to-mass ratio $e_{\rm
eff,LP}/m_{\rm eff,LP}$ of the charged polariton reaches a value of
$\sim\,$2400 $e_{0}/m_{0}$ [$m_{\rm eff,LP}$ is calculated from Eq. (3)].
Moreover, the charge fraction of polaritons can be further increased by blue-
detuning the cavity. The effective mass of electrons in organic semiconductors
is generally large due to the strong localized charge and can reach as high as
25 times that of the bare electron mass Coropceanu  _et al._ (2007). Thus, it
is expected that charged polaritons will have several orders of magnitude
higher charge-carrier mobility than typical charges in organic semiconductors.
However, for organic electronics, the charge transport most often occurs in
the ground state. Therefore, the formation of polaritonic states will have no
obvious effect on the charge transport. This explains why only little
attention has been devoted towards enhanced charge transport of organic
semiconductors in the strong coupling regime Nagarajan  _et al._ (2020); Orgiu
_et al._ (2015); Kang  _et al._ (2021); Bhatt  _et al._ (2021).

In the USC regime, the treatment of the system with the full Hopfield
Hamiltonian not only gives a more accurate description of the dispersion
relation; it also indicates that the ground state is a squeezed vacuum state,
which contains contributions from (virtual) photons and excitons. The effect
of the photon contribution on the ground state was first discussed by Ciuti et
al. Ciuti  _et al._ (2005), who proposed the possibility of extracting the
virtual photons by modulating the coupling strength, which is reminiscent of
the dynamical Casimir effect Moore (1970). Later, Cirio et al. showed that
electroluminescence can occur from the ground state in an ultrastrongly
coupled system Cirio  _et al._ (2016, 2019).

Here we want to emphasize the effect of the exciton contribution on the
polaritonic ground state. In our system, the ground state will carry a certain
fraction of charge inherited from the exciton component. The photon and
exciton components in the lower polariton and the ground state are shown in
the upper and lower panels of Fig. 4(b), respectively. In our red-detuned
cavity, the energy of the cavity moves closer to the exciton energy as the
angle increases and the LP becomes more exciton-like. However, both the
excitonic and photonic contributions to the ground state decrease with
increasing angle, a similar trend as in a previous report of an ultrastrongly
coupled system by Kéna-Cohen et al. Kéna-Cohen  _et al._ (2013). At zero
degrees, the exciton contribution to the ground state of the system is about
one percent. In this sense, the ground state will carry a fractional charge of
$0.01\,\mathrm{e_{0}}$. This charge is delocalized over all molecules that
contribute in the hybridization event that forms the polariton. Furthermore,
it is up for discussion what the charge to mass ratio is for this fractional
charge, although we expect it to be quite small. Of course, the ground state
of the individual molecule is to the largest degree unperturbed, but the
contribution of a delocalized fractional charge with a low charge to weight
ratio implies a possibility of increasing the ground-state charge transport in
organic materials. It is worth noting that this phenomenon only occurs when
the charged polariton is in the USC regime, in which the ground state has a
contribution from the charged excitons. Furthermore, how the fractional charge
of the ground-state could be interpreted in any change of eventual ground-
state mass, is open for discussion.

## Conclusion.

We have demonstrated the formation of charged polaritons in the USC regime at
room temperature using a simple planar metallic microcavity encapsulating a
carbocation film. The strategy using a transition from a lower lying orbital
to HOMO allowed for a very low exciton energy, resulting in the normalized
coupling strength reaching as high as 20 %, putting the system well into the
USC regime. As a “100 % doped” film, the formed polaritons can contain a
significant charge fraction ($0.55\,\mathrm{e_{0}}$ for the lower polariton)
and a large charge-to-mass ratio ($\sim\,$2400 $e_{0}/m_{0}$). Moreover, there
is a reflection of the excited state into the ground state in the USC regime,
allowing the ground state of the system to carry about one percent of the
elementary charge $e_{0}$, which is delocalized over the ensemble of
molecules. It therefore implies the possibility of enhanced ground-state
charge transport of organic materials in the USC regime through ground-state
photoconductivity.

###### Acknowledgements.

## Acknowledgments.

KB gratefully acknowledges financial support from the European Research
Council (ERC-2017-StG-757733), the Swedish Research Council (2016-03354), and
the Knut and Alice Wallenberg Foundation (KAW 2017.0192). AFK acknowledges
support from the Swedish Research Council (grant number 2019-03696) and from
the Knut and Alice Wallenberg Foundation through the Wallenberg Centre for
Quantum Technology (WACQT).

## References

  * Kockum  _et al._ (2019) A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, “Ultrastrong coupling between light and matter,” Nature Reviews Physics 1, 19 (2019), arXiv:1807.11636 .
  * Ciuti  _et al._ (2005) C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Physical Review B 72, 115303 (2005), arXiv:0504021 [cond-mat] .
  * Forn-Díaz  _et al._ (2019) P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Reviews of Modern Physics 91, 025005 (2019), arXiv:1804.09275 .
  * Ashhab and Nori (2010) S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Physical Review A 81, 042311 (2010), arXiv:0912.4888 .
  * Yu  _et al._ (2021) Y. Yu, S. Mallick, M. Wang, and K. Börjesson, “Barrier-free reverse-intersystem crossing in organic molecules by strong light-matter coupling,” Nature Communications 12, 3255 (2021).
  * Ye  _et al._ (2021) C. Ye, S. Mallick, M. Hertzog, M. Kowalewski, and K. Börjesson, “Direct Transition from Triplet Excitons to Hybrid Light-Matter States via Triplet-Triplet Annihilation,” Journal of the American Chemical Society 143, 7501 (2021).
  * Wang  _et al._ (2021) M. Wang, M. Hertzog, and K. Börjesson, “Polariton-assisted excitation energy channeling in organic heterojunctions,” Nature Communications 12, 1874 (2021).
  * Günter  _et al._ (2009) G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light–matter interaction,” Nature 458, 178 (2009).
  * De Liberato  _et al._ (2007) S. De Liberato, C. Ciuti, and I. Carusotto, “Quantum Vacuum Radiation Spectra from a Semiconductor Microcavity with a Time-Modulated Vacuum Rabi Frequency,” Physical Review Letters 98, 103602 (2007), arXiv:0611282 [cond-mat] .
  * Beaudoin  _et al._ (2011) F. Beaudoin, J. M. Gambetta, and A. Blais, “Dissipation and ultrastrong coupling in circuit QED,” Physical Review A 84, 043832 (2011), arXiv:1107.3990 .
  * De Liberato  _et al._ (2009) S. De Liberato, D. Gerace, I. Carusotto, and C. Ciuti, “Extracavity quantum vacuum radiation from a single qubit,” Physical Review A 80, 053810 (2009), arXiv:0906.2706 .
  * Takashima  _et al._ (2008) K. Takashima, N. Hatakenaka, S. Kurihara, and A. Zeilinger, “Nonstationary boundary effect for a quantum flux in superconducting nanocircuits,” Journal of Physics A: Mathematical and Theoretical 41, 164036 (2008).
  * Werlang  _et al._ (2008) 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,” Physical Review A 78, 053805 (2008), arXiv:0806.3475 .
  * Carusotto  _et al._ (2012) I. Carusotto, S. De Liberato, D. Gerace, and C. Ciuti, “Back-reaction effects of quantum vacuum in cavity quantum electrodynamics,” Physical Review A 85, 023805 (2012).
  * Garziano  _et al._ (2013) L. Garziano, A. Ridolfo, R. Stassi, O. Di Stefano, and S. Savasta, “Switching on and off of ultrastrong light-matter interaction: Photon statistics of quantum vacuum radiation,” Physical Review A 88, 063829 (2013).
  * Shapiro  _et al._ (2015) D. S. Shapiro, A. A. Zhukov, W. V. Pogosov, and Y. E. Lozovik, “Dynamical Lamb effect in a tunable superconducting qubit-cavity system,” Physical Review A 91, 063814 (2015), arXiv:1503.01666 .
  * Herrera and Spano (2016) F. Herrera and F. C. Spano, “Cavity-Controlled Chemistry in Molecular Ensembles,” Physical Review Letters 116, 238301 (2016), arXiv:1512.05017 .
  * Cirio  _et al._ (2016) M. Cirio, S. De Liberato, N. Lambert, and F. Nori, “Ground State Electroluminescence,” Physical Review Letters 116, 113601 (2016), arXiv:1508.05849 .
  * Gambino  _et al._ (2014) S. Gambino, M. Mazzeo, A. Genco, O. Di Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light–Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1, 1042 (2014).
  * Askenazi  _et al._ (2014) B. Askenazi, A. Vasanelli, A. Delteil, Y. Todorov, L. C. Andreani, G. Beaudoin, I. Sagnes, and C. Sirtori, “Ultra-strong light-matter coupling for designer Reststrahlen band,” New Journal of Physics 16, 043029 (2014).
  * Anappara  _et al._ (2009) A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Physical Review B 79, 201303 (2009), arXiv:0808.3720 .
  * Niemczyk  _et al._ (2010) T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Physics 6, 772 (2010), arXiv:1003.2376 .
  * Schwartz  _et al._ (2011) T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Physical Review Letters 106, 196405 (2011).
  * Mueller  _et al._ (2020) N. S. Mueller, Y. Okamura, B. G. M. Vieira, S. Juergensen, H. Lange, E. B. Barros, F. Schulz, and S. Reich, “Deep strong light-matter coupling in plasmonic nanoparticle crystals,” Nature 583, 780 (2020).
  * Sanvitto and Kéna-Cohen (2016) D. Sanvitto and S. Kéna-Cohen, “The road towards polaritonic devices,” Nature Materials 15, 1061 (2016).
  * Rapaport  _et al._ (2000) R. Rapaport, R. Harel, E. Cohen, A. Ron, E. Linder, and L. N. Pfeiffer, “Negatively Charged Quantum Well Polaritons in a GaAs/AlAs Microcavity: An Analog of Atoms in a Cavity,” Physical Review Letters 84, 1607 (2000).
  * Rapaport  _et al._ (2001) R. Rapaport, E. Cohen, A. Ron, E. Linder, and L. N. Pfeiffer, “Negatively charged polaritons in a semiconductor microcavity,” Physical Review B 63, 235310 (2001).
  * Daskalakis  _et al._ (2014) K. S. Daskalakis, S. A. Maier, R. Murray, and S. Kéna-Cohen, “Nonlinear interactions in an organic polariton condensate,” Nature Materials 13, 271 (2014).
  * Möhl  _et al._ (2018) C. Möhl, A. Graf, F. J. Berger, J. Lüttgens, Y. Zakharko, V. Lumsargis, M. C. Gather, and J. Zaumseil, “Trion-Polariton Formation in Single-Walled Carbon Nanotube Microcavities,” ACS Photonics 5, 2074 (2018).
  * Cheng  _et al._ (2018) C.-Y. Cheng, R. Dhanker, C. L. Gray, S. Mukhopadhyay, E. R. Kennehan, J. B. Asbury, A. Sokolov, and N. C. Giebink, “Charged Polaron Polaritons in an Organic Semiconductor Microcavity,” Physical Review Letters 120, 017402 (2018).
  * Krainova  _et al._ (2020) N. Krainova, A. J. Grede, D. Tsokkou, N. Banerji, and N. C. Giebink, “Polaron Photoconductivity in the Weak and Strong Light-Matter Coupling Regime,” Physical Review Letters 124, 177401 (2020).
  * Nishiuchi  _et al._ (2018) T. Nishiuchi, S. Aibara, and T. Kubo, “Synthesis and Properties of a Highly Congested Tri(9-anthryl)methyl Radical,” Angewandte Chemie International Edition 57, 16516 (2018).
  * Hertzog  _et al._ (2019) M. Hertzog, M. Wang, J. Mony, and K. Börjesson, “Strong light-matter interactions: a new direction within chemistry,” Chemical Society Reviews 48, 937 (2019).
  * (34) See the Supplemental Material at XXX.
  * Kéna-Cohen  _et al._ (2013) S. Kéna-Cohen, S. A. Maier, and D. D. C. Bradley, “Ultrastrongly Coupled Exciton-Polaritons in Metal-Clad Organic Semiconductor Microcavities,” Advanced Optical Materials 1, 827 (2013).
  * Todorov  _et al._ (2010) Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Physical Review Letters 105, 196402 (2010), arXiv:1301.1297 .
  * Jouy  _et al._ (2011) P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Applied Physics Letters 98, 231114 (2011), arXiv:1212.4439 .
  * Delteil  _et al._ (2012) A. Delteil, A. Vasanelli, Y. Todorov, C. Feuillet Palma, M. Renaudat St-Jean, G. Beaudoin, I. Sagnes, and C. Sirtori, “Charge-Induced Coherence between Intersubband Plasmons in a Quantum Structure,” Physical Review Letters 109, 246808 (2012), arXiv:1212.4422 .
  * Deng  _et al._ (2010) H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Reviews of Modern Physics 82, 1489 (2010).
  * Coropceanu  _et al._ (2007) V. Coropceanu, J. Cornil, D. A. da Silva Filho, Y. Olivier, R. Silbey, and J.-L. Brédas, “Charge Transport in Organic Semiconductors,” Chemical Reviews 107, 926 (2007).
  * Nagarajan  _et al._ (2020) K. Nagarajan, J. George, A. Thomas, E. Devaux, T. Chervy, S. Azzini, K. Joseph, A. Jouaiti, M. W. Hosseini, A. Kumar, C. Genet, N. Bartolo, C. Ciuti, and T. W. Ebbesen, “Conductivity and Photoconductivity of a p-Type Organic Semiconductor under Ultrastrong Coupling,” ACS Nano 14, 10219 (2020).
  * Orgiu  _et al._ (2015) E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, and T. W. Ebbesen, “Conductivity in organic semiconductors hybridized with the vacuum field,” Nature Materials 14, 1123 (2015), arXiv:1409.1900 .
  * Kang  _et al._ (2021) E. S. H. Kang, S. Chen, V. Derek, C. Hägglund, E. D. Głowacki, and M. P. Jonsson, “Charge transport in phthalocyanine thin-film transistors coupled with Fabry-Perot cavities,” Journal of Materials Chemistry C 9, 2368 (2021).
  * Bhatt  _et al._ (2021) P. Bhatt, K. Kaur, and J. George, “Enhanced Charge Transport in Two-Dimensional Materials through LightÐMatter Strong Coupling,” ACS Nano 15, 13616 (2021).
  * Moore (1970) G. T. Moore, “Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity,” Journal of Mathematical Physics 11, 2679 (1970).
  * Cirio  _et al._ (2019) M. Cirio, N. Shammah, N. Lambert, S. De Liberato, and F. Nori, “Multielectron Ground State Electroluminescence,” Physical Review Letters 122, 190403 (2019), arXiv:1811.08682 .