Motional Narrowing through Photonic Exchange: Rational Suppression of Excitonic Disorder from Molecular Cavity Polariton Formation

Abstract

Maximizing the coherence between the constituents of molecular materials remains a crucial goal toward the implementation of these systems into everyday optoelectronic technologies. Here we experimentally assess the ability of strong light–matter coupling in the collective limit to reduce energetic disorder using porphyrin-based chromophores in Fabry–Pérot (FP) microresonator structures. Following characterization of cavity polaritons formed from chemically distinct porphyrin dimers, we find that the peaks corresponding to the lower polariton (LP) state in each sample do not possess widths consistent with conventional theories. We model the behavior of the polariton peak widths effectively using the results of spectroscopic theory. We correlate differences in the suppression of excitonic energetic disorder between our samples with microscopic light–matter interactions and propose that the suppression stems from photonic exchange. Our results demonstrate that cavity polariton formation can suppress disorder and show researchers how to design coherence into hybrid molecular material systems.

The effective transduction of energy, charge, and information in molecular systems relies on the intricate spatial arrangements of material constituents. These arrangements allow overlaps between the orbitals defining valence electronic states and produce finite amounts of spatial coherence between the electronic excitations that would otherwise be localized on individual molecules.^1,2 Excitations of these delocalized electronic states of molecules can then be used to drive chemical reactions,³⁻¹⁰ produce photons possessing controllable energies,^11,12 or maintain electronic spin states amenable to information processing.^13,14

Researchers envision that increasing spatial coherence between molecular excitations can enhance the transport of energy, charge, and quantum information between the locations of specific excitations in molecular materials.² Despite this promise, the strong interactions among the electronic excitations, relatively larger energetic disorder, and coupling to vibrational degrees of freedom cause ultrafast loss of spatial coherence in molecular materials. The ultrashort lifetime of long-range electronic coherence in molecular materials limits the applicability of these systems in next-generation technologies for solar energy conversion, photocatalysis of chemical transformations, and quantum computing and information processing.

Unlike electronic excitations in molecular materials, photons interact weakly with one another and their environments, which increases both their relative spatial and temporal coherence. This increased spatial coherence relative to molecular electronic excitations enables the use of photons as carriers of classical and quantum information.¹⁵ However, questions remain whether the relatively larger spatial coherence of photons can be harnessed to diminish disorder in molecular or hybrid molecular systems.

The strong coupling of light and matter within electromagnetic resonators leads to the formation of hybrid light–matter states called cavity polaritons, which possess properties different from their photonic and material constituents.¹⁶⁻¹⁹ In the limit of one chemical species interacting strongly with cavity photons, these hybrid light–matter states can be represented by two-state linear superpositions of photonic and molecular excitations weighted by the so-called Hopfield coefficients, which are known as the upper polariton (UP) and lower (LP) polariton. Additionally, these states are split by an energy proportional to the vacuum Rabi frequency, Ω_R, at which the material and photonic constituents exchange energy. For most applications, strong light–matter coupling can be reached only in the collective limit in which a large ensemble of molecules couples to a single cavity photon. In this case, one considers material–photonic energy exchange to occur at the collective vacuum Rabi frequency, Ω^c_R. When using molecular chromophores for cavity polariton formation in the collective limit, researchers have demonstrated formation of exotic quantum states like Bose–Einstein condensates²⁰ and superfluids,²¹ controlled photophysical processes,²²⁻²⁵ and proposed that polariton formation can amend the structures of molecule-based excited states,²⁶⁻³¹ which would be critical for quantum-controlled photochemistry. Most strikingly, the cavity polariton states formed through strong light–matter coupling in microresonators possess spatial and temporal coherence like the photons from which one forms these hybrid light–matter states, as observed in their momentum-sensitive energies.³² However, it remains unclear how the maintenance of this coherence in the polaritonic states provides researchers a means to control the collective energetics of molecular ensembles characterized by large disorder.

In contrast to molecular systems, researchers have developed methods to control the disorder present in inorganic semiconducting systems to form long-lived polaritons capable of forming a wide range of devices, including low- or no-threshold lasers.^33,34 These sample preparation methods include using cleaner initial starting materials in vapor deposition systems, matching lattice parameters of different crystalline layers to form thin films with reduced interfacial strain, and operating these devices at low temperatures, i.e., T < 50 K. The development of these approaches has allowed researchers to show that the maintenance of photonic coherence in the polaritonic states provides a means to control the impact of excitonic disorder in the hybrid light–matter states through two distinct mechanisms.

First, changes in the overall absorption of cavity-embedded excitons whose energies are disordered randomly affect the spectra of both the UP and LP states. In the limit of moderately strong light–matter coupling (Ω^c_R > σ, where σ is the random distribution of energetic disorder³⁵), Houdré et al. showed that the excitonic contribution to UP and LP peak widths (Γ_UP and Γ_LP, respectively) is the sum of σ and the inverse lifetime of the photon within the cavity mode (γ_ph), weighted by the Hopfield coefficients describing the contributions of excitons (c_ex) and photons (c_ph) to each state.³⁶ By changing the angle that a probe electromagnetic field makes with the cavity structure (θ_inc), one can modulate the difference between the exciton and photon energies, called Δ_c(θ_inc), and affect these Hopfield coefficients. While the initial theoretical investigations of these effects considered excitons formed in III–V semiconductor quantum wells, more recent experimental studies showed that aspects of these results can be extended to cavity polaritons formed from the excitons of localized molecules.³² Additionally, these studies on molecular cavity polaritons formed from metalloporphyrin chromophores established the connection between the widths of peaks in the linear spectra of polaritons and the lifetimes of the polariton states.³²

By adding additional excitonic material to the intracavity region, one can increase the overall collective light–matter interaction and drive increasingly larger values of Ω^c_R. In the limit that Ω^c_R ≫ σ, Houdré proposed that the UP and LP peaks narrow to Γ_UP,LP = |c_ph|²γ_ph + |c_ex|²γ_ex, where σ gets replaced by the homogeneously broadened width γ_ex, which stems from the finite lifetime of the exciton state. In the case of many molecular chromophores, σ differs from γ_ex by at least an order of magnitude in amorphous media.³⁷ We refer to these conditions as the “intense” strong light–matter coupling limit, which differs from the ultrastrong coupling limit, where Ω^c_R approaches the bare exciton transition frequency.³⁸ While line narrowing upon reaching the intense strong coupling limit has been proposed to explain photoluminescence spectra emitted by cavity polaritons formed from excitons in inorganic crystalline materials,³⁹ no studies have shown experimentally how the overall intracavity absorption can be used to narrow the peak widths of polaritons formed from molecular chromophores in amorphous media.

As a second physical mechanism, the coherence of the photons confined within microresonator structures enables their ability to interact with ensembles of effective two-level systems whose energy levels are shifted relative to one another due to disorder in their local environments. While the presence of structural and electrostatic inhomogeneities stymie the ability of researchers to understand ensemble molecular dynamics from the linear optical spectra in the weak light–matter coupling limit,⁴⁰ studies have proposed that cavity polariton formation from strong light–matter coupling enables dynamical averaging over energetic disorder, which lengthens the polariton lifetime.^32,41−43 This physical picture of the photonic delocalization imparted on the polariton peak properties differs from that proposed by Houdré and co-workers in an important way. Unlike the linear dependence of the polariton peak widths expected from simple diagonalization models like those produced by Houdré et al., measurements of the dispersive width of the LP photoluminescence in inorganic microresonators possess nonlinear dependences on the state’s excitonic content. Kinsler and Whittaker explained this behavior in Green’s function models of the polariton peak when the excitonic ensemble becomes broadened inhomogeneously.⁴¹ When accounting for this broadening mechanism, the quantum theory predicts that the width of the polariton peaks should disperse parabolically with respect to the state’s excitonic content. However, it remains unclear how these two theories can be combined to assess the impacts of inhomogeneous broadening on polaritonic properties and methods to suppress these impacts using collective strong light–matter coupling in the microresonator environment.

In spite of these findings, some researchers have called the veracity of these proposals into question even in the case of cavity polaritons formed from excitons in high-quality inorganic crystalline materials and nanostructures maintained below 50 K.^39,42,44 Building off their previous results, Houdré and co-workers proposed that the dispersive narrowing observed in cavity polariton samples formed from high-quality III–V semiconductor quantum wells stems from the ability of the bound electron–hole pair to diffuse through the materials’ crystalline lattices and average over energetic disorder.⁴⁴⁵ No studies have considered these effects in the case of cavity polaritons formed from molecular excitons persisting under ambient conditions.

These previous studies left at least two issues related to polaritonic coherence unresolved. First, based on the smaller transition dipole moments of molecular excitons relative to their inorganic counterparts, it remains unclear whether one can leverage the strength of light–matter interactions and dynamical averaging when photons couple strongly to molecules in amorphous structures at room temperature, which possess substantially larger energetic disorder than their inorganic counterparts. Second, if researchers need excitonic delocalization to observe line narrowing, as proposed by Houdré and co-workers, then one should not expect to observe these effects using excitons localized on molecules in amorphous media, which cannot diffuse over long length scales due to the lack of translational symmetry. Addressing these issues to leverage dynamical averaging in strong coupling between light and molecular chromophores at room temperature could play a critical role in overcoming photonic losses in polaritonic platforms necessary to implement them effectively in optoelectronic and photocatalytic devices based on synthetically labile chemicals.

Researchers have demonstrated that exciton delocalization leads to the narrowing of spectral features due to the decoupling of electronic and vibrational excitations, which is explained clearly by the seminal work of Spano.^11,12 These models show that the alignment of molecules in cyanine dye aggregates leads to simple intermolecular exciton states, whose bright transitions correspond to collective dipole moments along a single direction. Spano further showed that the strong coupling of these collective dipole states to cavity photons can further decouple polaritons from vibrational reorganization.^22,45,46 These properties of J-aggregate states of cyanine dyes have enabled researchers to demonstrate important cavity polariton properties like long-range energy transport⁴⁷⁻⁴⁹ and Bose–Einstein condensation²⁰ using these intermolecular chromophores. However, since cyanine dyes are designed chemically to remain stable in the presence of high-density light excitation, these molecules do not represent good models to assess how cavity polariton formation affects photochemistry. This limitation implies that researchers need to understand how exciton delocalization in more complex chromophores affects the properties of cavity polaritons formed from such molecular systems.

Chromophores functionalized from the porphyrin macrocycle represent interesting systems to understand how exciton delocalization and inhomogeneous broadening affect the properties of the cavity polaritons these molecules form. The strong Soret transition in the near-UV region enables cavity polariton formation readily, as demonstrated by several studies.^{24,25,32,50−53} Additionally, porphyrins and porphyrin-based materials ligated with different transition metal cations can catalyze simple chemical reactions following photoexcitation.⁵⁴⁻⁵⁷ This property of metal-ligated porphyrins, known as metalloporphyrins, makes studying cavity polaritons formed from these chromophores interesting for the purposes of understanding how hybrid light–matter states affect photochemistry and photocatalysis. Despite the interest in understanding the properties of porphyrin cavity polaritons, these chromophores possess a more complex electronic structure than molecular light absorbers used in polaritonic applications.

Unlike cynanine dyes, metalloporphyrins possess a pair of highest occupied molecular orbitals (HOMOs) whose energies are almost degenerate accidentally.⁵⁸ By substituting functional groups for H atoms at different positions around the porphyrin ring, researchers can control the identity of the HOMO state via the electron-donating/withdrawing power of the substituent.^58,59 Additionally, the D_4h symmetry of metalloporphyrins leads to a pair of degenerate lowest-lying excited states whose atomic compositions are related by a 90° rotation. The existence of these pairs of frontier orbitals leads to the presence of two orthogonal transition dipoles within the plane of the porphyrin macrocycle, as we have detailed recently.⁶⁰ When one forms dimeric systems from porphyrin monomers, the exact bonding of the dimer determines how the orthogonal transition dipoles couple and reorganize spatially, which contrasts with the simple case of J-aggregates of cyanine dyes described above. These facets of the electronic structure of monomeric and dimeric porphyrins create an array of interactions when these chromophores are strongly coupled to cavity photons. Furthermore, it remains unclear how one would need to address these aspects of porphyrin electronic structure to understand how cavity polariton formation affects the suppression of inhomogeneous broadening in these systems central to forming long-lived hybrid light–matter states for photochemical and photocatalytic applications.

In this study, we demonstrate that control over the contributions of excitonic disorder to cavity polariton states formed from porphyrin excitons under ambient conditions can be achieved through a rational approach. We show that the delocalized nature of cavity polariton states enables dynamical averaging over the energetic disorder of porphyrin chromophores we embed in amorphous polymer matrices inside these structures. This dynamical averaging leads to a reduced width of the peaks of LP states that we measure in the transmission spectra of polariton samples formed from different porphyrin species. We effectively model this dynamical averaging using the same physical theory implemented to explain “motional narrowing” of the LP peak formed by strongly coupling photons to excitons in III–V semiconductor quantum wells at low temperatures.

In addition, we identified four key characteristics associated with this averaging process. First, unlike previous studies examining the dispersion of LP peaks in the photoluminescence spectra of cavity polariton systems, we use well-designed transmission spectra to show that the delocalized nature of the photons in microresonator modes leads to nonlinear dispersion of the UP peak width, which had not been observed previously in experiments. Second, we find that suppression of energetic disorder among the ensemble of excitons in our microresonators depends on the collective light–matter coupling (g^c), which can be proportional to collective vacuum Rabi splitting (ℏΩ^c_R) between the UP and LP states and had not been observed previously. Third, our analysis indicates that the models needed to elucidate our experimental findings necessitate the inclusion of a constant, represented as α, which effectively reduces σ in a phenomenological manner. Fourth, we use the standard theoretical description of polaritonic dynamics to propose that the parameter α corresponds to the ratio σ/ℏΩ_R, which leads us to conclude that “motional narrowing” of the LP peaks stems from a photonic exchange mechanism. These results suggest that researchers can utilize specific rules to average over the energetic disorder characteristic of molecular materials at room temperature and enable relatively increased spatial and temporal coherence in molecule-based excitations through cavity polariton formation.

To understand connections between intermolecular exciton delocalization, the coherence of cavity photons, and the suppression of energetic disorder among an ensemble of excitons, we synthesized chemically bound porphyrin dimers substituted differently at their meso positions using reported methods and loaded different concentrations of them into intracavity PMMA matrices, as described in the Supporting Information (SI). We substitute trimethylphenyl groups in 4,4′-bis[zinc(II)-5,10,15-trimesityl-20-porphinyl]diphenylacetylene (Zn₂U) and pentafluorophenyl groups in 4,4′-bis[zinc(II)-5,10,15-pentafluoro-20-porphinyl]diphenylacetylene (F₃₀Zn₂U), as shown schematically in Figure 1a,c, respectively. Differences in the electron-donating/withdrawing strengths of the ring substituents control coupling between the electronic states of each porphyrin ring.⁶¹ As shown schematically in Figure 1a, the mesityl groups bound at six of the eight meso positions of the porphyrin rings donate electron density to the molecules’ a_2u orbital, which destabilizes this state energetically and causes it to be the macromolecule’s HOMO. Bridging the two Zn-centered porphyrin rings through an acetylene group on the terminal carbons of phenyl groups bound to their meso positions drives weak electronic coupling between the two rings through the a_2u orbital of each molecule. Under this weak intermolecular coupling, models predict that the B_x and B_y states of each zinc(II) 5,10,15,20-(tetramesityl)porphyrin (ZnTMP) mix to form two bright and two dark excitons,⁶² which we show as solid and dashed lines, respectively, in the schematic of Figure 1b. As explained in the SI and using the absorption spectrum of polymer-embedded molecules shown in the right panel of Figure 2, we estimate the intermolecular exciton coupling between two rings in the x direction (J_x) and y direction (J_y), which we show in Figure 1a, are 36 and 30 meV, respectively.⁶² We expect that the energetic splitting of the intermolecular exciton states suggests that one may anticipate the formation of multipolaritons when these excitations strongly couple to photons within a Fabry–Pérot (FP) microresonator. However, the formation of these multipolaritons will depend sensitively on the light absorption strength of each respective exciton, which is discussed in detail below. We point out that the inhomogeneous broadening of the B exciton in Zn₂U is larger than its associated monomer, as we have reported previously.⁶⁰ This fact implies that exciton delocalization in this system is not strong enough to produce narrowed absorption spectra as observed in J-aggregates of cyanine dyes.^11,12

Figure 1.

Comparison between the structures and intermolecular state diagrams of (a, b) Zn₂U and (c, d) F₃₀Zn₂U. We show the atoms involved in the HOMO states of Zn₂U and F₃₀Zn₂U as black circles in (a) and (c), respectively. We show allowed transitions in Zn₂U and F₃₀Zn₂U consistent with intermolecular exciton models as vertical arrows in (b) and (d), respectively.

Figure 2.

(left) Comparison between the measured absorption spectrum of polymer-film-embedded Zn₂U in the Soret region (black) to inhomogeneously broadened models of intermolecular excitons polarized along the x (red) and y (green) directions defined in Figure 1. The blue peaks present in the absorption spectra of both molecules correspond to transitions to the first vibrational excited states of their respective B excitons, which couple to the cavity photons weakly. (right) Comparison between the measured absorption spectrum of polymer-film-embedded F₃₀Zn₂U in the Soret region (black) to an inhomogeneously broadened model of localized excitons (red).

In contrast to the methylated phenyl groups of Zn₂U, the fluorine atoms of F₃₀Zn₂U pull electron density away from the porphyrin rings, stabilize the energy of the a_2u state, and cause the a_1u orbital to become the rings’ HOMO, which we show schematically in Figure 1c. This change in the ordering of the orbital energies reduces the intermolecular electronic coupling mediated by the acetylene bridge and drives our observation of only a single, inhomogeneously broadened peak in the absorption spectrum of film-embedded F₃₀Zn₂U molecules, as shown in the left panel of Figure 2.⁶¹ While we cannot exclude the appearance of distinct inhomogeneously broadened peaks corresponding to coupled excitons in this molecule’s absorption spectrum shown in Figure 2, we use the appearance of a single peak to propose that the intermolecular coupling is negligible (i.e., J_xx = J_yy ≈ 0). The nonexistent coupling between the zinc(II) 5,10,15,20-tetrakis(pentafluorophenyl)porphyrin (ZnTFP) subunits of F₃₀Zn₂U leads us to propose that the two sets of transitions polarized along the x and y directions of the dimer systems remain bright and can contribute to cavity polariton formation, as described below. By synthesizing these two similar porphyrin dimers, we can assess the impact of exciton delocalization on cavity polariton spectra directly to help develop principles with which researchers can connect molecular properties with those of the polaritons they form.

Ultrafast pump–probe measurements suggest that the B excitons in Zn₂U and F₃₀Zn₂U live for 1.0 and 0.45 ps, respectively, before decaying nonradiatively to lower-lying Q excitons in each molecule.⁶³⁵ These lifetimes indicate that the lower limits on homogeneous line widths of the B exciton absorption transitions in Zn₂U and F₃₀Zn₂U would be 4.1 and 9.2 meV, respectively.

The panels in the top row of Figure 3 show the behavior of peaks in the angularly resolved transmission spectrum of λ-mode FP microresonators when we form the intracavity polymer layers from solutions containing different concentrations of F₃₀Zn₂U. All these panels display the characteristic dispersion of the cavity polariton states expected from the spatial coherence of the photons within the FP microresonator modes. We model the angular-dependent F₃₀Zn₂U cavity polariton energetics by diagonalizing a 2 × 2 matrix that describes the coupling of photons in the λ mode in the FP microresonators to excitons possessing a single transition energy, given our ability to model the absorption spectrum shown in the right panel of Figure 2 using a single peak broadened inhomogeneously. This method leads to the following analytic equations:³²

1a

1b

where E_ex and E_ph are the energies of the molecular excitons and cavity photons, respectively, Δ_c = E_ph – E_ex, and ℏg^c is the collective light–matter interaction energy. Given the spatial coherence of the photons within the microresonator modes, both E_ph and Δ_c will depend on θ_inc. We report the parameters used to model the polariton dispersion spectra in Table 1. This table includes E_cutoff, which represents the cutoff energy of the optical cavity, and n_eff, denoting the effective refractive index within the optical cavity in the presence of molecules. Our model predicts that localized excitons on each ZnTFP subunit of F₃₀Zn₂U polarized along the x and y directions detailed in Figure 1 couple to cavity photons to form both the UP and LP states. Using this interpretation, our model results allow us to assess how the relative exciton–photon energies at θ_inc = 0 (k = 0) vary across these samples.

Figure 3.

(top row) Comparison between the measured positions of the transmission peaks we assign as the upper polariton (UP) (blue circles) and lower polariton (LP) (red circles) in samples formed from polymer precursor solutions containing 1 mM (left), 2 mM (middle left), 2.5 mM (middle right), and 3 mM (right) F₃₀Zn₂U to models of these dispersion spectra using the parameters detailed in Table 1 (dashed lines). (middle row) Comparison between the contributions of photonic (black) and molecular excitons (red) to the UP state formed from these constituents in samples formed from polymer precursor solutions containing 1 mM (left), 2 mM (middle left), 2.5 mM (middle right), and 3 mM (right) F₃₀Zn₂U as determined by models using the parameters detailed in Table 1. (bottom row) Comparison between the contributions of photonic (black) and molecular excitons (red) to the LP state formed from these constituents in samples formed from polymer precursor solutions containing 1 mM (left), 2 mM (middle left), 2.5 mM (middle right), and 3 mM (right) F₃₀Zn₂U as determined by models using the parameters detailed in Table 1. Error bars are shown on the peak positions estimated from nonlinear least-squares fits for each incidence angle where a measurement was carried out.

Table 1. Parameters Used to Model the Dispersive Real and Imaginary Parts of the Cavity Polariton States Formed from the Porphyrin-Based Chromophores Considered in This Study.

Sample	Eex [eV]	Ecutoff [eV]	neff	Δc(0) [meV]	ℏσ1 [meV]	ℏγph [meV]	ℏgc1 [meV]	α
Zn2U 1 mM	2.90	2.84	2.0	–60	1055	75	85	0.65
Zn2U 2 mM	2.90	2.89	2.0	–10	105	70	112	0.53
Zn2U 3 mM	2.90	2.91	1.8	10	105	75	125	0.36
Zn2U 4 mM	2.90	2.87	1.8	–30	105	84	140	0.33
F30Zn2U 1 mM	2.92	2.86	2.0	–60	116	75	100	0.49
F30Zn2U 2 mM	2.92	2.81	1.9	–110	116	77	133	0.22
F30Zn2U 2.5 mM	2.92	2.71	1.7	–210	116	82	145	0.19
F30Zn2U 3 mM	2.92	2.83	1.7	–90	116	85	155	0.16

The results shown in the panels of Figures 3 and 4 demonstrate the ability of the models in eqs 1a and 1b to explain the dispersion of the peak positions for all of the samples formed from F₃₀Zn₂U and those formed from 1 mM and 2 mM Zn₂U solutions. Upon forming cavity polaritons from 3 and 4 mM precursor solutions, we find that the y-polarized intermolecular excitons of Zn₂U couple more significantly to resonator photons and must be considered. However, we find that using a 3 × 3 Hamiltonian model leads to polariton states whose coupling to the y-polarized intermolecular excitons does not exceed the cavity photon decay rate, which would not satisfy the strong light–matter coupling condition. Based on these conditions, we use eqs 1a and 1b to model the energetics of the LP and UP states in all of our Zn₂U samples. We detail these results in the SI.

Figure 4.

(top row) Comparison between the measured positions of the transmission peaks we assign as the upper polariton (UP) (blue circles) and lower polariton (LP) (red circles) in samples formed from polymer precursor solutions containing 1 mM (left), 2 mM (middle left), 3 mM (middle right), and 4 mM (right) Zn₂U to three-level models of these dispersion spectra using the parameters detailed in Table 1 (dashed lines). (middle row) Comparison between the contributions of photonic (black) and x-polarized intermolecular excitons (red) to the UP state formed from these constituents in samples formed from polymer precursor solutions containing 1 mM (left), 2 mM (middle left), 3 mM (middle right), and 4 mM (right) Zn₂U as determined by models using the parameters detailed in Table 1. (bottom row) Comparison between the contributions of photonic (black) and x-polarized intermolecular excitons (red) to the LP state formed from these constituents in samples formed from polymer precursor solutions containing 1 mM (left), 2 mM (middle left), 3 mM (middle right), and 4 mM (right) Zn₂U as determined by models using the parameters detailed in Table 1. Error bars are shown on the peak positions estimated from nonlinear least-squares fits for each incidence angle where a measurement was carried out.

While there could be cavities where photonic density exists at the same energies as the y-polarized intermolecular excitons of Zn₂U, the samples we fabricate lead to the formation of cavity polaritons using the x-polarized exciton transition. Polariton formation pushes the photonic density out of resonance with the y-polarized excitonic transition by values on the order of 100 meV. Moreover, the orthogonal directions of the transition dipoles corresponding to the x- and y-polarized excitons indicate that molecules participating in cavity polariton formation are oriented such that the polarized light we launch into the cavity mode will not be absorbed by y-polarized excitons. This fact also means that the LP state of interest to our analysis will not couple to its y-polarized excitons radiatively. Based on these considerations, we do not consider the y-polarized excitons in our analysis of polariton behavior in our samples formed from Zn₂U.

While there is an existing notion that the heights of the UP and LP peaks should match when the cavity photon has the same energy as the molecular exciton, one must correctly account for the spectral extent of the peaks corresponding to these states. To this accounting, we propose that the integrated intensities of the UP and LP peaks should be equal at the photon–exciton resonance condition. In this physical picture, one should expect the UP peak height to be smaller than that of the LP even at the photon–exciton resonance, since the UP peak possesses a systematically broader width than the LP peak. This relatively larger width of the UP peak stems from relaxation to dark polariton states, as shown in previous studies.

To test this hypothesis, we calculated the integrated intensities of the UP and LP peaks in cavity samples formed from 1 and 2 mM polymer precursor solutions of F₃₀Zn₂U and Zn₂U. Figure S9 shows plots of these integrate intensities as a function of the c_ex values we extract from our models of polariton spectra. We find that the integrated intensities of these peaks become equal when |c_ex|² = 0.5, as we propose above.

In addition to the different values of Δ_c(0) we find consistent with our dispersion spectra, inspection of the parameters in Table 1 shows that a transition in the absorption spectrum of Zn₂U couples to cavity photons collectively with systematically smaller strengths than the transition in F₃₀Zn₂U, which we quantify with the parameter g^c. These values of the collective light–matter coupling strength can be related to the vacuum Rabi splitting energy, ℏΩ^c_R, by doubling them. As stated above, g^c depends on both the number of molecules that couple to the photonic fluctuations within the resonators and g, the strength of the interaction between the photons and individual molecules of each chemical species. This light–matter coupling strength is proportional to μ_eg·E, where E is the electric field of the cavity-confined photon and μ_eg is the single-molecule transition dipole moment. We note that the light absorption by the Zn₂U films is less than that of F₃₀Zn₂U even though coupling between the subunits of Zn₂U should preserve the overall magnitude of their respective dipole moments. Since we synthesize these molecules to possess nearly the same structures and embed them in the same environments, we propose that the difference in their absorption stems from the identities of their HOMO states. Similar changes have been observed in comparison of the linear absorption of porphyrins substituted at α and β positions relative to those substituted at their meso positions.⁶³ Given the known dependence of the collective coupling on the square root of the number of absorbers interacting with the cavity photons, √N, we can use the values of ℏg^c to compare the concentration dependence of ℏΩ_R between F₃₀Zn₂U and Zn₂U.

As shown in Figure 5, we find that modeling our estimated values of ℏΩ^c_R against the square root of the concentration of chromophores we add to polymer precursor solutions leads to linear trends for the cases of both F₃₀Zn₂U and Zn₂U. However, the slopes of these trends differ by √2. This numerical difference in the slopes of the trends stems from the fact that Zn₂U absorbs less light than F₃₀Zn₂U. Given this fact and our use of the same concentrations of Zn₂U and F₃₀Zn₂U in precursor solutions to form the cavity polaritons whose dispersion we show in the panels of Figures 3 and 4, we propose that the smaller light absorption characteristic of Zn₂U molecules leads to a smaller number of macromolecules participating in polariton formation than those in samples fabricated from F₃₀Zn₂U. The difference in the slopes reinforces our conclusion that changes in the identity of the HOMO state of the porphyrin molecule can have significant impact on the strength of the light–matter interactions. When we substitute our molecules with F atoms, the stabilization of the a_2u level forces the a_1u to become the HOMO and likely leads to higher light absorption than can take place in Zn₂U. This larger absorption leads to larger ℏΩ^c_R values in samples formed from F₃₀Zn₂U than in those formed from the same concentration of Zn₂U.

Figure 5.

Comparison between the dependence of the collective vacuum Rabi splitting energy, ℏΩ^c_R, on the square root of the concentration of absorbers in polymer precursor solutions used to form cavity polaritons from F₃₀Zn₂U (blue squares) and Zn₂U (red diamonds). Fits to linear trends of these dependences are shown as blue and red dotted lines for F₃₀Zn₂U and Zn₂U, respectively.

We have extensively considered the effects of solubility on the concentrations of our porphyrin chromophores in the films we form in cavity polariton samples. The results of these studies suggest that F₃₀Zn₂U molecules dissolve less easily in the polymer precursor solutions (PMMA in anisole) than Zn₂U. We propose that this difference in the solubility results from the F substitution on the peripheral phenyl groups of F₃₀Zn₂U. It is this relatively decreased solubility that limits our ability to form well-defined polariton samples from 4 mM solutions of F₃₀Zn₂U. At those concentrations, the molecules crash out as precipitate and ruin the surface quality of the polymer film, which cannot be used to form a Fabry–Pérot cavity. Based on this analysis, we conclude that the differences in the slopes shown in Figure 5 result from differences in the fundamental light–matter interactions taking place in samples formed from each chromophore. However, it is not clear how this difference in the number of molecules participating in polariton formation affects the delocalization of the polariton states themselves, which could be used to reduce the impact of energetic disorder on polaritonic relaxation

The panels of Figure 6 compare dispersion of the LP peak width we expect to find theoretically in the moderately strong light–matter coupling limit [Γ_LP(θ_inc) = ∑_m|c^LP_ex,m|²σ_m + |c_ph|²γ^LP_ph] for each of the samples we consider in this study to the values we measure experimentally in steady-state transmission measurements under ambient conditions. In the case of all the samples we form from both porphyrin macromolecular chromophores, we find that the measured widths of the peaks corresponding to the LP state in each sample disperse differently from a weighted summation of the homogeneous and inhomogeneous widths of the resonator photons and molecular spectra, respectively. In particular, we find that Γ_LP changes in a nonlinear fashion as we modulate the excitonic content of the LP state using different values of θ_inc, as predicted by Green’s function theories of polariton line shapes.⁴¹ Analysis of the dispersion of the UP peak width in the transmission spectra of the lower-concentration samples shows that this quantity changes in a qualitatively similar fashion as we modulate the excitonic content of the UP state using the incidence angle, as shown in Figure S10. In addition to these confirmations of the Green’s functions predictions, we find that Γ_LP possesses values significantly smaller than those predicted by simpler theories of polaritonic relaxation.

Figure 6.

Comparisons between the expected dispersion of the LP decay rate (dashed black), the measured LP peak widths (red circles), and predictions of a phenomenological theory of a “motionally narrowed” LP decay rate (solid black) for cavity polaritons formed from precursor solutions containing different concentrations of F₃₀Zn₂U (top panels) and Zn₂U (bottom panels).

To model the experimental results, we use the results of a phenomenological theory developed to explain “motional narrowing” in LP photoluminescence spectra of cavity polaritons formed from III–V semiconductor quantum wells grown in dielectric microresonators.^42,44 As we motivate in the SI, we propose that the peaks we assign to the LP state in a transmission spectrum obey the equation

2

where we introduce the factor α, which is a phenomenological constant between 1 and a subunity value that produces the homogeneous width of the excitonic transition, γ_ex. As described below, we argue that α describes the extent of polaritonic averaging over the energetic disorder among the constituents of the intracavity excitonic ensemble due to photonic exchange. We propose that we can assess the values of α across different samples since there is no averaging over the exciton energetic disorder in polymer film samples whose absorption spectra are shown in Figure 2. These spectra allows us to estimate α in the polariton samples using the inhomogeneous broadening in the absorption spectra and ℏΩ_R found from modeling the polariton transmission spectra.

Inspection of the panels in Figure 6 shows the ability of the model in eq 2 to explain the qualitative dispersion of Γ_LP(θ_inc) for each sample and allows us to estimate a suppression of the expected LP peak width due to dynamical averaging over energetic disorder. However, the extent of this suppression is dependent on the identity of the macromolecular chromophore. The top row of panels in Figure 6 shows that the angle-dependent suppression of the LP peak width in the transmission spectra of our F₃₀Zn₂U cavity polariton samples depends sensitively on the chromophore concentration. For the sample we form from a 1 mM F₃₀Zn₂U solution, we find that the LP peak sustains a width of 60 meV at the lowest values of the excitonic Hopfield coefficient, |c_ex|², but quickly increases to the amount expected from conventional theory at higher values of |c_ex|². In contrast to this significant dispersion as a function of the excitonic content within the LP state, the values of Γ_LP(θ_inc) depend much less sensitively on |c_ex|² for those samples we form from 2, 2.5, and 3 mM F₃₀Zn₂U.

We observe a distinct trend in the concentration-dependent dispersion of Γ_LP(θ_inc) for the samples we form from Zn₂U. As can be seen in the bottom row of panels in Figure 6, we find that Γ_LP(θ_inc) disperses significantly as a function of |c_ex|² for all samples formed from Zn₂U. In the case of samples formed from precursor solutions containing 1 and 2 mM Zn₂U, we find that the measured Γ_LP(θ_inc) nearly matches the amount we expect from conventional theory in the moderate strong light–matter coupling limit for the highest values of |c_ex|² we consider. For those samples we form from 3 and 4 mM Zn₂U solutions, we observe that the LP peak width stays below the expected value but the dispersion of Γ_LP(θ_inc) as a function of |c_ex|² remains more significant than what we find for similar samples fabricated with F₃₀Zn₂U. Despite these qualitative differences in the dispersive values of Γ_LP(θ_inc) between samples made with the different macromolecular chromophores, we find regions of excitonic content in which the LP peak widths are significantly suppressed from the amount we expect from conventional theory.

As can be seen in the top row of panels in Figure 6, we find minimum Γ_LP(θ_inc) values of 58, 50, 51, and 50 meV for cavity polariton samples fabricated with 1, 2, 2.5, and 3 mM precursor solutions of F₃₀Zn₂U, respectively. These widths represent approximately 50% of the amounts predicted by theory in the moderately strong coupling limit. Similarly, we observe minimum Γ_LP(θ_inc) values of 62, 59, 57, and 58 meV for cavity polariton samples fabricated with 1, 2, 3, and 4 mM precursor solutions of Zn₂U, respectively, which represent nearly 35% suppression of the expected peak widths.

Overall, we find qualitatively similar behavior in the changes in the LP peak width in cavity polariton samples formed from each chromophore. However, we note that the width reduction is relatively larger for those samples formed from F₃₀Zn₂U, which is shown in Table 1 by the values of α needed to model the dispersion of Γ_LP(θ_inc). We argue that this quantitative difference in the values of α that characterize samples formed from each chromophore stems from larger collective light–matter interactions taking place in those samples. The samples formed from F₃₀Zn₂U excitons possess collective vacuum Rabi splitting energies that are larger than those of the samples formed from Zn₂U excitons. The relatively larger light–matter interactions in the F₃₀Zn₂U cavity polariton samples lead to more suppression of the exciton disorder than we observe in samples formed from Zn₂U.

The comparison of Γ_LP(θ_inc) between polariton samples formed from F₃₀Zn₂U and Zn₂U shows that the width suppression differs quantitatively. As noted above, we propose that F₃₀Zn₂U interacts with light more strongly than Zn₂U due to differences in the identity of the HOMO in each dimer stemming from the electron-withdrawing/donating power of the ring substituents. We propose that this light absorption within each porphyrin subunit of the dimer enables F₃₀Zn₂U molecules in a larger diversity of disordered environments to couple strongly to the delocalized cavity photons, which should increase the dynamical averaging over the energetic disorder among those chromophores relative to their Zn₂U counterparts. This finding leads us to propose that researchers interested in using hybrid light–matter states to affect photochemical and photocatalytic processes that necessitate more than 100 fs to take place should seek to form cavity polaritons from molecular materials possessing the strongest light–matter interactions possible.

While the panels of Figure 6 show that some differences in the details of suppressing Γ_LP(θ_inc) exist when considering the behavior of cavity polariton samples from F₃₀Zn₂U and Zn₂U, we find that we need to use decreasing values of α to model the dispersion of the LP peak width upon increasing the concentration of both macromolecular chromophores, as detailed in Table 1. As stated in our explanation of eq 2, we propose that using smaller values of α in the modeling of Γ_LP(θ_inc) for polariton samples formed from increasing macromolecular chromophore concentrations stems from more extensive averaging over the energetic disorder among the ensemble of excitons participating in collective light–matter coupling.

We present a detailed analysis of the dispersion of only the LP state in the transmission spectra of our samples for two reasons. First, many studies demonstrate that the peaks corresponding to the LP and UP states in cavity polariton transmission spectra possess systematically different widths. In all of these studies, the width of the UP peak is broader than that of the LP peak. As shown in Figures S3–S8, we find similar results in the transmission spectra of our samples. Experimental pump–probe spectroscopic studies show this difference stems from the ultrafast relaxation of the UP-state population into the dark state reservoir,⁶⁴ as predicted by several theoretical studies.⁶⁵ Despite the known existence of this relaxation channel, methods to characterize how it depends on polariton momentum (incidence angle) remain unclear. This uncertainty limits our ability to determine how much of the dispersive behavior we observe in the UP peak stems from changes in the relaxation to dark states and how much results from motional narrowing for cavity polariton samples formed from polymer precursor solutions containing lower concentrations of our porphyrin dimers.

Second, the large collective vacuum Rabi splitting energies we generate in our samples derived from 3 and 4 mM polymer precursor solutions of our porphyrin dimers drive the UP state into the high-energy edge of the photonic stopband of our distributed Bragg reflector (DBR) mirrors. This situation causes the DBR mirror to possess a reduced reflectivity on the high-energy side of the UP peak compared to that on its low-energy side, which creates an energy-dependent photon lifetime given that this parameter stems from mirror losses. The shape of the peak in the transmission spectrum then becomes increasingly asymmetric, since the photon relaxes faster at higher light energies. The presence of this dispersive relaxation process washes out the parabolic dependence of the UP peak width on its excitonic Hopfield coefficient that we observe in cavity polariton samples formed from polymer precursor solutions containing higher concentrations of our porphyrin dimers.

Despite their presence in our samples’ absorption spectra, we conclude that the y-polarized excitons lie over 100 meV above the LP state for all the cavity polariton samples formed from Zn₂U. This energy ordering indicates that there should be minimal population transfer from the LP state to the y-polarized excitons at room temperature. Based on this consideration, we do not consider the y-polarized excitons in our analysis of the LP peak behavior in our samples formed from Zn₂U.

As described above, we expect that the interaction strength we infer from the splitting between the UP and LP states relates to single-molecule transition dipole moments and the number of coupled chromophores, N, through the equation ℏg^c = μ_eg·E_ph√N. When doubled, this collective interaction strength gives the collective vacuum Rabi splitting ℏΩ^c_R, where Ω^c_R is the collective vacuum Rabi frequency, which can help rationalize the physical explanation for the behavior we observe in the panels of Figure 6. In the theory of motional narrowing pioneered in the context of magnetic spectroscopies, Anderson and Weiss proposed that the width of a paramagnetic resonance line can narrow when the rate of spin exchange (ω_e) becomes comparable to or larger than the magnitude of frequency deviations from their mean value stemming from environmental magnetic fluctuations (ω_p).⁶⁶ In the limit of homogeneous broadening, the width of the Lorentzian line shape stemming from absorption becomes ω_p²/ω_e. We propose that we can use this physical picture to motivate an understanding of the meaning of α in our models of the dispersive LP widths.

In the case of cavity polaritons, we developed a phenomenological theory in which polariton peak narrowing can be related to collective energy exchange between excitons and photons, which is parametrized by Ω^c_R. To model the peaks in the transmission spectra of our polariton samples under strong light–matter coupling, we propose that the first polariton spectral moment is a convolution of those characterizing photon and molecular excitons at different relative energy detunings,^41,66 which we write as

3

where

4a

and

4b

where γ_ph, σ, and ϕ_Δω(t) represent the decay rate of the cavity photon, the inhomogeneous broadening of the molecular exciton transitions, and the time dependence of transition energy fluctuations for the molecular excitons. We propose that ϕ_Δω(t) captures both static and dynamic contributions to the inhomogeneous broadening of molecular transition energies. The factors |c^±_ph| and |c^±_ex| represent the photonic and excitonic Hopfield coefficients, respectively. Additionally, the plus and minus signs on those coefficients correspond to the UP and LP states, respectively.

In the limit that the collective vacuum Rabi frequency, Ω^c_R, is much larger than σ, we propose that ϕ_Δω(t) becomes⁶⁶

5

In this limit, we propose that the molecular exciton transition energies decouple from their environments on the time scales of the photon–exciton exchange rate, Ω_R. The exciton contribution to the polariton spectral moment then becomes

6

where α = σ/Ω_R. Inserting this relation into the definition of S^±_tot(τ), applying eq 4b, and taking a Fourier transformation gives the polariton peak functions as

7

where ω_± are the frequencies of the UP (+) and LP (−) states. This model does not account for the dispersion of γ_ph, which is observed in our measured spectra and contributes to our needing to use asymmetric Lorentzian models to fit our experimental spectra, as described in the SI.

To test this model, we used the values of σ and Ω^c_R extracted from models of the linear absorption spectra and dispersive polariton transmission spectra to construct expected values of α and compared them to those stemming from our phenomenological narrowing model. We show these comparisons in Figure 7. Inspection of these comparisons shows that the α values we construct using model parameters and those we measure experimentally behave in similar qualitative ways. As the collective Rabi frequency, Ω^c_R, increases, α decreases nonmonotonically. This qualitative agreement between the measured and modeled values of α suggests that our physical picture of “motional” narrowing through photonic exchange can explain the suppressed influence of excitonic disorder on the polaritonic spectra. The small differences between the expected and experimental α values must be explained by a more detailed theory of the polariton properties, which is beyond the scope of this study.

Figure 7.

Comparison between the values of the disorder averaging parameter α we find consistent with models of the dispersive peak widths of LP states (diamonds) and those we construct from measured absorption spectra and values of the collective vacuum Rabi splitting energy, ℏΩ_R (squares). The results we find for cavity polaritons formed from F₃₀Zn₂U and Zn₂U are colored blue and red, respectively.

While some error exists in our estimates of the parameters characterizing cavity polaritons in our samples, these errors lead to less than 10% uncertainties in our predictions of α for each of our samples, especially at larger values of ℏΩ^c_R. These uncertainties do not affect the conclusions we draw regarding the behavior of our samples.

The results of our measurements and analysis suggest that the parameters pertinent to motional narrowing (disorder suppression) are σ and ℏΩ^c_R. When σ/ℏΩ^c_R becomes a small fraction, researchers should expect to observe motional narrowing. Our results suggest that the physical reason for this effect differs from the mechanism used to explain line narrowing in molecular aggregates. In that case, one presumes relatively strong electron–phonon coupling and that exciton delocalization occurs on a time scale during which nuclei cannot react and reorganize. If a similar effect occurred in our measurements, then we would expect the pertinent time scale for inhomogeneous broadening to be the period of the vibration that has the largest Huang–Rhys factor as determined by absorption spectroscopy. This physical picture indicates that motional narrowing should take place primarily when the energy exchange between the cavity photon and exciton takes place faster than the vibrations can change the excitonic energy.

Using the spectra in the panels of Figure 2, we find a vibronic overtone at 140 meV (1129 cm^–1) for F₃₀Zn₂U and an overtone at 128 meV (1032 cm^–1) for Zn₂U. In the theory of vibrational decoupling, this difference in the energies of the modes with the largest Huang–Rhys factors would suggest that we should expect more substantial narrowing for Zn₂U than for F₃₀Zn₂U given the same value of ℏΩ^c_R. In contrast, we find that α characterizing the LP peak for our F₃₀Zn₂U polariton samples are systematically smaller than those we find for our Zn₂U samples. This difference from what would be expected from the vibrational decoupling limit likely stems from the distinctions in the level of exciton–phonon coupling between porphyrins and molecules used to test these theories.

Unlike the cyanine dye molecules, whose J-aggregates are used as models for polaron and polariton decoupling theories developed by Spano, porphyrin absorption spectra suggest that the B exciton couples weakly to vibrations, which leads to the weak 0–1 peak in both absorption spectra of Figure 2. In this limit, the primary source of inhomogeneous broadening results from the fluctuations of electrostatic background of the chromophores environment, which causes each molecule to possess a slightly different transition energy. Our observation of motional narrowing in this limit implies that the light–matter energy exchange takes place faster than these fluctuations, such that they do not affect the excitons’ energies to the same extent as in the case without polariton formation.

As explained in the introduction, many studies predict that the widths of the polariton peaks should be simple combinations of the excitonic disorder and photonic lifetimes. Our results show that models of this type cannot explain the behavior of our samples. The main distinction seems to stem from the theoretical treatment of inhomogeneous broadening. We have proposed that if one handles the broadening as modulations of the transition frequency due to fluctuations of the background electrostatic environment surrounding the chromophore, then one can explain the line narrowing effect as resulting from exciton–photon energy exchange taking place faster than those fluctuations. We produced a model of this behavior that produces a model peak function that agrees qualitatively with the behavior of our data. We refer to this effect as motional narrowing through photonic exchange.

While we have demonstrated a microscopic model based on the time scales of collective light–matter and relaxation in disordered environments to explain the behavior of the LP peak in the transmission spectra of our polariton samples, different studies have shown that macroscopic electrodynamics calculations can capture the essential features in the transmission spectra of cavities filled with resonantly absorbing molecules. For example, Zhu et al. considered changes in the phase shift experienced by a light wave traveling between the cavity mirror as the means to explain polariton spectra.⁶⁷ They proposed that changes in the cavity transmission spectra observed as a function of the overall light absorption taking place between the resonator mirrors stem from differences in the light frequencies where the overall light phase shift goes to zero. In the case of an empty cavity, the phase shift becomes zero at integer values in the free spectral range. However, an absorbing medium produces two separate frequencies at which the light phase shift is zero, which are separated by Ω_R. Building on this work, Houdré et al. considered an ensemble of inhomogeneously broadened excitons coupled to a single photon to reproduce Zhu’s basic results while also showing that the width of the polariton peaks changes as a function of Ω_R,³⁶ which we described above. However, they explained that this change in the polariton peak width appears at higher values since the new eigenfrequencies overlap with the wings of the Drude response of charge carriers in inorganic semiconductor quantum wells. Based on these results, we would expect that macroscopic electromagnetic calculations using transfer matrix methods would produce many of the results that we find in our experimental measurements. In contrast to inorganic semiconductor systems studied previously that behave according to the Drude model, we propose that the motional narrowing model developed in this study is the physical mechanism that accounts for our results.

Our results indicate a path toward improving the applicability of molecular cavity polaritons for quantum information science (QIS) instead of other materials systems. For example, some solid-state and molecular materials rely primarily on spin excitations to implement QIS protocols, which can be engineered to possess coherence lifetimes on the orders of milliseconds to seconds.^{13,14,68−73} Given these long time scales, the subpicosecond lifetimes of cavity polaritons formed by molecular chromophores may appear as a significant limitation on researchers’ ability to use these platforms in QIS applications. However, one must acknowledge the fundamental physical reasons for needing such long spin coherence times.

Spin coherences must be formed through excitation with microwave and radiofrequency sources, which possess oscillatory periods between hundreds of nanoseconds and 1 ms. Therefore, researchers’ ability to address spins coherently is limited to those time scales, and one must achieve very long spin coherence lifetimes to write and read classical and quantum information. Conversely, one can drive polaritonic excitations like those in our samples with light pulses limited by optical periods on the order of 5 fs. This limit means that polaritonic lifetimes of 750 fs would enable up to several hundred write and read cycles using an appropriately compressed optical pulse source. Recovery of the molecular ground state on the order 1 ns via nonradiative relaxation processes would allow researchers to implement 10⁹ operations per second. While there are many aspects of engineering polaritons to achieve these performance metrics, there remain no fundamental limits on this vision.

While we find that the LP peak width of F₃₀Zn₂U can be suppressed by a factor of 2 via dynamical averaging over energetic disorder, equating the inverse of Γ_LP with this state’s lifetime implies substantial decay of the polaritonic population in less than 90 fs, which outpaces the rate of most chemical processes. The properties of FP microresonator samples without loaded porphyrin chromophores indicate that this ultrafast decay rate stems mostly from photonic losses through the end mirrors. The use of higher-reflectivity mirrors and longer microresonators should reduce the photonic loss rate and provide the opportunity to form LP states limited only by the finite lifetime of the molecular excitons.⁷⁴⁻⁷⁶ Future work into the engineering of resonators with sufficiently high reflectivity mirrors and low internal scattering losses will help assess such a proposal but is beyond the scope of this initial demonstration of motional narrowing in molecular cavity polaritons.

In conclusion, we have designed, fabricated, and characterized cavity polariton samples from distinct porphyrin-based chromophores to assess how the delocalization of light enables the suppression of energetic disorder among a large ensemble of molecular excitons at room temperature. Using angle-resolved transmission spectroscopy of these samples, we find the telltale dispersive signs of dynamical averaging over inhomogeneities in the local environments of chemically bound porphyrin dimers in Fabry–Pérot microresonators. For each of these samples, we use a modified Green’s function theory to model the dependence of the LP peak width on its excitonic content and find that the strength of the collective light–matter coupling determines whether specific transitions contribute to the averaging effect. Our results demonstrate that the properties of the molecular chromophores coupled strongly to microresonator photons play an important role in the ability of cavity polariton formation to suppress inhomogeneous broadening. Even small changes in the structure of model molecules can lead to important changes in the light–matter interactions in which these molecules participate. Under these conditions, researchers must take significant care to assess how changes to the molecular structure will affect the collective light–matter coupling and the suppression of excitonic disorder to understand polariton behavior. These results demonstrate that the informed design of electromagnetic resonator structures and molecular chromophores can be used to leverage the relatively larger spatial and temporal coherence of cavity photons to dynamically average over the substantial energetic disorder present in molecular systems and further the use of polaritonic systems in real-world applications.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.3c03217.

• Schematic of the cavity structures, experimental methods, comparisons between modeled and measured transmission spectra, estimates of the integrated polariton intensities as functions of exciton Hopfield coefficients, and comparison of dispersive upper polariton peak widths for different collective light–matter coupling strengths (PDF)

The authors declare no competing financial interest.