In the simulations, the details of which can be found in the “Methods” section and in the Supplementary Information (section 2), 512 HBQ molecules solvated in cyclohexane, were placed inside a single-mode cavity. The configurations of these molecules were extracted from a classical MD trajectory in the electronic ground state, which sampled the Boltzmann distribution at 300 K25. The energy of the cavity mode was resonant with the absorption maximum of our molecular model (see below) at ℏωcav = 4.02 eV. In all simulations, the strength of the vacuum field was \(\sqrt{\hslash {\omega }_{{{{{{\rm{cav}}}}}}}/2{\epsilon }_{0}{V}_{{{{{{\rm{cav}}}}}}}}=\) 0.77 MV cm−1. With only 512 molecules coupled to the cavity mode, this field needs to be stronger than in experiments, where the collective coupling regime is typically achieved with 105 molecules or more26,27,28,29.As shown in Fig. 2a, the calculated QM/MM S0 → S1 absorption spectrum of HBQ at 300 K (Supplementary Information, subsection 2.5) splits inside the cavity, suggesting that the molecule-cavity system is in the strong coupling regime with a Rabi splitting of 230 meV. We performed 22 MD simulations, starting in different adiabatic eigenstates of the molecule-cavity system, that are indicated by arrows in Fig. 2a. In all simulations, intra-molecular proton transfer occurs irrespective of the polaritonic eigenstate that was initially excited (Fig. S13b, Supplementary Information ). In Fig. 2d, we plot the O-H distances of the 512 strongly coupled HBQ molecules in one of the trajectories. In this trajectory, a proton transfer reaction occurs in HBQ molecule 400 within 25 fs after excitation into the 19th eigenstate, as indicated by an increase of the O-H distance (blue curve). The other 511 molecules remain in their ground state geometries, sampling O-H bond distances around the S0 equilibrium value of 0.1 nm. Because the reaction rate in QM/MM simulations of HBQ outside of the cavity is very similar (Fig. S13a, Supplementary Information), these results suggest that strong coupling does not have an appreciable effect on the reaction. Thus, even though the Rabi splitting implies strong coupling, the formation of polaritonic states does not lead to a suppression of the photo-chemical reaction in HBQ, in contrast to theoretical predictions15, and experiments on spiropyran and norbornadiene in Fabry–Pérot cavities1,9,30,31, nor to an acceleration, as observed in experiments on fulgide photo-switching in an optical cavity32.Fig. 2: Results of molecular dynamics simulations of HBQ molecules collectively coupled to a cavity.a Absorption spectra of HBQ in cyclohexane at 300 K outside (blue) and of 512 HBQ molecules inside (magenta) a single-mode micro-cavity that is resonant with the absorption maximum of HBQ (4.02 eV at the CAM-B3LYP/6-31G(d)//Gromos96 level of hybrid quantum mechanics/molecular mechanics (QM/MM) theory). Arrows indicate the eigenstates in which molecular dynamics simulations were started. b Contribution of the cavity mode (∣αm∣2, Eq. (S16), Supplementary Information) to the eigenstates of the coupled HBQ-cavity system. c Overlap between the polaritonic absorption spectrum and the molecular density of states as a function of the number of strongly-coupled molecules (black). The red line shows the losses due to cavity decay. Data are presented as mean values ± standard deviation, obtained from all trajectories performed for a specific number of molecules (see Supplementary Information 2.7.2 for an overview of the number of trajectories for each HBQ ensemble size). The numbers under the black data points give the Rabi splitting in meV. d Time evolution of the O-H distances in each of the 512 strongly-coupled HBQ molecules (all colors) after excitation into an optically bright polaritonic state (i.e., state 19, second arrow from left in (a)). As schematically illustrated in the inset, the OH distance is the reaction coordinate for excited-state intra-molecular proton transfer, and a distance of ~0.10 nm corresponds to the situation where the proton is bound to the phenol oxygen, whereas a distance around 0.19 nm indicates that the reaction has occurred and the proton has transferred to the nitrogen. Here, the latter happened in molecule 400, for which the OH distance is shown in blue. Source data are provided as a Source Data file.To understand why excitation into a polaritonic eigenstate of the molecule-cavity system does not suppress the reactivity in our simulations, we inspected the composition of these states. As shown in Fig. 2b, the cavity mode is distributed over virtually all eigenstates of the molecule-cavity system. As pointed out by Houdré et al.26 for atoms, and later by Mony et al.9 for molecules, this is due to structural, and hence energetic disorder among the HBQ molecules at 300 K. Without disorder, only the optically accessible upper and lower polariton states include contribution of the cavity mode and thus have a different potential energy surface on which reactivity can be suppressed (Fig. 1). The other N − 1 eigenstates are dark, i.e., without contribution from the cavity mode, and have potential energy surfaces that are similar to the S1 surface of the uncoupled molecule. In contrast, when there is disorder, which is unavoidable in experiments under ambient conditions, all states are optically accessible, but because molecular excitations dominate these states, rather than the cavity mode, the potential energy surfaces are hardly perturbed with respect to the bare molecules—not even for the brightest polaritonic states.In our simulations, a perfect cavity was assumed, without any losses. However, in reality, photon leakage through the mirrors is unavoidable and hence provides an additional decay channel for the excited population that could reduce the quantum yield and hence suppress the reaction. Under the assumption that the rate of radiative decay during an MD timestep, Δt, from a polaritonic state is proportional to its cavity mode contribution18,33,34, we accounted for such reduction in the quantum yield a posteriori by recomputing the evolution of the polaritonic wave function under the influence of cavity losses along the MD trajectories (Supplementary Information, subsection 2.4). In these calculations we assumed a cavity decay rate of γcav = 250 ps−1, which is typical for a low quality metallic cavity with Q ~ 15. The losses estimated under these assumptions, plotted for various ensemble sizes in Fig. 2c, suggest an average loss of only 5% for the 512 molecule-cavity system.The extent of the radiative loss depends on how rapidly the population transfers from a bright polaritonic state with cavity mode contribution and hence susceptible to radiative decay, into a dark state that is localized on a single molecule and therefore lacks cavity mode contribution35,36. Because the rate of this non-adiabatic population transfer process is inversely proportional to the energy difference between the states37, the radiative loss depends on the overlap between the optically-bright states and the molecular dark states18. Because that overlap is determined by the Rabi splitting, the loss can be controlled by varying the HBQ concentration18.However, because adding more molecules inside the cavity mode volume not only increases the Rabi splitting, but also the number of dark states, the overlap between the polaritonic absorption spectrum (Fig. 2a), which represents the distribution of the optically-bright states (Fig. 2b), on the one hand, and the molecular absorption spectrum, which represents the distribution of the molecular dark states18, on the other hand, has a maximum at a specific Rabi splitting, or equivalently, a specific number of molecules, as shown in Fig. 2c. Therefore, also the suppression of the reaction due to radiative loss has a minimum around that Rabi splitting and increases again at higher concentrations. Losses estimated for simulations with a different number of molecules in the same cavity, confirm this correlation between Rabi splitting and losses, at least qualitatively (Fig. 2c).With 2048 HBQ molecules in the cavity and a collective Rabi splitting of 520 meV, the losses reduce the formation of the photo-product by 30%, in line with a smaller overlap. To remove the overlap and hence suppress photo-product emission, the Rabi splitting must exceed 800 meV (Supplementary Information, Fig. S15), placing the system in the ultra-strong coupling regime. Such coupling strengths are not only challenging to achieve experimentally due to the limited solubility of HBQ in PMMA, but also difficult to simulate, as the rotating wave approximation (RWA), on which our model is based33, may loose its validity in this regime38. Notwithstanding the potential limitations of the RWA, we observed full suppression of the reaction in simulations at a Rabi splitting of 820 meV (Fig. S15b).Summarizing, the results of our calculations suggest that within the strong coupling regime, the thermal disorder at 300 K prevents the modification of the potential energy surfaces, in line with recent results from quantum dynamics simulations39 and experiments30,31,40. Instead, ultra-strong coupling would be required to create a polaritonic potential energy surface with a sufficiently deep local minimum to reduce the reaction rate. In both regimes, cavity decay provides a competing loss channel that suppresses the overall reaction quantum yield and our calculations suggest that the extent of such suppression can be tuned via the HBQ concentration (Fig. 2c).To verify the validity of these findings experimentally, we fabricated metallic Fabry–Pérot micro-cavities containing HBQ molecules and measured the photo-luminescence associated with the photo-product at 620 nm as a function of light-matter coupling strength and excitation wavelength. As shown schematically in Fig. 1a, a ~100 nm PMMA film doped with HBQ, was covered with a 20 nm thick semitransparent aluminum (Al) mirror on top and a 120 nm non-transparent Al mirror on the bottom41. The top mirror is sufficiently thin for the HBQ photo-product emission around 620 nm to leak through and be detected. The thickness of the cavities was tuned to match the first-order cavity mode with the HBQ absorption maximum at 375 nm. To control the collective light-matter coupling strength (\(\propto \,\,\sqrt{N}\)), we varied the concentration of HBQ in the PMMA film. Because the first-order cavity mode is sufficiently higher in energy than the emission maximum of the HBQ photo-product, we can exclude fluorescence enhancement due to the Purcell effect42. Further details on the design, fabrication and characterization of the cavity systems are provided in the Supplementary Information (section 1).Three micro-cavities were fabricated with HBQ/PMMA ratios of 0.5 (low), 1.0 (mid), and 1.6 (high concentration). In addition, three bare films were fabricated with the same HBQ/PMMA ratios as in the cavities. To provide a similar geometry for the reflection measurements, these films were also deposited on a 120 nm thick non-transparent Al mirror, i.e., the structure was identical to the cavity geometry shown in Fig. 1a except for the top mirror.We measured angle-dependent steady-state absorption spectra of the cavities, which are shown as contour maps in Fig. 3. The anti-crossings between the bright polaritonic branches around 40°–50° incident angle, suggest that the cavities are in the strong coupling regime and that the first-order cavity mode is hybridized with the two lowest-energy electronic transitions in HBQ, namely the main peak at 375 nm and the (vibronic) shoulder at 360 nm (Fig. 1b). These molecular transitions are shown as black dotted horizontal lines, together with the complete absorption spectrum of the HBQ/PMMA film in pink. The energies of LP and UP, extracted from the angle-resolved experimental spectra, are shown as black crosses.Fig. 3: Measured and modeled dispersions of strongly coupled HBQ cavities.Angle-resolved absorption (contour map) of cavities containing HBQ at (a) low, (b) mid, and (c) high concentration (C). The absorption spectra of the bare HBQ/PMMA films are shown in pink on the left axis. The white dashed curves represent the upper, middle, and lower polariton branches obtained from fitting the coupled harmonic oscillator model (CHOM, Supplementary Information, subsection 1.7) to the measured spectral positions (black crosses). The middle polariton branches were too faint to be resolved, and therefore not included in the fitting. The black dotted curves depict the dispersion of an undoped cavity (i.e., containing only PMMA), while the horizontal black dotted lines show the molecular absorption peaks at 360 nm and 375 nm of HBQ. Source data are provided as a Source Data file.While in previous works on strong coupling with organic molecules, coupling strengths and cavity mode dispersions were often extracted from the measured spectra by means of the coupled harmonic oscillator model (CHOM)9,13,32,43,44,45, a straightforward application of this model to our reflectivity data is compromised by the limited visibility of the Middle Polariton (MP), situated between the two vibronic transitions of HBQ. The limited visibility of this MP is due the heterogeneous broadening of the transitions46. As demonstrated by Musser et al., applying the CHOM to organic molecules with broad absorption spectra, provides coupling constants, g, that do not reflect the actual strength of the light-matter interaction46. Therefore, criteria for strong coupling based on the coupling constants obtained from a fit of the CHOM to the experimental data (i.e., 2g ≥ κmol + γcav, with κmol and γcav the decay rates of the molecule and the cavity, respectively), cannot be used to determine if our system is in the strong coupling regime.We, therefore, instead focus on the observable splitting of the molecular absorption into clearly visible upper and lower branches with dispersion, and report the minimum energy gap between these branches in Table 1 as a proxy for the coupling strength. Because this gap, which is similar to the Rabi splitting of 240 meV in the MD simulations, scales with the expected square-root of the molecular concentration in all samples46, we consider our systems to be in the strong coupling regime. Although the CHOM may not be very suitable for extracting the coupling strengths, we nevertheless used it to visualize the polariton dispersions and to estimate the cavity dispersion, shown as white dashed lines and black dotted lines, respectively, in the spectra of Fig. 3.Table 1 Energy difference between the upper (UP) and lower polariton (LP) for cavities with low, mid and high concentration (C)To verify the main finding in our simulations that exciting any eigenstate of the molecule-cavity system leads to proton transfer and the formation of the photo-product, we recorded cavity excitation spectra by measuring the intensity of the steady-state emission of the photo-product at 620 nm as a function of excitation wavelength and angle. Since the energy gap between the lower polariton and the fluorescence spectrum of HBQ (Fig. 1b) is more than an eV at all angles, we can rule out photo-product emission through the optically transparent polaritonic branches. The cavity system was excited with ~5 ns pulses at a 100 Hz repetition rate from a tunable laser source. Because the fluorescence is emitted from uncoupled molecules without angular dependence, the emission was always collected at the sample surface normal (i.e., at 0°).The observation that the yield of the reaction in our simulations depends on the overlap between bright and dark states (Fig. 2c)18, suggests that the excitation spectra of the HBQ-cavity systems can be obtained by multiplying the probability to absorb a photon, determined by the absorption spectrum of the HBQ cavity, and the probability to undergo ESIPT, which is determined by the density of molecular states. Because for HBQ the absorption and excitation spectra are the same in solution (Supplementary Information, Fig. S3) and very similar in the PMMA film (Supplementary Information, Fig. S4), we obtained this density of states by measuring the excitation spectra of the HBQ/PMMA films.In Fig. 4, we show the absorption spectra (a,b) and excitation spectra (c,d) at various incidence angles for the mid C (left column) and the high C (right column) HBQ/PMMA cavities, as well as the excitation spectra of films with the same HBQ/PMMA doping ratios as the cavities (c,d). The qualitative agreement between the measured cavity excitation spectra (Fig. 4c, d), on the one hand, and the spectra obtained by multiplying the cavity absorption spectra and film excitation spectra (Fig. 4e, f), on the other hand, confirm the results from the simulations that the efficiency of the reaction is primarily controlled by the overlap between the bright polaritons and the molecular dark states. Likewise, dividing the excitation spectra of the HBQ/PMMA-cavity systems by the excitation spectra of the HBQ/PMMA films, yields the polaritonic absorption spectra (Fig. 4g, h), affirming our conjecture. We note that the agreement between the calculated and measured spectra is not perfect for all angles, which we attribute to uncertainties in the baseline corrections that were applied to the cavity absorption spectra (Supplementary Information, Section 1.4).Fig. 4: Measured and predicted excitation spectra of strongly coupled HBQ-cavities.Absorption spectra of (a) mid concentration (C) and (b) high C HBQ/PMMA cavities at various excitation angles. Excitation spectra for emission at 620 nm of (c) mid C and (d) high C HBQ/PMMA cavities as a function of excitation angle. The excitation spectrum of the films are scaled down and shown in light gray. Scaling of the film excitation spectra was done to compensate for the absence of the top mirror and to facilitate comparison. The product of the cavity absorption spectrum and film excitation spectrum for (e) mid C and (f) high C cavities. The scaling of the film excitation spectra has no effect on the shape of these product spectra. Cavity excitation spectrum divided by the film excitation spectrum for (g) mid C and (h) high C HBQ/PMMA cavities. The curves are normalized so that the highest value within a group of spectra in each panel (c–h) is scaled to one, i.e., the relative intensities of the curves are preserved to facilitate comparison. Source data are provided as a Source Data file.Additional support is provided by the lower yield of the photo-product emission at the largest angles where the overlap between the polaritonic absorption maxima and film excitation spectrum is smallest. Simulations, in which the cavity is red-detuned to mimic excitation at such angles, confirm this (Supplementary Information, Fig. S14). Thus, the results of both our MD simulations and excitation spectra measurements suggest that in the strong coupling regime the bright polaritonic states act as a gate-way to access the reactive dark states and that the efficiency of this gate-way, or optical filter, depends on the overlap between the polaritonic absorption spectrum and the molecular density of states18.Our simulations furthermore suggest that within the strong coupling regime, increasing HBQ concentration enhances the overlap at the resonance angle (Fig. 2c), and hence the efficiency of the ESIPT reaction. To verify also this finding, we measured the steady-state emission intensity at 620 nm from our HBQ cavities while exciting directly into the lower polariton at the resonance angle, i.e., the angle at which the excitation energy of bare HBQ matches the dispersion of the cavity, and the energy gap between UP and LP is minimum. These excitation wavelengths, \({\lambda }_{{{{{{\rm{res}}}}}}}\), and angles, \({\theta }_{{{{{{\rm{res}}}}}}}\), are listed for each sample in Table 1. As reference, we also measured the emission from the HBQ/PMMA films with the excitation tuned to the absorption maximum (λex = 375 nm) of the film. As in the measurements of the excitation spectra, the samples were excited with ~5 ns laser pulses at a 100 Hz repetition rate. Details of these experiments are provided in the Supplementary Information (section 1.5).We quantify the emission yield (η) in these experiments as:$${\eta }^{\exp}=I({\lambda }_{{{{{{\rm{em}}}}}}})/A({\theta }_{{{{{{\rm{res}}}}}}},\, {\lambda }_{{{{{{\rm{res}}}}}}})$$
(1)
with I(λem) the intensity at the maximum of the emission band (λem = 620 nm) and \(A({\theta }_{{{{{{\rm{res}}}}}}},\, {\lambda }_{{{{{{\rm{res}}}}}}})\) the baseline-corrected absorption at the excitation wavelength \({\lambda }_{{{{{{\rm{res}}}}}}}\), and incident angle \({\theta }_{{{{{{\rm{res}}}}}}}\). In Fig. 5, we plot the yields as a function of the HBQ/PMMA doping ratio, which is correlated with both the number of HBQ molecules within the mode volume of the cavity and the coupling strength (Table 1). The films show almost constant emission yield with only a minor decrease at higher concentrations, presumably due to quenching47. The absorption, \(A({\theta }_{{{{{{\rm{res}}}}}}},{\lambda }_{{{{{{\rm{res}}}}}}})\), was also computed with the transfer matrix method and the optical finite element method (Supplementary Information, section 1.6). While both approaches provide similar trends, the assumptions of a perfect cavity geometry is rather strong. We, therefore, only report yields, ηexp, that were derived from the experimental spectra. Although the relative increase of the cavity emission yield is larger than in the simulations, presumably due to the overestimation of population transfer rates in small ensembles of molecules37, the increase is in line with our calculations. Therefore, both simulations and experiments suggest that increasing the coupling by adding more molecules, decreases the suppression by enhancing the rate at which population transfers from the lossy polariton modes into the reactive dark state manifold.Fig. 5: Measured emission yields as a function of coupling strength.Emission yield, \({\eta }^{\exp}\), in HBQ-cavity systems and films as a function of HBQ/PMMA doping ratio. The emission yield is normalized to the highest value. Source data are provided as a Source Data file.However, experiments in cavities with different Q-factors, as was done for example by Pandya et al. for investigating the effect of cavity mode lifetime on polariton-mediated exciton transport48, would be needed to further confirm our interpretation that suppression of photo-chemistry in the strong coupling regime is due to cavity loss, rather than to a modified potential energy surface. In addition, experiments at higher HBQ concentration are needed to confirm the turn-over between the decrease and increase of losses, predicted by our simulations (Fig. 2c). However, due to the limited solubility in PMMA, either other polymer matrices or chemical modifications49 would be required to reduce the aggregation propensity of HBQ in such experiments and reach the Rabi splittings that are necessary for observing the turn-over.In conclusion, we have investigated how strong light-matter coupling affects an ultra-fast photo-chemical reaction that occurs on the same timescale as the cavity lifetime. While the coupling leads to the characteristic Rabi splitting in the absorption spectra, the cavity mode excitations are smeared out over so many states that their contributions are too small to significantly perturb the potential energy surface of the electronic excited state and affect the reaction dynamics. The redistribution of the cavity mode contribution is due to disorder, which suppresses the collective response, and, by localizing the excitation, reduces polaritonic effects not only on reactivity9,39, but also on other properties, such as polariton-mediated transport50,51,52,53,54,55,56. While radiative decay from the polaritonic states in a lossy cavity can reduce the excited state population, the efficiency with which such losses suppress the reaction, depends on the competition with non-adiabatic population transfer into the molecular dark states. Since the rate of population transfer between bright and dark states is inversely proportional to the energy gap37, this rate is determined by the overlap between the polaritonic absorption spectrum and the molecular density of states. Because this overlap depends on the number of molecules in the mode volume18, the extent of suppression can be controlled by tuning the cavity Q-factor and the concentration. In addition, by providing additional non-reactive decay channels, cavities can also affect the excitation spectrum, and thereby selectively enhance excitation of states at the edges of the molecular excitation spectrum, where a system may be more reactive, as for example in Photoactive Yellow Protein57. Although we focused specifically on the effect of strong coupling on the ultra-fast ESIPT reaction in HBQ, we believe our findings, obtained by combining simulations and experiments, provide important new insights into the possibilities of altering chemistry with strong coupling in general as well as the limitations.
Thermal disorder prevents the suppression of ultra-fast photochemistry in the strong light-matter coupling regime
