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# From enhanced diffusion to ultrafast ballistic motion of hybrid light–matter excitations

## Abstract

Transport of excitons and charge carriers in molecular systems can be enhanced by coherent coupling to photons, giving rise to the formation of hybrid excitations known as polaritons. Such enhancement has far-reaching technological implications; however, the enhancement mechanism and the transport nature of these hybrid excitations remain elusive. Here we map the ultrafast spatiotemporal dynamics of polaritons formed by mixing surface-bound optical waves with Frenkel excitons in a self-assembled molecular layer, resolving polariton dynamics in energy/momentum space. We find that the interplay between the molecular disorder and long-range correlations induced by coherent mixing with light leads to a mobility transition between diffusive and ballistic transport, which can be controlled by varying the light–matter composition of the polaritons. Furthermore, we show that coupling to light enhances the diffusion coefficient of molecular excitons by six orders of magnitude and even leads to ballistic flow at two-thirds the speed of light.

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## Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

This research was supported by the Israel Science Foundation, grant number 1435/19 and 1993/13. The authors thank G. Markovich, T. Ellenbogen, S. Reuveni, C. Genet, G. Groenhof and A. Nitzan for useful discussions. T. S. is grateful to M. Segev for his kind support.

## Author information

Authors

### Contributions

M.B. and T.S. conceived the idea and designed the experiments. M.B. conducted the majority of the experimental measurements, data analysis and modelling. A.S. and A.G. carried out the sample preparation. G.S. participated in the optical measurements. G.A. fabricated the dielectric DBR structures. M.B., A.G. and T.S. wrote the manuscript.

### Corresponding author

Correspondence to Tal Schwartz.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Materials thanks Ivan Shelykh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 Characterisation of TDBC molecular layers.

(a) The absorbance of the TDBC layers deposited on the DBR substrate, measured after the addition of each successive bilayer, beginning with the deposition of a layer of PDAC. (b) The value of the absorbance measured at 582 nm as a function of the number of bilayers deposited on the DBR. The black line represents a linear fit to the data.

### Extended Data Fig. 2 Steady state characterisation of BSWP.

(a) A sketch of the Kretschmann spectral imaging set-up used for either angle-resolved or spatially resolved reflection/emission steady-state measurements. (b,c) Dispersion of the BSWP modes measured via angle-resolved reflection (b) and emission (c) spectroscopy (represented by the false-colour plots). The sharp signal corresponds to the lower BSW polariton mode, while the white dashed lines represent the simulated dispersion (using the T-matrix method). The solid white lines indicate the bare BSW dispersion and the exciton energy (fixed at 2.13 eV), the red dashed line indicates the light line and the inset in (b) shows the typical linewidth of the reflection dip corresponding to the BSWP resonance, as measured around 1.91 eV. Note that in the reflection measurement (b), unlike similar angle-resolved reflectivity measurements conducted on polaritons in normal Fabry–Perot cavities,7,49 here only the lower BSWP branch is observed. Since such reflectometry measurements are sensitive to absorption into the modes of the system the fact that the upper polariton is not observed probably results from inefficient coupling between incoming photons and the upper polariton modes via the prism. Moreover, in the emission measurements (c) the upper polariton is also missing, which is consistent with previous measurements and results from the fast, nonradiative decay of the upper polaritons49,60.

### Extended Data Fig. 3 Properties of BSWPs.

Quality factor (blue circles) and photonic weight (red line) as a function of energy of the lower polariton branch. As the polariton energy shifts away from the bare exciton energy, its Q-factor (and lifetime) increases while it becomes more photon-like.

### Extended Data Fig. 4 BSWP steady state spatial profile.

(a) Representative steady state emission profiles (note logarithmic scale) measured at the points A and B indicated in Extended Data Fig. 2c. The black solid lines show the exponential fits to the data. (b) Decay length as a function of photonic weight (blue circles), extracted from the exponential fit to the tails of the steady-state distributions given in Fig. 1c. The red circles and the black solid line show the decay lengths calculated as the inverse of the width in Fourier space, from both experimental reflectivity measurements and transfer-matrix simulations respectively.

### Extended Data Fig. 5 Pump–probe microscopy set-up.

Detailed illustration of the pump–probe microscopy set-up, as described in Methods.

### Extended Data Fig. 6 Spectral and temporal transient response of BSWP.

(a) Transient reflection spectra, measured using a pump–probe spectrometer (Helios, Ultrafast Systems) at τ = 1 ps for probe incident angles of θ ~ 43, 45 and 46. The spectra show two resonant features, similar to the transient spectra observed in strongly coupled Fabry–Perot cavities49: a prominent, angle-dependent feature around the energy of the lower BSWP (corresponding to $${\left\vert {\alpha }_{ph}\right\vert }^{2}$$ values of 0.82, 0.66 and 0.54) and a second, weaker one that occurs at the bare exciton energy and does not show any angular dependence. The shaded regions mark the 5 nm-wide spectral band which is probed by the time-resolved imaging set-up. (b) Temporal dynamics of the spectral features observed in (a) showing the decay kinetics of the BSWP signals corresponding to $${\left\vert {\alpha }_{ph}\right\vert }^{2}$$ values of 0.82, 0.66 and 0.54 and at the bare exciton energy. The measured lifetime for the BSWPs are 3.8, 6.5 and 6.6 ps respectively while at the bare exciton energy we observe a lifetime of 6.6 ps.

### Extended Data Fig. 7 Long-time evolution of BSWP distribution.

Horizontal cross sections of the ΔR/R distribution measured during the rise (a) and decay (b) of the signal for $${\left\vert {\alpha }_{ph}\right\vert }^{2}=0.86$$.

### Extended Data Fig. 8 Verification of signal linearity.

Magnitude (a) and normalized cross sections (b) of the ΔR/R signal under various pump energy densities (measured at a time delay of 1 psec). The dotted lines in (a) show the 95% confidence bounds for the linear fit.

## Supplementary information

### Supplementary Information

Supplementary discussion, Figs. 1–6.

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Balasubrahmaniyam, M., Simkhovich, A., Golombek, A. et al. From enhanced diffusion to ultrafast ballistic motion of hybrid light–matter excitations. Nat. Mater. (2023). https://doi.org/10.1038/s41563-022-01463-3

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• DOI: https://doi.org/10.1038/s41563-022-01463-3