Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Steady-state measurements of BSWPs.
Fig. 2: Pump–probe microscopy of BSWPs.
Fig. 3: Time-resolved dynamics of BSWPs.
Fig. 4: Kinetics of BSWP expansion.
Fig. 5: Polariton transport parameters.

Data availability

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

References

  1. Scholes, G. D., Fleming, G. R., Olaya-Castro, A. & Van Grondelle, R. Lessons from nature about solar light harvesting. Nature Chemistry 3, 763–774 (2011).

    Article  CAS  Google Scholar 

  2. Forrest, S. R. Organic Electronics: Foundations to Applications (Oxford Univ. Press, 2020).

  3. Tessler, N., Preezant, Y., Rappaport, N. & Roichman, Y. Charge transport in disordered organic materials and its relevance to thin-film devices: a tutorial review. Advanced Materials 21, 2741–2761 (2009).

    Article  CAS  Google Scholar 

  4. Ginsberg, N. S. & Tisdale, W. A. Spatially resolved photogenerated exciton and charge transport in emerging semiconductors. Annual Review of Physical Chemistry 71, 1–30 (2020).

    Article  CAS  Google Scholar 

  5. Orgiu, E. et al. Conductivity in organic semiconductors hybridized with the vacuum field. Nature Materials 14, 1123–1129 (2015).

    Article  CAS  Google Scholar 

  6. Lerario, G. et al. High-speed flow of interacting organic polaritons. Light Sci. Appl. 6, e16212 (2017).

  7. Rozenman, G. G., Akulov, K., Golombek, A. & Schwartz, T. Long-range transport of organic exciton–polaritons revealed by ultrafast microscopy. ACS Photonics 5, 105–110 (2018).

    Article  CAS  Google Scholar 

  8. Zakharko, Y. et al. Radiative pumping and propagation of plexcitons in diffractive plasmonic crystals. Nano Letters 18, 4927–4933 (2018).

    Article  CAS  Google Scholar 

  9. Nagarajan, K. et al. Conductivity and photoconductivity of a p-type organic semiconductor under ultrastrong coupling. ACS Nano 14, 10219–10225 (2020).

    Article  CAS  Google Scholar 

  10. Hou, S. et al. Ultralong-range energy transport in a disordered organic semiconductor at room temperature via coherent exciton–polariton propagation. Adv. Mater. 32, 2002127 (2020).

    Article  CAS  Google Scholar 

  11. Bhatt, P., Kaur, K. & George, J. Enhanced charge transport in two-dimensional materials through light–matter strong coupling. ACS Nano 15, 13616–13622 (2021).

    Article  CAS  Google Scholar 

  12. Pandya, R. et al. Microcavity-like exciton–polaritons can be the primary photoexcitation in bare organic semiconductors. Nat. Commun. 12, 6519 (2021).

    Article  Google Scholar 

  13. Pandya, R. et al. Tuning the coherent propagation of organic exciton polaritons through dark state delocalization. Advanced Science 2, 2105569 (2022).

    Article  Google Scholar 

  14. Berghuis, A. M. et al. Controlling exciton propagation in organic crystals through strong coupling to plasmonic nanoparticle arrays. ACS Photonics 9, 2263–2272 (2022).

    Article  CAS  Google Scholar 

  15. Garcia-Vidal, F. J., Ciuti, C. & Ebbesen, T. W. Manipulating matter by strong coupling to vacuum fields. Science 373, eabd0336 (2021).

    Article  CAS  Google Scholar 

  16. Aberra Guebrou, S. et al. Coherent emission from a disordered organic semiconductor induced by strong coupling with surface plasmons. Phys. Rev. Lett. 108, 066401 (2012).

    Article  Google Scholar 

  17. Shi, L. et al. Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes. Phys. Rev. Lett. 112, 153002 (2014).

    Article  CAS  Google Scholar 

  18. Zhong, X. et al. Energy transfer between spatially separated entangled molecules. Angew. Chem. Int. Ed. 56, 9034–9038 (2017).

    Article  CAS  Google Scholar 

  19. Du, M. et al. Theory for polariton-assisted remote energy transfer. Chem. Sci. 9, 6659–6669 (2018).

    Article  CAS  Google Scholar 

  20. Georgiou, K., Jayaprakash, R., Othonos, A. & Lidzey, D. G. Ultralong-range polariton-assisted energy transfer in organic microcavities. Angew. Chem. Int. Ed. 60, 16661–16667 (2021).

    Article  CAS  Google Scholar 

  21. Freixanet, T., Sermage, B., Tiberj, A. & Thierry-Mieg, V. Propagation of excitonic polaritons in a microcavity. Physica Status Solidi A 178, 133–138 (2000).

    Article  CAS  Google Scholar 

  22. Feist, J. & Garcia-Vidal, F. J. Extraordinary exciton conductance induced by strong coupling. Phys. Rev. Lett. 114, 196402 (2015).

    Article  Google Scholar 

  23. Schachenmayer, J., Genes, C., Tignone, E. & Pupillo, G. Cavity-enhanced transport of excitons. Phys. Rev. Lett. 114, 196403 (2015).

    Article  Google Scholar 

  24. Gonzalez-Ballestero, C., Feist, J., Gonzalo Badía, E., Moreno, E. & Garcia-Vidal, F. J. Uncoupled dark states can inherit polaritonic properties. Phys. Rev. Lett. 117, 156402 (2016).

    Article  Google Scholar 

  25. Hagenmüller, D., Schachenmayer, J., Schütz, S., Genes, C. & Pupillo, G. Cavity-enhanced transport of charge. Phys. Rev. Lett. 119, 223601 (2017).

    Article  Google Scholar 

  26. Paravicini-Bagliani, G. L. et al. Magneto-transport controlled by Landau polariton states. Nat. Phys. 15, 186–190 (2018).

    Article  Google Scholar 

  27. Sentef, M. A., Ruggenthaler, M. & Rubio, A. Cavity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on superconductivity. Sci. Adv. 4, eaau6969 (2018).

  28. Thomas, A. et al. Exploring superconductivity under strong coupling with the vacuum electromagnetic field. Preprint at https://arxiv.org/abs/1911.01459 (2019).

  29. Botzung, T. et al. Dark state semilocalization of quantum emitters in a cavity. Phys. Rev. B 102, 144202 (2020).

    Article  CAS  Google Scholar 

  30. Chávez, N. C., Mattiotti, F., Méndez-Bermúdez, J. A., Borgonovi, F. & Celardo, G. L. Disorder-enhanced and disorder-independent transport with long-range hopping: application to molecular chains in optical cavities. Phys. Rev. Lett. 126, 153201 (2021).

  31. Guo, Q. et al. Boosting exciton transport in WSe2 by engineering its photonic substrate. ACS Photonics 9, 2817–2824 (2022).

    Article  CAS  Google Scholar 

  32. Xu, D. et al. Ultrafast imaging of coherent polariton propagation and interactions. Preprint at https://arxiv.org/abs/2205.01176 (2022).

  33. Engelhardt, G. & Cao, J. Polarition localization and spectroscopic properties of disordered quantum emitters in spatially-extended microcavities. Preprint at https://arxiv.org/abs/2209.02909 (2022).

  34. Myers, D. M. et al. Polariton-enhanced exciton transport. Phys. Rev. B 98, 235302 (2018).

    Article  CAS  Google Scholar 

  35. Su, R. et al. Room temperature long-range coherent exciton polariton condensate flow in lead halide perovskites. Sci. Adv 4, eaau0244 (2018).

  36. Wurdack, M. et al. Motional narrowing, ballistic transport, and trapping of room-temperature exciton polaritons in an atomically-thin semiconductor. Nat. Commun. 12, 1–8 (2021).

  37. Virgili, T. et al. Confocal ultrafast pump–probe spectroscopy: a new technique to explore nanoscale composites. Nanoscale 4, 2219–2226 (2012).

  38. Akselrod, G. M. et al. Visualization of exciton transport in ordered and disordered molecular solids. Nat. Commun. 5, 3646 (2014).

    Article  CAS  Google Scholar 

  39. Zhu, T., Wan, Y. & Huang, L. Direct imaging of Frenkel exciton transport by ultrafast microscopy. Acc. Chem. Res. 50, 1725–1733 (2017).

    Article  CAS  Google Scholar 

  40. Wan, Y. et al. Cooperative singlet and triplet exciton transport in tetracene crystals visualized by ultrafast microscopy. Nat. Chem. 7, 785–792 (2015).

    Article  CAS  Google Scholar 

  41. Delor, M., Weaver, H. L., Yu, Q. Q. & Ginsberg, N. S. Imaging material functionality through three-dimensional nanoscale tracking of energy flow. Nat. Mater. 19, 56–62 (2020).

    Article  CAS  Google Scholar 

  42. Berghuis, A. M. et al. Effective negative diffusion of singlet excitons in organic semiconductors. J. Phys. Chem. Lett. 12, 1360–1366 (2021).

    Article  CAS  Google Scholar 

  43. Michetti, P. & La Rocca, G. C. Polariton states in disordered organic microcavities. Phys. Rev. B 71, 1–7 (2005).

    Article  Google Scholar 

  44. Agranovich, V. M. & Gartstein, Y. N. Nature and dynamics of low-energy exciton polaritons in semiconductor microcavities. Phys. Rev. B 75, 075302 (2007).

    Article  Google Scholar 

  45. Yeh, P., Yariv, A. & Cho, A. Y. Optical surface waves in periodic layered media. Appl. Phys. Lett. 32, 104–105 (1978).

    Article  CAS  Google Scholar 

  46. Lerario, G. et al. Room temperature Bloch surface wave polaritons. Opt. Lett. 39, 2068–2071 (2014).

  47. Ohad, A. et al. Spatially resolved measurement of plasmon dispersion using Fourier-plane spectral imaging. Photon. Res. 6, 653–658 (2018).

  48. Fischer, M. C., Wilson, J. W., Robles, F. E. & Warren, W. S. Pump–probe microscopy. Rev. Sci. Instrum. 87, 031101 (2016).

    Article  Google Scholar 

  49. Schwartz, T. et al. Polariton dynamics under strong light-molecule coupling. ChemPhysChem 14, 125–131 (2013).

    Article  CAS  Google Scholar 

  50. Mewes, L., Wang, M., Ingle, R. A., Börjesson, K. & Chergui, M. Energy relaxation pathways between light–matter states revealed by coherent two-dimensional spectroscopy. Commun. Phys. 3, 1–10 (2020).

    Article  Google Scholar 

  51. Klafter, J. & Sokolov, I. M. First Steps in Random Walks (Oxford Univ. Press, 2013).

  52. Barthelemy, P., Bertolotti, J. & Wiersma, D. S. A Lévy flight for light. Nature 453, 495–498 (2008).

    Article  CAS  Google Scholar 

  53. Litinskaya, M. Propagation and localization of polaritons in disordered organic microcavities. Phys. Lett. A 372, 3898–3903 (2008).

    Article  CAS  Google Scholar 

  54. Ishimaru, A. Wave Propagation and Scattering in Random Media (Elsevier, 1978).

  55. Datta, S. in Lessons from Nanoelectronics: A New Perspective on Transport, Vol. 5 (eds Lundstrom, M. & Datta S.) 43–49 (World Scientific, 2018).

  56. Lagendijk, A. & Van Tiggelen, B. A. Resonant multiple scattering of light. Physics Report 29, 143–215 (1996).

    Article  Google Scholar 

  57. Tallon, B., Brunet, T., Leng, J. & Page, J. H. Energy velocity of multiply scattered waves in strongly scattering media. Phys. Rev. B 101, 054202 (2020).

  58. Sanvitto, D. & Kéna-Cohen, S. The road towards polaritonic devices. Nat. Mater. 15, 1061–1073 (2016).

    Article  CAS  Google Scholar 

  59. Bradley, M. S. & Bulović, V. Intracavity optical pumping of J-aggregate microcavity exciton polaritons. Phys. Rev. B 82, 033305 (2010).

    Article  Google Scholar 

  60. Agranovich, V. M., Litinskaia, M. & Lidzey, D. G. Cavity polaritons in microcavities containing disordered organic semiconductors. Phys. Rev. B 67, 085311 (2003).

    Article  Google Scholar 

Download references

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 and Affiliations

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.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Reporting Summary

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

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

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing