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Ultrafast longitudinal and transverse dielectric response of collective polar modes in liquids

Matthias Runge, Michael Woerner*, and Thomas Elsaesser

  • *Contact author: woerner@mbi-berlin.de
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Phys. Rev. Research 7, 023304 – Published 24 June, 2025

DOI: https://doi.org/10.1103/45x5-vztx

Abstract

Electrons solvated in polar liquids are a prototypical many-body system, in which electric interactions on different length scales have a strong impact on quantum states and elementary excitations. Impulsively excited polarons in liquid water and alcohols display coupled coherent motions of electrons and their solvation shells at terahertz (THz) frequencies, affecting both the longitudinal and transverse dielectric function. To address the barely characterized connection between the longitudinal and transverse dielectric response in experiment, an ultrafast pump-probe scheme is employed. Two femtosecond near-infrared pump pulses in sequence generate solvated electrons by ionization of isopropanol solvent molecules. The resulting changes of the dielectric function are mapped in time-resolved measurements by a broadband THz probe pulse, which is detected in a phase-resolved way. Longitudinal polaron oscillations modulate both the longitudinal and transverse dielectric function with a frequency set by the partial electron concentration generated in the separate excitation steps. On top, the transverse response includes steplike components, which are governed by the total electron concentration and well described by Clausius-Mossotti theory. The different longitudinal and transverse response is caused by the different character and spatial range of the underlying electric interactions.

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References (31)

  1. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, Oxford, 1984).
  2. J. J. Hopfield and D. G. Thomas, Theoretical and experimental effects of spatial dispersion on the optical properties of crystals, Phys. Rev. 132, 563 (1963).
  3. V. Ballenegger and J.-P. Hansen, Dielectric permittivity profiles of confined polar fluids, J. Chem. Phys. 122, 114711 (2005).
  4. V. M. Agranovich and Y. Gartstein, Spatial dispersion and negative refraction of light, Phys.-Usp. 49, 1029 (2006).
  5. G. E. H. Reuter and E. H. Sondheimer, The theory of the anomalous skin effect in metals, Proc. R. Soc. Lond. A 195, 336 (1948).
  6. R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, Nonlocal nature of the electrodynamic response of colloidal systems, Phys. Rev. B 75, 184202 (2007).
  7. P. A. Bopp, A. A. Kornyshev, and G. Sutmann, Static nonlocal dielectric function of liquid water, Phys. Rev. Lett. 76, 1280 (1996).
  8. P. A. Bopp, A. A. Kornyshev, and G. Sutmann, Frequency and wave-vector dependent dielectric function of water: Collective modes and relaxation spectra, J. Chem. Phys. 109, 1939 (1998).
  9. D. C. Elton and M. Fernández-Serra, The hydrogen-bond network of water supports propagating optical phonon-like modes, Nat. Commun. 7, 10193 (2016).
  10. L. Turi and P. J. Rossky, Theoretical studies of spectroscopy and dynamics of hydrated electrons, Chem. Rev. 112, 5641 (2012).
  11. B. C. Webster, The polaron viewpoint of solvated electrons, Nat. Phys. Sci. 239, 79 (1972).
  12. G. A. Kenney-Wallace and C. D. Jonah, Picosecond spectroscopy and solvation clusters. The dynamics of localizing electrons in polar fluids, J. Phys. Chem. 86, 2572 (1982).
  13. X. Shi, F. H. Long, H. Lu, and K. B. Eisenthal, Electron solvation in neat alcohols, J. Phys. Chem. 99, 6917 (1995).
  14. I. A. Taub, D. A. Harter, M. C. Sauer, and L. M. Dorfman, Pulse radiolysis studies. IV. the solvated electron in the aliphatic alcohols, J. Chem. Phys. 41, 979 (1964).
  15. A. Migus, Y. Gauduel, J. L. Martin, and A. Antonetti, Excess electrons in liquid water: First evidence of a prehydrated state with femtosecond lifetime, Phys. Rev. Lett. 58, 1559 (1987).
  16. J. C. Alfano, P. K. Walhout, Y. Kimura, and P. F. Barbara, Ultrafast transient-absorption spectroscopy of the aqueous solvated electron, J. Chem. Phys. 98, 5996 (1993).
  17. M. F. Emde, A. Baltuška, A. Kummrow, M. S. Pshenichnikov, and D. A. Wiersma, Ultrafast librational dynamics of the hydrated electron, Phys. Rev. Lett. 80, 4645 (1998).
  18. J. Savolainen, F. Uhlig, S. Ahmed, P. Hamm, and P. Jungwirth, Direct observation of the collapse of the delocalized excess electron in water, Nat. Chem. 6, 697 (2014).
  19. H. Fröhlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954).
  20. T.-D. Lee and D. Pines, Interaction of a nonrelativistic particle with a scalar field with application to slow electrons in polar crystals, Phys. Rev. 92, 883 (1953).
  21. A. Ghalgaoui, B. P. Fingerhut, K. Reimann, T. Elsaesser, and M. Woerner, Terahertz polaron oscillations of electrons solvated in liquid water, Phys. Rev. Lett. 126, 097401 (2021).
  22. P. Singh, J. Zhang, A. Ghalgaoui, K. Reimann, B. P. Fingerhut, M. Woerner, and T. Elsaesser, Coherent polaron dynamics of electrons solvated in polar liquids, PNAS Nexus 1, pgac078 (2022).
  23. M. Woerner, B. P. Fingerhut, and T. Elsaesser, Field-induced electron generation in water: Solvation dynamics and many-body interactions, J. Phys. Chem. B 126, 2621 (2022).
  24. M. Runge, K. Reimann, M. Woerner, and T. Elsaesser, Nonlinear terahertz polarizability of electrons solvated in a polar liquid, Phys. Rev. Lett. 131, 166902 (2023).
  25. K. Reimann, M. Woerner, and T. Elsaesser, Two-dimensional terahertz spectroscopy of condensed-phase molecular systems, J. Chem. Phys. 154, 120901 (2021).
  26. J. H. Hannay, The Clausius-Mossotti equation: An alternative derivation, Eur. J. Phys. 4, 141 (1983).
  27. M. Runge, M. Woerner, D. I. Bondar, and T. Elsaesser, Solvated electrons in polar liquids as ε-near-zero materials tunable in the terahertz frequency range, Phys. Rev. Lett. 134, 056901 (2025).
  28. T. D. Lee, F. E. Low, and D. Pines, The Motion of slow electrons in a polar crystal, Phys. Rev. 90, 297 (1953).
  29. F. M. Peeters and J. T. Devreese, Radius, self-induced potential, and number of virtual optical phonons of a polaron, Phys. Rev. B 31, 4890 (1985).
  30. P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, Internal motions of a quasiparticle governing its ultrafast nonlinear response, Nature (London) 450, 1210 (2007).
  31. P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and C. Flytzanis, Nonlinear electron transport in an electron-hole plasma, Phys. Rev. B 85, 165206 (2012).

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Phys. Rev. Research 7, 023304– Published 24 June, 2025
  • Received 21 March 2025
  • Accepted 12 June 2025
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