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Rydberg States with a Liquid Core

Juan Carlos Acosta Matos, P. Giannakeas, and Jan M. Rost

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Phys. Rev. Lett. 137, 123402 – Published 16 September, 2026

DOI: https://doi.org/10.1103/pdby-ss2t

Abstract

We develop a self-consistent approach that provides an explicit potential for a Rydberg electron whose ionic core consists of a polarizable medium, typically realized with superfluid droplets. The electron’s motion remains separable in spherical coordinates, but the radial force exerted by the droplet breaks degeneracy of the angular momentum states nonperturbatively. The ensuing electron spectrum reveals intriguing properties dependent on droplet size and electron excitation. Deviations of the polarizable medium from the continuous spherical distribution can be taken into account as a perturbation of this redefined Rydberg dynamics. We discuss specific but paradigmatic examples for superfluid helium and also propose a way to probe droplet properties, including its possible crystallized fraction through stimulated transitions of the Rydberg electron.

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References (38)

  1. C. Greene, U. Fano, and G. Strinati, Phys. Rev. A 19, 1485 (1979).
  2. T. F. Gallagher, Quantum defect theory, in Rydberg Atoms, Cambridge Monographs on Atomic, Molecular and Chemical Physics (Cambridge University Press, Cambridge, England, 1994), pp. 415–428.
  3. S. Scheidegger, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Rev. A 108, 042803 (2023).
  4. C. H. Greene, A. S. Dickinson, and H. R. Sadeghpour, Phys. Rev. Lett. 85, 2458 (2000).
  5. V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, Nature (London) 458, 1005 (2009).
  6. E. L. Hamilton, C. H. Greene, and H. Sadeghpour, J. Phys. B 35, L199 (2002).
  7. P. Giannakeas, M. T. Eiles, F. Robicheaux, and J. M. Rost, Phys. Rev. Lett. 125, 123401 (2020).
  8. V. Bendkowsky, B. Butscher, J. Nipper, J. B. Balewski, J. P. Shaffer, R. Löw, T. Pfau, W. Li, J. Stanojevic, T. Pohl, and J. M. Rost, Phys. Rev. Lett. 105, 163201 (2010).
  9. Perttu J. J. Luukko and J.-M. Rost, Phys. Rev. Lett. 119, 203001 (2017).
  10. F. Camargo, R. Schmidt, J. D. Whalen, R. Ding, G. Woehl, S. Yoshida, J. Burgdörfer, F. B. Dunning, H. R. Sadeghpour, E. Demler, and T. C. Killian, Phys. Rev. Lett. 120, 083401 (2018).
  11. Aileen A. T. Durst and M. T. Eiles, Phys. Rev. Res. 6, L042009 (2024).
  12. S. Chowdhury and J. Perez-Ríos, Nat. Sci. 4, e20240006 (2024).
  13. M. T. Eiles, J. Pérez-Ríos, F. Robicheaux, and C. H. Greene, J. Phys. B 49, 114005 (2016).
  14. F. Dunning, S. Kanungo, and S. Yoshida, J. Phys. B 57, 212002 (2024).
  15. A. L. Hunter, M. T. Eiles, A. Eisfeld, and J. M. Rost, Phys. Rev. X 10, 031046 (2020).
  16. E. Fermi, Il Nuovo Cimento (1924–1942) 11, 157 (1934).
  17. J. C. A. Matos, P. Giannakeas, M. Ciardi, T. Pohl, and J. M. Rost, Phys. Rev. Lett. 134, 186001 (2025).
  18. D. Mateo and J. Eloranta, J. Chem. Phys. A 118, 6407 (2014).
  19. S. Müller, M. Mudrich, and F. Stienkemeier, J. Chem. Phys. 131, 044319 (2009).
  20. I. Chikina, V. Shikin, and A. A. Varlamov, Phys. Rev. B 75, 184518 (2007).
  21. E. Zunzunegui-Bru, E. Gruber, T. Lázaro, M. Bartolomei, M. I. Hernández, J. Campos-Martínez, T. González-Lezana, S. Bergmeister, F. Zappa, P. Scheier, R. Pérez de Tudela, J. Hernández-Rojas, and J. Bretón, J. Phys. Chem. Lett. 14, 3126 (2023).
  22. P. Bartl, C. Leidlmair, S. Denifl, P. Scheier, and O. Echt, J. Chem. Phys. A 118, 8050 (2014).
  23. P. Slavíček and M. Lewerenz, Phys. Chem. Chem. Phys. 12, 1152 (2010).
  24. F. Tramonto, P. Salvestrini, M. Nava, and D. E. Galli, J. Low Temp. Phys. 180, 29 (2015).
  25. D. E. Galli, D. M. Ceperley, and L. Reatto, J. Phys. Chem. A 115, 7300 (2011).
  26. K. Fedus, Atoms 9, 91 (2021).
  27. A. Golov and S. Sekatskii, Z. Phys. D 27, 349 (1993).

  28. Formally, all bound states with a given ℓ,m could be enumerated according to their number of radial nodes. The classification with n and ν, however, is more physical, as it reflects the number of nodes in a spatial region where the eigenstate has significant amplitude.

  29. For the droplet with Rd=250  a.u., the critical manifolds are 11 and 12.

  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/pdby-ss2t for the evolution of the ground oDDR state, the corresponding energy spectrum, and the normalized average-momentum-resolved density of states as the ion is displaced from the droplet center.
  31. K. von Haeften, T. Laarmann, H. Wabnitz, and T. Möller, J. Phys. B 38, S373 (2005).
  32. E. Loginov and M. Drabbels, Phys. Rev. Lett. 106, 083401 (2011).
  33. F. Lackner, G. Krois, M. Theisen, M. Koch, and W. E. Ernst, Phys. Chem. Chem. Phys. 13, 18781 (2011).
  34. E. Loginov, C. Callegari, F. Ancilotto, and M. Drabbels, J. Phys. Chem. A 115, 6779 (2011).
  35. J. V. Pototschnig, F. Lackner, A. W. Hauser, and W. E. Ernst, Phys. Chem. Chem. Phys. 19, 14718 (2017).
  36. J. C. A. Matos, P. Giannakeas, and J. M. Rost (to be published).
  37. J. Dupont-Roc, M. Himbert, N. Pavloff, and J. Treiner, J. Low Temp. Phys. 81, 31 (1990).
  38. S. A. Gurvitz and G. Kalbermann, Phys. Rev. Lett. 59, 262 (1987).

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Phys. Rev. Lett. 137, 123402– Published 16 September, 2026
  • Received 6 October 2025
  • Revised 5 August 2026
  • Accepted 26 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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