- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Fate of an Impurity Strongly Interacting with a Thermal Bose Gas

Jiří Etrych1, Sebastian J. Morris1, Simon M. Fischer1, Gevorg Martirosyan1, Christopher J. Ho1, Moritz Drescher2, Manfred Salmhofer2, Zoran Hadzibabic1, Tilman Enss2 et al.

Christoph Eigen1,*

  • *Contact author: ce330@cam.ac.uk
PDF

Phys. Rev. Lett. 137, 193405 – Published 5 November, 2026

DOI: https://doi.org/10.1103/g8gh-vsyq

Abstract

We spectroscopically study mobile impurities immersed in a homogeneous bosonic bath (a box-trapped Bose gas), varying the bath temperature and the strength of impurity-bath interactions. We compare our results to those for a quasipure Bose-Einstein condensate, and find that for strong impurity-bath interactions, the spectra narrow with increasing temperature, while the impurity energy shift is suppressed. Near the critical temperature for condensation, many-body effects still play an important role, and only for a nondegenerate bath the system approaches the classical Boltzmann-gas behavior. The key spectral features are reproduced within the theory of the ideal Bose polaron.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (54)

  1. L. D. Landau, Electron motion in crystal lattices, Phys. Z. Sowjetunion 3, 664 (1933).
  2. S. I. Pekar, Autolocalization of the electron in an inertially polarizable dielectric medium, Zh. Eksp. Teor. Fiz. 16, 335 (1946).
  3. Polarons in Advanced Materials, edited by A. S. Alexandrov (Springer, New York, 2008).
  4. C. Franchini, M. Reticcioli, M. Setvin, and U. Diebold, Polarons in materials, Nat. Rev. Mater. 6, 560 (2021).
  5. F. Scazza, M. Zaccanti, P. Massignan, M. M. Parish, and J. Levinsen, Repulsive Fermi and Bose polarons in quantum gases, Atoms 10, 55 (2022).
  6. C. Baroni, G. Lamporesi, and M. Zaccanti, Quantum mixtures of ultracold gases of neutral atoms, Nat. Rev. Phys. 6, 736 (2024).
  7. F. Grusdt, N. Mostaan, E. Demler, and L. A. P. Ardila, Impurities and polarons in bosonic quantum gases: A review on recent progress, Rep. Prog. Phys. 88, 066401 (2025).
  8. P. Massignan, R. Schmidt, G. E. Astrakharchik, A. İmamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, Polarons in atomic gases and two-dimensional semiconductors, Rev. Mod. Phys. 98, 035002 (2026).
  9. A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwierlein, Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms, Phys. Rev. Lett. 102, 230402 (2009).
  10. C. Kohstall, M. Zaccanti, M. Jag, A. Trenkwalder, P. Massignan, G. M. Bruun, F. Schreck, and R. Grimm, Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture, Nature (London) 485, 615 (2012).
  11. Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Boiling a unitary Fermi liquid, Phys. Rev. Lett. 122, 093401 (2019).
  12. S. M. Yoshida, S. Endo, J. Levinsen, and M. M. Parish, Universality of an impurity in a Bose-Einstein condensate, Phys. Rev. X 8, 011024 (2018).
  13. N.-E. Guenther, R. Schmidt, G. M. Bruun, V. Gurarie, and P. Massignan, Mobile impurity in a Bose-Einstein condensate and the orthogonality catastrophe, Phys. Rev. A 103, 013317 (2021).
  14. M.-G. Hu, M. J. Van de Graaff, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, Bose polarons in the strongly interacting regime, Phys. Rev. Lett. 117, 055301 (2016).
  15. N. B. Jørgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, Observation of attractive and repulsive polarons in a Bose-Einstein condensate, Phys. Rev. Lett. 117, 055302 (2016).
  16. M. G. Skou, T. G. Skov, N. B. Jørgensen, K. K. Nielsen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Non-equilibrium quantum dynamics and formation of the Bose polaron, Nat. Phys. 17, 731 (2021).
  17. M. G. Skou, K. K. Nielsen, T. G. Skov, A. M. Morgen, N. B. Jørgensen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Life and death of the Bose polaron, Phys. Rev. Res. 4, 043093 (2022).
  18. H. Cayla, P. Massignan, T. Giamarchi, A. Aspect, C. I. Westbrook, and D. Clément, Observation of 1/k4-tails after expansion of Bose-Einstein condensates with impurities, Phys. Rev. Lett. 130, 153401 (2023).
  19. J. Etrych, G. Martirosyan, A. Cao, C. J. Ho, Z. Hadzibabic, and C. Eigen, Universal quantum dynamics of Bose polarons, Phys. Rev. X 15, 021070 (2025).
  20. R. Schmidt, H. R. Sadeghpour, and E. Demler, Mesoscopic Rydberg impurity in an atomic quantum gas, Phys. Rev. Lett. 116, 105302 (2016).
  21. N.-E. Guenther, P. Massignan, M. Lewenstein, and G. M. Bruun, Bose polarons at finite temperature and strong coupling, Phys. Rev. Lett. 120, 050405 (2018).
  22. V. Pastukhov, Polaron in the dilute critical Bose condensate, J. Phys. A 51, 195003 (2018).
  23. D. Dzsotjan, R. Schmidt, and M. Fleischhauer, Dynamical variational approach to Bose polarons at finite temperatures, Phys. Rev. Lett. 124, 223401 (2020).
  24. B. Field, J. Levinsen, and M. M. Parish, Fate of the Bose polaron at finite temperature, Phys. Rev. A 101, 013623 (2020).
  25. G. Pascual and J. Boronat, Quasiparticle nature of the Bose polaron at finite temperature, Phys. Rev. Lett. 127, 205301 (2021).
  26. M. Drescher, M. Salmhofer, and T. Enss, Bosonic functional determinant approach and its application to polaron spectra, Phys. Rev. A 110, 063303 (2024).
  27. Z. Z. Yan, Y. Ni, C. Robens, and M. W. Zwierlein, Bose polarons near quantum criticality, Science 368, 190 (2020).
  28. M. Drescher, M. Salmhofer, and T. Enss, Quench dynamics of the ideal Bose polaron at zero and nonzero temperatures, Phys. Rev. A 103, 033317 (2021).
  29. R. Schmidt, J. D. Whalen, R. Ding, F. Camargo, G. Woehl, S. Yoshida, J. Burgdörfer, F. B. Dunning, E. Demler, H. R. Sadeghpour, and T. C. Killian, Theory of excitation of Rydberg polarons in an atomic quantum gas, Phys. Rev. A 97, 022707 (2018).
  30. A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose-Einstein condensation of atoms in a uniform potential, Phys. Rev. Lett. 110, 200406 (2013).
  31. C. Eigen, A. L. Gaunt, A. Suleymanzade, N. Navon, Z. Hadzibabic, and R. P. Smith, Observation of weak collapse in a Bose–Einstein condensate, Phys. Rev. X 6, 041058 (2016).
  32. N. Navon, R. P. Smith, and Z. Hadzibabic, Quantum gases in optical boxes, Nat. Phys. 17, 1334 (2021).

  33. To avoid trapping atoms outside of the optical box, we always start our measurements with a quasipure BEC in a shallow trap of depth UD≈kB×50  nK. We then raise the depth to UD≈kB×1  μK, inject energy by sinusoidally forcing the system using a magnetic-field gradient, and allow the gas to rethermalize at ab≈100a0.

  34. To minimize Fourier broadening and stay in the linear-response regime, here we use pulse durations trf={0.8–6.4}  ms and always limit the injection fractions to ≲10%.

  35. Note that in the ideal-polaron theory, the spectra are expected to evolve continuously as the bath temperature is increased, with no sharp change at Tc, and we have experimentally checked that the injection spectra do not qualitatively change just below Tc.

  36. Y. E. Shchadilova, R. Schmidt, F. Grusdt, and E. Demler, Quantum dynamics of ultracold Bose polarons, Phys. Rev. Lett. 117, 113002 (2016).
  37. J. Levinsen, L. A. Peña Ardila, S. M. Yoshida, and M. M. Parish, Quantum behavior of a heavy impurity strongly coupled to a Bose gas, Phys. Rev. Lett. 127, 033401 (2021).
  38. A. Y. Chuang, H. Q. Bui, A. Christianen, Y. Zhang, Y. Ni, D. Ahmed-Braun, C. Robens, and M. Zwierlein, Observation of a halo trimer in an ultracold Bose–Fermi mixture, Phys. Rev. X 15, 021098 (2025).
  39. C. Robens, A. Christianen, A. Y. Chuang, H. Q. Bui, Y. Zhang, R. Schmidt, and M. Zwierlein, Polaronic hybridization of atoms, dimers and trimers in a Bose-Einstein condensate, arXiv:2606.20440.
  40. B. Mukherjee, P. B. Patel, Z. Yan, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Spectral response and contact of the unitary Fermi gas, Phys. Rev. Lett. 122, 203402 (2019).

  41. We always correct Γ for residual Fourier broadening arising from our finite rf-pulse times, trf, using Γ=(Γe2−Γt2)1/2, where Γe is the raw extracted width and Γt≈2.78/trf is the width of our response function [19].

  42. D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas, Phys. Rev. A 66, 053616 (2002).
  43. M. W. Zwierlein, Z. Hadzibabic, S. Gupta, and W. Ketterle, Spectroscopic insensitivity to cold collisions in a two-state mixture of fermions, Phys. Rev. Lett. 91, 250404 (2003).

  44. Note that similar conclusions were obtained in interferometric experiments with single-component Bose gases [45]; for nλ3=0.13 (T/Tc≈7) the measurements were consistent with the two-body theory, but measurements for nλ3=0.54 (T/Tc≈3) revealed effects of three-body correlations.

  45. R. J. Fletcher, R. Lopes, J. Man, N. Navon, R. P. Smith, M. W. Zwierlein, and Z. Hadzibabic, Two- and three-body contacts in the unitary Bose gas, Science 355, 377 (2017).
  46. M. Sun, H. Zhai, and X. Cui, Visualizing the Efimov correlation in Bose polarons, Phys. Rev. Lett. 119, 013401 (2017).
  47. A. Christianen, J. I. Cirac, and R. Schmidt, Phase diagram for strong-coupling Bose polarons, SciPost Phys. 16, 067 (2024).
  48. R. Henke, J. Levinsen, M. M. Parish, J. Boronat, G. E. Astrakharchik, H. Moritz, and C. R. Cabrera, Realization of repulsive polarons in the strongly correlated regime, Phys. Rev. X (2026).
  49. R. Alhyder, G. M. Bruun, T. Pohl, M. Lemeshko, and A. G. Volosniev, Phenomenological model of decaying Bose polarons, Phys. Rev. Res. 8, L012034 (2026).
  50. T. A. Hilker, L. H. Dogra, C. Eigen, J. A. P. Glidden, R. P. Smith, and Z. Hadzibabic, First and second sound in a compressible 3D Bose fluid, Phys. Rev. Lett. 128, 223601 (2022).
  51. C. Baroni, B. Huang, I. Fritsche, E. Dobler, G. Anich, E. Kirilov, R. Grimm, M. A. Bastarrachea-Magnani, P. Massignan, and G. M. Bruun, Mediated interactions between Fermi polarons and the role of impurity quantum statistics, Nat. Phys. 20, 68 (2024).
  52. J. Etrych, S. J. Morris, S. M. Fischer, G. Martirosyan, C. J. Ho, M. Drescher, M. Salmhofer, Z. Hadzibabic, T. Enss, and C. Eigen, Research data supporting “Fate of an impurity strongly interacting with a thermal Bose gas” (2026), 10.17863/CAM.134561.
  53. M. Drescher, M. Salmhofer, and T. Enss, Theory of a resonantly interacting impurity in a Bose-Einstein condensate, Phys. Rev. Res. 2, 032011(R) (2020).
  54. R. Lopes, C. Eigen, N. Navon, D. Clément, R. P. Smith, and Z. Hadzibabic, Quantum depletion of a homogeneous Bose-Einstein condensate, Phys. Rev. Lett. 119, 190404 (2017).

Outline

Information

Phys. Rev. Lett. 137, 193405– Published 5 November, 2026
  • Received 2 September 2025
  • Revised 24 June 2026
  • Accepted 28 September 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation