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  • Letter
  • Open Access

Phenomenological model of decaying Bose polarons

R. Alhyder1,2,*, G. M. Bruun2, T. Pohl2,3, M. Lemeshko1, and A. G. Volosniev2,1

  • *Contact author: ragheed.alhyder@ist.ac.at

Phys. Rev. Research 8, L012034 – Published 6 February, 2026

DOI: https://doi.org/10.1103/16dk-5dgx

Abstract

Cold atom experiments show that a mobile impurity particle immersed in a weakly interacting Bose-Einstein condensate forms a well-defined quasiparticle (Bose polaron) for weak to moderate impurity-boson interaction strengths, whereas a significant line broadening is consistently observed for strong interactions. Motivated by this, we introduce a phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson, since they have the largest overlap with the uncorrelated states to which the most common experimental probes couple. These experimentally relevant states can, however, decay to lower energy states characterized by correlations involving multiple bosons, and we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. We first motivate this approach by comparing to a more elaborate theory that includes correlations with up to two bosons. Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the nonequilibrium properties of the Bose polaron. Our work offers an intuitive framework for analyzing experimental data and highlights the importance of understanding the complicated problem of the Bose polaron decay in a many-body setting.

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References (73)

  1. 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).
  2. S. Nascimbène, N. Navon, K. J. Jiang, L. Tarruell, M. Teichmann, J. McKeever, F. Chevy, and C. Salomon, Collective oscillations of an imbalanced Fermi gas: Axial compression modes and polaron effective mass, Phys. Rev. Lett. 103, 170402 (2009).
  3. 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).
  4. M. Koschorreck, D. Pertot, E. Vogt, B. Frohlich, M. Feld, and M. Köhl, Attractive and repulsive Fermi polarons in two dimensions, Nature (London) 485, 619 (2012).
  5. F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Amico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, Repulsive Fermi polarons in a resonant mixture of ultracold Li6 atoms, Phys. Rev. Lett. 118, 083602 (2017).
  6. N. Darkwah Oppong, L. Riegger, O. Bettermann, M. Höfer, J. Levinsen, M. M. Parish, I. Bloch, and S. Fölling, Observation of coherent multiorbital polarons in a two-dimensional Fermi gas, Phys. Rev. Lett. 122, 193604 (2019).
  7. G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Observation of a smooth polaron-molecule transition in a degenerate Fermi gas, Phys. Rev. X 10, 041019 (2020).
  8. I. Fritsche, C. Baroni, E. Dobler, E. Kirilov, B. Huang, R. Grimm, G. M. Bruun, and P. Massignan, Stability and breakdown of Fermi polarons in a strongly interacting Fermi-Bose mixture, Phys. Rev. A 103, 053314 (2021).
  9. T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauß, S. Hild, D. Bellem, U. Schollwöck, T. Giamarchi, C. Gross, I. Bloch, and S. Kuhr, Quantum dynamics of a mobile spin impurity, Nat. Phys. 9, 235 (2013).
  10. M.-G. Hu, M. J. 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).
  11. N. B. Jorgensen, 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).
  12. Z. Z. Yan, Y. Ni, C. Robens, and M. W. Zwierlein, Bose polarons near quantum criticality, Science 368, 190 (2020).
  13. 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).
  14. P. Massignan, M. Zaccanti, and G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases, Rep. Prog. Phys. 77, 034401 (2014).
  15. M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, Decoherence of impurities in a Fermi sea of ultracold atoms, Phys. Rev. Lett. 115, 135302 (2015).
  16. M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, Ultrafast many-body interferometry of impurities coupled to a Fermi sea, Science 354, 96 (2016).
  17. 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).
  18. 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).
  19. A. M. Morgen, S. S. Balling, K. K. Nielsen, T. Pohl, G. M. Bruun, and J. J. Arlt, Quantum beat spectroscopy of repulsive Bose polarons, Phys. Rev. Res. 7, L022002 (2025).
  20. 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).
  21. 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).
  22. W. Casteels, J. Tempere, and J. T. Devreese, Polaronic properties of an impurity in a Bose-Einstein condensate in reduced dimensions, Phys. Rev. A 86, 043614 (2012).
  23. F. Grusdt and M. Fleischhauer, Tunable polarons of slow-light polaritons in a two-dimensional Bose-Einstein condensate, Phys. Rev. Lett. 116, 053602 (2016).
  24. O. Hryhorchak, G. Panochko, and V. Pastukhov, Mean-field study of repulsive 2D and 3D Bose polarons, J. Phys. B: At. Mol. Opt. Phys. 53, 205302 (2020).
  25. L. A. P. Ardila, G. E. Astrakharchik, and S. Giorgini, Strong coupling Bose polarons in a two-dimensional gas, Phys. Rev. Res. 2, 023405 (2020).
  26. F. Isaule, I. Morera, P. Massignan, and B. Juliá-Díaz, Renormalization-group study of Bose polarons, Phys. Rev. A 104, 023317 (2021).
  27. L. F. Cárdenas-Castillo and A. Camacho-Guardian, Strongly interacting Bose polarons in two-dimensional atomic gases and quantum fluids of polaritons, Atoms 11, 3 (2022).
  28. R. Alhyder and G. M. Bruun, Mobile impurity probing a two-dimensional superfluid phase transition, Phys. Rev. A 105, 063303 (2022).
  29. Y. Nakano, M. M. Parish, and J. Levinsen, Variational approach to the two-dimensional Bose polaron, Phys. Rev. A 109, 013325 (2024).
  30. P. Massignan, R. Schmidt, G. E. Astrakharchik, A. Imamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, Polarons in atomic gases and two-dimensional semiconductors, arXiv:2501.09618.
  31. E. Braaten and H.-W. Hammer, Universality in few-body systems with large scattering length, Phys. Rep. 428, 259 (2006).
  32. S. P. Rath and R. Schmidt, Field-theoretical study of the Bose polaron, Phys. Rev. A 88, 053632 (2013).
  33. G. M. Bruun and C. J. Pethick, Effective theory of Feshbach resonances and many-body properties of Fermi gases, Phys. Rev. Lett. 92, 140404 (2004).
  34. A. O. Gogolin, C. Mora, and R. Egger, Analytical solution of the bosonic three-body problem, Phys. Rev. Lett. 100, 140404 (2008).
  35. 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).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/16dk-5dgx for details, which includes Refs. [17, 39, 51].
  37. W. Li and S. Das Sarma, Variational study of polarons in Bose-Einstein condensates, Phys. Rev. A 90, 013618 (2014).
  38. J. Levinsen, M. M. Parish, and G. M. Bruun, Impurity in a Bose-Einstein condensate and the Efimov effect, Phys. Rev. Lett. 115, 125302 (2015).
  39. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003).
  40. Y. Saad, Numerical Methods for Large Eigenvalue Problems (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2011).
  41. J. Liesen and Z. Strakos, Krylov Subspace Methods Principles and Analysis, Numerical Mathematics and Scientific Computation (Oxford University Press, Oxford, 2012).
  42. P. Nandy, A. S. Matsoukas-Roubeas, P. Martínez-Azcona, A. Dymarsky, and A. del Campo, Quantum dynamics in Krylov space: Methods and applications, Phys. Rep. 1125–1128, 1 (2025).
  43. 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).
  44. J. Levinsen, L. A. P. 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).
  45. A. Christianen, J. I. Cirac, and R. Schmidt, Phase diagram for strong-coupling Bose polarons, SciPost Phys. 16, 067 (2024).
  46. R. Schmidt and T. Enss, Self-stabilized Bose polarons, SciPost Phys. 13, 054 (2022).
  47. K. Yamamoto, M. Nakagawa, K. Adachi, K. Takasan, M. Ueda, and N. Kawakami, Theory of non-Hermitian fermionic superfluidity with a complex-valued interaction, Phys. Rev. Lett. 123, 123601 (2019).
  48. I. Bouchoule, B. Doyon, and J. Dubail, The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas, SciPost Phys. 9, 044 (2020).
  49. K. Yamamoto, M. Nakagawa, N. Tsuji, M. Ueda, and N. Kawakami, Collective excitations and nonequilibrium phase transition in dissipative fermionic superfluids, Phys. Rev. Lett. 127, 055301 (2021).
  50. I. Bouchoule and J. Dubail, Breakdown of Tan's relation in lossy one-dimensional Bose gases, Phys. Rev. Lett. 126, 160603 (2021).
  51. C. Wang, C. Liu, and Z.-Y. Shi, Complex contact interaction for systems with short-range two-body losses, Phys. Rev. Lett. 129, 203401 (2022).
  52. M. Drescher, M. Salmhofer, and T. Enss, Bosonic functional determinant approach and its application to polaron spectra, Phys. Rev. A 110, 063303 (2024).
  53. For each interaction value (1/kna), we analyze the zero-momentum impurity spectral function A(ω) on the relevant branch and fit a simple parametric line shape to a local window around the peak. When the branch is well described by a Lorentzian (attractive branch for a<0; repulsive branch for a>0), we fit L(ω)=AΓ2(ω−ω0)2+Γ2+Cand define the peak position and width as Ep≡ω0,Γpol≡Γ (HWHM). For the attractive branch at a>0, consistent with Ref. [20], we use a Gaussian profile G(ω)=Ae−(ω−ω0)2/(2σ2)+Cand report Ep≡ω0,Γpol≡σ. Fits are performed with nonlinear least squares, and initial guesses are set by the local maximum of A(ω).
  54. F. Scazza, M. Zaccanti, P. Massignan, M. M. Parish, and J. Levinsen, Repulsive Fermi and Bose polarons in quantum gases, Atoms 10, 55 (2022).
  55. J. Etrych, S. J. Morris, S. M. Fischer, G. Martirosyan, C. J. Ho, M. Drescher, M. Salmhofer, Z. Hadzibabic, T. Enss, and C. Eigen, Fate of an impurity strongly interacting with a thermal Bose gas, arXiv:2508.06493.
  56. J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, and T. Busch, Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas, Phys. Rev. A 84, 063632 (2011).
  57. M. Knap, A. Shashi, Y. Nishida, A. Imambekov, D. A. Abanin, and E. Demler, Time-dependent impurity in ultracold fermions: Orthogonality catastrophe and beyond, Phys. Rev. X 2, 041020 (2012).
  58. R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Universal many-body response of heavy impurities coupled to a Fermi sea: A review of recent progress, Rep. Prog. Phys. 81, 024401 (2018).
  59. It is easy to understand the time dynamics of A(t) for a noninteracting Bose gas (aB=0) using the following ansatz for A(t), which fits the numerical data well [36]: A(t)=Ze−iω1t+(1−Z)e−iω2t, (6)where |Z|=8πna(12πna−ω)−1 is the residue and ω1 (ω2) is the solution of Eq. (4) with Im(ω)<0; in the limit Γ=0, ω1 (ω2) is the standard attractive (repulsive) polaron [12]. The coefficients B read Bk(t)=ω1Zfk(ω1)(2π)3/2(ω1−2εk)+ω2(1−Z)fk(ω2)(2π)3/2(ω2−2εk),(7)where fk(ω)=e−iωt−e−2iεkt. The first term in fk is due to the pole, and the second one is due to the bosonic continuum. The latter contribution describes the particles that move away from the impurity and do not interact with it at later times. For an interacting Bose gas, this would correspond to sound waves emitted by the impurity (see, e.g., Ref. [73] for a further visualization of this process).
  60. Note that our phenomenological model agrees with the variational ansatz in Eq. (2) regarding the dynamics when Γ=0.01 and γ=0.1.
  61. For example, for the data shown in Fig. 3, a weighted goodness-of-fit analysis yields a reduced χ2=3.15 and a Pearson correlation coefficient of 0.996, confirming that the theoretical model reproduces the experimental trend accurately. The somewhat elevated χ2 value primarily reflects the very small experimental uncertainties (≈1%), which do not include systematic effects such as magnetic field jittering and amplitude calibration. When a realistic systematic uncertainty of a few percent is taken into account, the reduced χ2 approaches unity, indicating statistical consistency.
  62. Note that we performed a trap averaging for Ref. [19] (see Ref. [36]) and concluded that it has a weak effect on the time dynamics as the decoherence dynamics mainly happens at shorter timescales. It is known, however, that the presence of the trap broadens the polaron peak in the spectroscopic experiments [11].
  63. D. Dzsotjan, R. Schmidt, and M. Fleischhauer, Dynamical variational approach to Bose polarons at finite temperatures, Phys. Rev. Lett. 124, 223401 (2020).
  64. 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).
  65. V. Pastukhov, Polaron in dilute 2D Bose gas at low temperatures, J. Phys. B: At. Mol. Opt. Phys. 51, 155203 (2018).
  66. B. Field, J. Levinsen, and M. M. Parish, Fate of the Bose polaron at finite temperature, Phys. Rev. A 101, 013623 (2020).
  67. F. Isaule and I. Morera, Weakly-interacting Bose–Bose mixtures from the functional renormalisation group, Condens. Matter 7, 9 (2022).
  68. F. Grusdt, A. Shashi, D. Abanin, and E. Demler, Bloch oscillations of bosonic lattice polarons, Phys. Rev. A 90, 063610 (2014).
  69. V. E. Colussi, F. Caleffi, C. Menotti, and A. Recati, Lattice polarons across the superfluid to Mott insulator transition, Phys. Rev. Lett. 130, 173002 (2023).
  70. M. Santiago-García, S. G. Castillo-López, and A. Camacho-Guardian, Lattice polaron in a Bose–Einstein condensate of hard-core bosons, New J. Phys. 26, 063015 (2024).
  71. R. Alhyder, V. E. Colussi, M. Čufar, J. Brand, A. Recati, and G. M. Bruun, Lattice Bose polarons at strong coupling and quantum criticality, SciPost Phys. 19, 002 (2025).
  72. R. Alhyder, Phenomenological model of decaying Bose polarons [Dataset], Zenodo (2025), doi:10.5281/zenodo.16085401.
  73. O. Marchukov and A. Volosniev, Shape of a sound wave in a weakly-perturbed Bose gas, SciPost Phys. 10, 025 (2021).

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