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  • Letter
  • Open Access

Unified theory of attractive and repulsive polarons in a one-dimensional Bose gas

Nikolay Yegovtsev1,*, T. Alper Yoğurt2,†, Matthew T. Eiles2,3, and Victor Gurarie4

  • *Contact author: nikolay.yegovtsev@colorado.edu
  • †Contact author: ayogurt@pks.mpg.de
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Phys. Rev. A 113, L041306 – Published 21 April, 2026

DOI: https://doi.org/10.1103/4tcn-t6y2

Abstract

We present a unified description of attractive and repulsive polarons, formed in a one-dimensional Bose gas hosting an impurity particle, by obtaining all ground- and excited-state solutions to the Gross-Pitaevskii equation. Modeling the impurity with an attractive square-well potential, we characterize the excited-state energy branches as a function of interaction strength. As the impurity-bath coupling increases, the excited states change from distinct soliton configurations to hybridized soliton-polaron states, eventually crossing over from repulsive to attractive polarons at unitarity. We identify a universal regime near this crossover where the polaron properties are accurately characterized by the zero-energy scattering length.

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  56. Note that while we fixed the behavior of the solution at y→∞ of the tail in (4), the solutions inside the impurity potential still possess a Z2 symmetry, so when we numerically match (10) with (4) or (11) with (4) and their derivatives, we also need to consider the case when ϕs→−ϕs and ϕp→−ϕp to obtain all possible solutions.
  57. The applicability condition of these expansions for an arbitrary finite-ranged potential can be derived by demanding that the contribution to the energy from the interior of the well is much smaller than the contribution from the tail of the polaron, and reads rc/a≪1. Once a∼rc, we start to see other details of the potential that are not universal.

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Phys. Rev. A 113, L041306– Published 21 April, 2026
  • Received 1 October 2025
  • Revised 2 January 2026
  • Accepted 30 March 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 Max Planck Society.

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