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Shift of the Bose-Einstein condensation transition in the presence of a second atomic species

P. M. Gaspar1,*, V. S. Bagnato1,2, and P. C. M. Castilho1,†

  • *Present address: Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, CNRS UMR 7538, 99 av. J.-B. Clément, F-93430 Villetaneuse, France.
  • †Contact author: patricia.castilho@ifsc.usp.br
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APS Open Sci. 1, 000060 – Published 13 July, 2026

DOI: https://doi.org/10.1103/3gr1-mcmm

Abstract

Atomic interactions play an important role in the properties of ultracold atomic gases. In single-component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain semianalytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species considering the mean-field framework. We treat differently the cases in which the second species is above or below its own critical temperature and apply the obtained relations to the case of a Na23−K39 bosonic mixture that can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures.

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References (31)

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APS Open Sci. 1, 000060– Published 13 July, 2026
Vol. 1
  • Received 16 February 2026
  • Accepted 24 June 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.

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