- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

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

Quantum droplets in one-dimensional mixtures of quasi–Bose-Einstein condensates and Tonks-Girardeau gases

Wen-Bin He1,2,*, Su Yi3,†, and Thomas Busch4,‡

  • *Contact author: wenbin.he@oist.jp
  • †Contact author: yisu@nbu.edu.cn
  • ‡Contact author: thomas.busch@oist.jp
PDF

Phys. Rev. A 114, 023327 – Published 31 August, 2026

DOI: https://doi.org/10.1103/f6p4-p6b9

Abstract

While binary atomic Bose-Einstein condensates (BECs) are typically prone to collapse under strong interspecies attraction, it has been shown that higher-order fluctuation corrections, known as Lee-Huang-Yang corrections, can stabilize the mixture. In this work we demonstrate an alternative stabilization mechanism based on kinetic energy. Specifically, we consider a one-dimensional mixture of a quasi-BEC and a Tonks-Girardeau (TG) gas and show that the kinetic energy of the TG component can counteract the interspecies attraction, thereby preventing collapse. This balance leads to the formation of a self-bound quantum droplet, which exhibits two distinct regimes: a low-density droplet and a high-density droplet. We argue that these regimes are smoothly connected by a crossover. Furthermore, an analysis of the derivatives of the ground-state energy and bulk modulus reveals that the transition from a miscible mixture to the droplet phase is of third order. Our findings extend the theoretical understanding of quantum droplets in low-dimensional quantum gases, and the proposed system may be experimentally accessible within current ultracold-atom platforms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (43)

  1. D. S. Petrov, Quantum mechanical stabilization of a collapsing Bose-Bose mixture, Phys. Rev. Lett. 115, 155302 (2015).
  2. T. D. Lee, K. Huang, and C. N. Yang, Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties, Phys. Rev. 106, 1135 (1957).
  3. H. Hu and X.-J. Liu, Consistent theory of self-bound quantum droplets with bosonic pairing, Phys. Rev. Lett. 125, 195302 (2020).
  4. M. Tylutki, G. E. Astrakharchik, B. A. Malomed, and D. S. Petrov, Collective excitations of a one-dimensional quantum droplet, Phys. Rev. A 101, 051601(R) (2020).
  5. H. Hu and X.-J. Liu, Collective excitations of a spherical ultradilute quantum droplet, Phys. Rev. A 102, 053303 (2020).
  6. G. Spada, S. Pilati, and S. Giorgini, Attractive solution of binary Bose mixtures: Liquid-vapor coexistence and critical point, Phys. Rev. Lett. 131, 173404 (2023).
  7. L. He, H. Li, W. Yi, and Z.-Q. Yu, Quantum criticality of liquid-gas transition in a binary Bose mixture, Phys. Rev. Lett. 130, 193001 (2023).
  8. D. Rakshit, T. Karpiuk, P. Zin, M. Brewczyk, M. Lewenstein, and M. Gajda, Self-bound Bose–Fermi liquids in lower dimensions, New J. Phys. 21, 073027 (2019).
  9. I. Ferrier-Barbut, H. Kadau, M. Schmitt, M. Wenzel, and T. Pfau, Observation of quantum droplets in a strongly dipolar Bose gas, Phys. Rev. Lett. 116, 215301 (2016).
  10. G. Natale, R. M. W. van Bijnen, A. Patscheider, D. Petter, M. J. Mark, L. Chomaz, and F. Ferlaino, Excitation spectrum of a trapped dipolar supersolid and its experimental evidence, Phys. Rev. Lett. 123, 050402 (2019).
  11. R. N. Bisset, L. A. Peña Ardila, and L. Santos, Quantum droplets of dipolar mixtures, Phys. Rev. Lett. 126, 025301 (2021).
  12. L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe-Tolra, B. L. Lev, and T. Pfau, Dipolar physics: A review of experiments with magnetic quantum gases, Rep. Prog. Phys. 86, 026401 (2023).
  13. A. Yang, G. Li, X. Jiang, Z. Fan, Z. Chen, B. Liu, and Y. Li, Two-dimensional quantum droplets in binary dipolar Bose-Bose mixture, Photonics 10, 405 (2023).
  14. Z.-H. Luo, W. Pang, B. Liu, Y.-Y. Li, and B. A. Malomed, A new form of liquid matter: Quantum droplets, Front. Phys. 16, 32201 (2021).
  15. C. R. Cabrera, L. Tanzi, J. Sanz, B. Naylor, P. Thomas, P. Cheiney, and L. Tarruell, Quantum liquid droplets in a mixture of Bose-Einstein condensates, Science 359, 301 (2018).
  16. G. Semeghini, G. Ferioli, L. Masi, C. Mazzinghi, L. Wolswijk, F. Minardi, M. Modugno, G. Modugno, M. Inguscio, and M. Fattori, Self-bound quantum droplets of atomic mixtures in free space, Phys. Rev. Lett. 120, 235301 (2018).
  17. C. D'Errico, A. Burchianti, M. Prevedelli, L. Salasnich, F. Ancilotto, M. Modugno, F. Minardi, and C. Fort, Observation of quantum droplets in a heteronuclear bosonic mixture, Phys. Rev. Res. 1, 033155 (2019).
  18. M. Ota and G. E. Astrakharchik, Beyond Lee-Huang-Yang description of self-bound Bose mixtures, SciPost Phys. 9, 020 (2020).
  19. T. G. Skov, M. G. Skou, N. B. Jørgensen, and J. J. Arlt, Observation of a Lee-Huang-Yang fluid, Phys. Rev. Lett. 126, 230404 (2021).
  20. A. Boudjemâa and K. Abbas, Quantum droplets in one-dimensional Bose-Bose mixtures: Beyond the Lee-Huang-Yang description, New J. Phys. 25, 093052 (2023).
  21. T. Kinoshita, T. Wenger, and D. S. Weiss, Observation of a one-dimensional Tonks-Girardeau gas, Science 305, 1125 (2004).
  22. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. W. Hänsch, and I. Bloch, Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature (London) 429, 277 (2004).
  23. T. Keller, T. Fogarty, and T. Busch, Self-pinning transition of a Tonks-Girardeau gas in a Bose-Einstein condensate, Phys. Rev. Lett. 128, 053401 (2022).
  24. M. Girardeau, Relationship between systems of impenetrable bosons and fermions in one dimension, J. Math. Phys. 1, 516 (1960).
  25. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  26. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
  27. T. Karpiuk, M. Brewczyk, S. Ospelkaus-Schwarzer, K. Bongs, M. Gajda, and K. Rzążewski, Soliton trains in Bose-Fermi mixtures, Phys. Rev. Lett. 93, 100401 (2004).
  28. G. Filatrella and B. A. Malomed, Interfaces between Bose–Einstein and Tonks–Girardeau atomic gases, New J. Phys. 18, 025005 (2016).
  29. F. Gómez-Lozada, H. Hiyane, T. Busch, and T. Fogarty, Bose–Fermi N-polaron state emergence from correlation-mediated blocking of phase separation, Phys. Rev. Res. 7, 023053 (2025).
  30. D. Breu, E. V. Marcos, M. Will, and M. Fleischhauer, Impurities in a trapped one-dimensional Bose gas of arbitrary interaction strength: Localization-delocalization transition and absence of self-localization, Phys. Rev. A 111, 023326 (2025).
  31. G. E. Astrakharchik and B. A. Malomed, Dynamics of one-dimensional quantum droplets, Phys. Rev. A 98, 013631 (2018).
  32. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation and Superfluidity (Oxford University Press, Oxford, 2016), Vol. 164.
  33. R. Fletcher, Practical Methods of Optimization (Wiley, New York, 2000).
  34. Y.-Z. Jiang, Y.-Y. Chen, and X.-W. Guan, Understanding many-body physics in one dimension from the Lieb-Liniger model, Chin. Phys. B 24, 050311 (2015).
  35. G. Spada, S. Pilati, and S. Giorgini, Quantum droplets in two-dimensional Bose mixtures at finite temperature, Phys. Rev. Lett. 133, 083401 (2024).
  36. D. S. Petrov and G. E. Astrakharchik, Ultradilute low-dimensional liquids, Phys. Rev. Lett. 117, 100401 (2016).
  37. D. J. Gross and E. Witten, Possible third-order phase transition in the large-N lattice gauge theory, Phys. Rev. D 21, 446 (1980).
  38. T. Eisele, On a third-order phase transition, Commun. Math. Phys. 90, 125 (1983).
  39. S. N. Majumdar and G. Schehr, Top eigenvalue of a random matrix: Large deviations and third order phase transition, J. Stat. Mech. (2014) P01012.
  40. F. D. Cunden, P. Facchi, M. Ligabò, and P. Vivo, Universality of the third-order phase transition in the constrained Coulomb gas, J. Stat. Mech. (2017) 053303.
  41. Z. Zhao, G. Li, Z. Chen, H.-B. Luo, B. Liu, B. A. Malomed, and Y. Li, Bulk modulus of three-dimensional quantum droplets, Phys. Rev. A 113, 043315 (2026).
  42. X. Du, Y. Fei, X.-L. Chen, and Y. Zhang, Ground-state properties and Bogoliubov modes of a harmonically trapped one-dimensional quantum droplet, Phys. Rev. A 108, 033312 (2023).
  43. K. Patel, G. Cai, H. Ando, and C. Chin, Sound propagation in a Bose-Fermi mixture: From weak to strong interactions, Phys. Rev. Lett. 131, 083003 (2023).

Outline

Information

Phys. Rev. A 114, 023327– Published 31 August, 2026
  • Received 27 August 2025
  • Revised 27 July 2026
  • Accepted 30 July 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