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

Heterosymmetric states of rotating quantum droplets under confinement

S. Nikolaou1, G. M. Kavoulakis1,2, and M. Ögren2,3

Phys. Rev. A 114, 033301 – Published 1 September, 2026

DOI: https://doi.org/10.1103/sh9r-k9rw

Abstract

We investigate the rotational response of confined two-dimensional quantum droplets, which emerge in a binary Bose mixture that is stabilized against collapse by beyond-mean-field effects. We consider both a harmonic and an anharmonic external confining potential. We go beyond the widely employed single-order-parameter model, maintaining separate order parameters for the two components, and calculating the lowest-energy state for various values of the angular momentum. For a population-balanced quantum droplet and sufficiently strong confinement, we find that for certain values of the angular momentum the droplet is excited in a “heterosymmetric” manner, with the two components carrying different vorticities. We additionally investigate the effects of a small population imbalance in the droplet. Apart from an energy increase associated with the population difference, the imbalance also lifts the double degeneracy of the heterosymmetric states, which characterizes the Z2-symmetric balanced droplet. The heterosymmetric mode is found to be favored by the energy term that captures the beyond-mean-field effects in the mixture.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198 (1995).
  2. K. B. Davis, M.-O. Mewes, M. R. Andrews, M. J. Van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75, 3969 (1995).
  3. C. C. Bradley, C. A. Sackett, and R. G. Hulet, Bose-Einstein condensation of lithium: Observation of limited condensate number, Phys. Rev. Lett. 78, 985 (1997).
  4. C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Production of two overlapping Bose-Einstein condensates by sympathetic cooling, Phys. Rev. Lett. 78, 586 (1997).
  5. D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H.-J. Miesner, J. Stenger, and W. Ketterle, Optical confinement of a Bose-Einstein condensate, Phys. Rev. Lett. 80, 2027 (1998).
  6. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, Spin domains in ground-state Bose–Einstein condensates, Nature (London) 396, 345 (1998).
  7. T.-L. Ho and V. B. Shenoy, Binary mixtures of Bose condensates of alkali atoms, Phys. Rev. Lett. 77, 3276 (1996).
  8. H. Pu and N. P. Bigelow, Properties of two-species Bose condensates, Phys. Rev. Lett. 80, 1130 (1998).
  9. D. S. Petrov, Quantum mechanical stabilization of a collapsing Bose-Bose mixture, Phys. Rev. Lett. 115, 155302 (2015).
  10. 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).
  11. D. S. Petrov and G. E. Astrakharchik, Ultradilute low-dimensional liquids, Phys. Rev. Lett. 117, 100401 (2016).
  12. C. 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).
  13. P. Cheiney, C. R. Cabrera, J. Sanz, B. Naylor, L. Tanzi, and L. Tarruell, Bright soliton to quantum droplet transition in a mixture of Bose-Einstein condensates, Phys. Rev. Lett. 120, 135301 (2018).
  14. 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).
  15. G. Ferioli, G. Semeghini, L. Masi, G. Giusti, G. Modugno, M. Inguscio, A. Gallemí, A. Recati, and M. Fattori, Collisions of self-bound quantum droplets, Phys. Rev. Lett. 122, 090401 (2019).
  16. 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).
  17. Z. Guo, F. Jia, L. Li, Y. Ma, J. M. Hutson, X. Cui, and D. Wang, Lee-Huang-Yang effects in the ultracold mixture of Na23 and Rb87 with attractive interspecies interactions, Phys. Rev. Res. 3, 033247 (2021).
  18. 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).
  19. F. Böttcher, J.-N. Schmidt, J. Hertkorn, K. S. H. Ng, S. D. Graham, M. Guo, T. Langen, and T. Pfau, New states of matter with fine-tuned interactions: Quantum droplets and dipolar supersolids, Rep. Prog. Phys. 84, 012403 (2021).
  20. K. Mukherjee, T. A. Cardinale, L. Chergui, P. Stürmer, and S. M. Reimann, Droplets and supersolids in ultra-cold atomic quantum gases, Eur. Phys. J. Spec. Top. 232, 3417 (2023).
  21. A. J. Leggett, Superfluidity, Rev. Mod. Phys. 71, S318 (1999).
  22. Y. V. Kartashov, B. A. Malomed, L. Tarruell, and L. Torner, Three-dimensional droplets of swirling superfluids, Phys. Rev. A 98, 013612 (2018).
  23. Y. Li, Z. Chen, Z. Luo, C. Huang, H. Tan, W. Pang, and B. A. Malomed, Two-dimensional vortex quantum droplets, Phys. Rev. A 98, 063602 (2018).
  24. X. Zhang, X. Xu, Y. Zheng, Z. Chen, B. Liu, C. Huang, B. A. Malomed, and Y. Li, Semidiscrete quantum droplets and vortices, Phys. Rev. Lett. 123, 133901 (2019).
  25. M. N. Tengstrand, P. Stürmer, E. Ö. Karabulut, and S. M. Reimann, Rotating binary Bose-Einstein condensates and vortex clusters in quantum droplets, Phys. Rev. Lett. 123, 160405 (2019).
  26. R. T. Thiruvalluvar, S. Sabari, K. Porsezian, and P. Muruganandam, Vortex formation and vortex lattices in a Bose-Einstein condensate with Lee-Huang-Yang (LHY) correction, Phys. E 107, 54 (2019).
  27. P. Examilioti and G. M. Kavoulakis, Ground state and rotational properties of two-dimensional self-bound quantum droplets, J. Phys. B: At. Mol. Opt. Phys. 53, 175301 (2020).
  28. Y. V. Kartashov, B. A. Malomed, and L. Torner, Structured heterosymmetric quantum droplets, Phys. Rev. Res. 2, 033522 (2020).
  29. L. Dong and Y. V. Kartashov, Rotating multidimensional quantum droplets, Phys. Rev. Lett. 126, 244101 (2021).
  30. M. Caldara and F. Ancilotto, Vortices in quantum droplets of heteronuclear Bose mixtures, Phys. Rev. A 105, 063328 (2022).
  31. T. A. Yoğurt, U. Tanyeri, A. Keleş, and M. Ö. Oktel, Vortex lattices in strongly confined quantum droplets, Phys. Rev. A 108, 033315 (2023).
  32. S. Nikolaou, G. M. Kavoulakis, and M. Ögren, Rotating quantum droplets confined in a harmonic potential, Phys. Rev. A 108, 053309 (2023).
  33. Q. Gu and X. Cui, Self-bound vortex lattice in a rapidly rotating quantum droplet, Phys. Rev. A 108, 063302 (2023).
  34. S. Nikolaou, G. M. Kavoulakis, and M. Ögren, Rotating quantum droplets confined in an anharmonic potential, Phys. Rev. A 109, 043304 (2024).
  35. S.-C. Cheng, Y.-W. Wang, and W.-H. Kuan, Dynamics of rapidly rotating Bose–Einstein quantum droplets, Phys. Scr. 99, 065410 (2024).
  36. S. Nikolaou, G. M. Kavoulakis, and M. Ögren, Rapidly rotating quantum droplets confined in a harmonic potential, Phys. Rev. A 110, 043302 (2024).
  37. S. B. Prasad, T. P. Billam, and N. G. Parker, Axially confined binary quantum droplets: Ground states and central vortices, arXiv:2507.21805.
  38. I. Poparić, L. Vranješ Markić, and J. Boronat, Empty and filled vortices in squeezed K39 Bose-Bose liquid drops, Phys. Rev. A 112, 053317 (2025).
  39. M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, Vortices in a Bose-Einstein condensate, Phys. Rev. Lett. 83, 2498 (1999).
  40. K. Kasamatsu, M. Tsubota, and M. Ueda, Vortex molecules in coherently coupled two-component Bose-Einstein condensates, Phys. Rev. Lett. 93, 250406 (2004).
  41. K. Kasamatsu, M. Tsubota, and M. Ueda, Spin textures in rotating two-component Bose-Einstein condensates, Phys. Rev. A 71, 043611 (2005).
  42. S. Bargi, J. Christensson, G. M. Kavoulakis, and S. M. Reimann, Mixtures of Bose gases under rotation, Phys. Rev. Lett. 98, 130403 (2007).
  43. J. Christensson, S. Bargi, K. Kärkkäinen, Y. Yu, G. M. Kavoulakis, M. Manninen, and S. M. Reimann, Rotational properties of a mixture of two Bose gases, New J. Phys. 10, 033029 (2008).
  44. S.-J. Yang, Q.-S. Wu, S.-N. Zhang, and S. Feng, Giant vortex and skyrmion in a rotating two-species Bose-Einstein condensate, Phys. Rev. A 77, 033621 (2008).
  45. P. Mason and A. Aftalion, Classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate, Phys. Rev. A 84, 033611 (2011).
  46. E. Ö. Karabulut, F. Malet, G. M. Kavoulakis, and S. M. Reimann, Phase diagram of a rapidly rotating two-component Bose gas, Phys. Rev. A 87, 043609 (2013).
  47. D. M. Larsen, Binary mixtures of dilute Bose gases with repulsive interactions at low temperature, Ann. Phys. (NY) 24, 89 (1963).
  48. P. Ao and S. T. Chui, Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases, Phys. Rev. A 58, 4836 (1998).
  49. P. Kuopanportti, J. A. M. Huhtamäki, and M. Möttönen, Exotic vortex lattices in two-species Bose-Einstein condensates, Phys. Rev. A 85, 043613 (2012).
  50. D. S. Petrov and G. V. Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Phys. Rev. A 64, 012706 (2001).
  51. Y. Sekino, H. Tajima, and S. Uchino, Spin conductivity spectrum and spin superfluidity in a binary Bose mixture, Phys. Rev. Res. 5, 023058 (2023).
  52. Y. Li, Z. Luo, Y. Liu, Z. Chen, C. Huang, S. Fu, H. Tan, and B. A. Malomed, Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates, New J. Phys. 19, 113043 (2017).
  53. S. R. Otajonov, E. N. Tsoy, and F. Kh. Abdullaev, Variational approximation for two-dimensional quantum droplets, Phys. Rev. E 102, 062217 (2020).
  54. S. R. Otajonov, E. N. Tsoy, and F. Kh. Abdullaev, Modulational instability and quantum droplets in a two-dimensional Bose-Einstein condensate, Phys. Rev. A 106, 033309 (2022).
  55. M. Gulliksson and M. Ögren, Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions, J. Phys. A: Math. Theor. 54, 275304 (2021).
  56. In Refs.  [32, 36], this value was erroneously reported to be 98.7. The value presented in this work is the corrected value for the transition.
  57. G. M. Kavoulakis, B. Mottelson, and C. J. Pethick, Weakly interacting Bose-Einstein condensates under rotation, Phys. Rev. A 62, 063605 (2000).
  58. T. F. Scott, R. J. Ballagh, and K. Burnett, Formation of fundamental structures in Bose - Einstein condensates, J. Phys. B: At. Mol. Opt. Phys. 31, L329 (1998).
  59. A. D. Jackson, G. M. Kavoulakis, and C. J. Pethick, Solitary waves in clouds of Bose-Einstein condensed atoms, Phys. Rev. A 58, 2417 (1998).
  60. P. B. Walczak and J. R. Anglin, Exact Bogoliubov–de Gennes solutions for gray-soliton backgrounds, Phys. Rev. A 84, 013611 (2011).
  61. A. J. Beekman, L. Rademaker, and J. van Wezel, An introduction to spontaneous symmetry breaking, SciPost Phys. Lect. Notes 11 (2019).
  62. V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Fast rotation of a Bose-Einstein condensate, Phys. Rev. Lett. 92, 050403 (2004).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation