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Heterosymmetric states of rotating quantum droplets under confinement
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 -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.
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References (62)
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- T.-L. Ho and V. B. Shenoy, Binary mixtures of Bose condensates of alkali atoms, Phys. Rev. Lett. 77, 3276 (1996).
- H. Pu and N. P. Bigelow, Properties of two-species Bose condensates, Phys. Rev. Lett. 80, 1130 (1998).
- D. S. Petrov, Quantum mechanical stabilization of a collapsing Bose-Bose mixture, Phys. Rev. Lett. 115, 155302 (2015).
- 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).
- D. S. Petrov and G. E. Astrakharchik, Ultradilute low-dimensional liquids, Phys. Rev. Lett. 117, 100401 (2016).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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 and with attractive interspecies interactions, Phys. Rev. Res. 3, 033247 (2021).
- 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).
- 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).
- 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).
- A. J. Leggett, Superfluidity, Rev. Mod. Phys. 71, S318 (1999).
- Y. V. Kartashov, B. A. Malomed, L. Tarruell, and L. Torner, Three-dimensional droplets of swirling superfluids, Phys. Rev. A 98, 013612 (2018).
- 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).
- 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).
- 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).
- 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).
- 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).
- Y. V. Kartashov, B. A. Malomed, and L. Torner, Structured heterosymmetric quantum droplets, Phys. Rev. Res. 2, 033522 (2020).
- L. Dong and Y. V. Kartashov, Rotating multidimensional quantum droplets, Phys. Rev. Lett. 126, 244101 (2021).
- M. Caldara and F. Ancilotto, Vortices in quantum droplets of heteronuclear Bose mixtures, Phys. Rev. A 105, 063328 (2022).
- T. A. Yoğurt, U. Tanyeri, A. Keleş, and M. Ö. Oktel, Vortex lattices in strongly confined quantum droplets, Phys. Rev. A 108, 033315 (2023).
- S. Nikolaou, G. M. Kavoulakis, and M. Ögren, Rotating quantum droplets confined in a harmonic potential, Phys. Rev. A 108, 053309 (2023).
- Q. Gu and X. Cui, Self-bound vortex lattice in a rapidly rotating quantum droplet, Phys. Rev. A 108, 063302 (2023).
- S. Nikolaou, G. M. Kavoulakis, and M. Ögren, Rotating quantum droplets confined in an anharmonic potential, Phys. Rev. A 109, 043304 (2024).
- S.-C. Cheng, Y.-W. Wang, and W.-H. Kuan, Dynamics of rapidly rotating Bose–Einstein quantum droplets, Phys. Scr. 99, 065410 (2024).
- S. Nikolaou, G. M. Kavoulakis, and M. Ögren, Rapidly rotating quantum droplets confined in a harmonic potential, Phys. Rev. A 110, 043302 (2024).
- S. B. Prasad, T. P. Billam, and N. G. Parker, Axially confined binary quantum droplets: Ground states and central vortices, arXiv:2507.21805.
- I. Poparić, L. Vranješ Markić, and J. Boronat, Empty and filled vortices in squeezed Bose-Bose liquid drops, Phys. Rev. A 112, 053317 (2025).
- 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).
- K. Kasamatsu, M. Tsubota, and M. Ueda, Vortex molecules in coherently coupled two-component Bose-Einstein condensates, Phys. Rev. Lett. 93, 250406 (2004).
- K. Kasamatsu, M. Tsubota, and M. Ueda, Spin textures in rotating two-component Bose-Einstein condensates, Phys. Rev. A 71, 043611 (2005).
- S. Bargi, J. Christensson, G. M. Kavoulakis, and S. M. Reimann, Mixtures of Bose gases under rotation, Phys. Rev. Lett. 98, 130403 (2007).
- 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).
- 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).
- 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).
- 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).
- D. M. Larsen, Binary mixtures of dilute Bose gases with repulsive interactions at low temperature, Ann. Phys. (NY) 24, 89 (1963).
- P. Ao and S. T. Chui, Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases, Phys. Rev. A 58, 4836 (1998).
- P. Kuopanportti, J. A. M. Huhtamäki, and M. Möttönen, Exotic vortex lattices in two-species Bose-Einstein condensates, Phys. Rev. A 85, 043613 (2012).
- D. S. Petrov and G. V. Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Phys. Rev. A 64, 012706 (2001).
- Y. Sekino, H. Tajima, and S. Uchino, Spin conductivity spectrum and spin superfluidity in a binary Bose mixture, Phys. Rev. Res. 5, 023058 (2023).
- 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).
- S. R. Otajonov, E. N. Tsoy, and F. Kh. Abdullaev, Variational approximation for two-dimensional quantum droplets, Phys. Rev. E 102, 062217 (2020).
- 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).
- M. Gulliksson and M. Ögren, Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions, J. Phys. A: Math. Theor. 54, 275304 (2021).
- 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.
- G. M. Kavoulakis, B. Mottelson, and C. J. Pethick, Weakly interacting Bose-Einstein condensates under rotation, Phys. Rev. A 62, 063605 (2000).
- 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).
- 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).
- P. B. Walczak and J. R. Anglin, Exact Bogoliubov–de Gennes solutions for gray-soliton backgrounds, Phys. Rev. A 84, 013611 (2011).
- A. J. Beekman, L. Rademaker, and J. van Wezel, An introduction to spontaneous symmetry breaking, SciPost Phys. Lect. Notes 11 (2019).
- V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Fast rotation of a Bose-Einstein condensate, Phys. Rev. Lett. 92, 050403 (2004).