Dipolar Bose gas with SU(3) spin−orbit coupling held under a toroidal trap

Fang Wang, Jia Liu, Si-Lin Chen, Lin Wen, Xue-Ying Yang, Xiao-Fei Zhang

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Front. Phys. ›› 2025, Vol. 20 ›› Issue (2) : 022202. DOI: 10.15302/frontphys.2025.022202
RESEARCH ARTICLE

Dipolar Bose gas with SU(3) spin−orbit coupling held under a toroidal trap

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Abstract

We consider a dipolar spin-1 Bose gas with SU(3) spin−orbit coupling trapped in a two-dimensional toroidal trap. Due to the combined effects of SU(3) spin−orbit coupling, dipole−dipole interaction, and spin−exchange interaction, the system exhibits a rich variety of ground-state phases and topological defects, including modified stripe, azimuthal distributed petal and triangular lattice, double-quantum spin vortices, and so on. In particular, by studying the spin texture of such a system, it is found that the formation and transformation between meron and skyrmion topological spin textures can be realized by a choice of dipole−dipole interaction, SU(3) spin−orbit coupling, and spin−exchange interaction. We also give an experimental protocol to observe such novel states within current experimental capacity.

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Keywords

Bose−Einstein condensate / spin−orbit coupling / dipolar condensate / quantum vortex

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Fang Wang, Jia Liu, Si-Lin Chen, Lin Wen, Xue-Ying Yang, Xiao-Fei Zhang. Dipolar Bose gas with SU(3) spin−orbit coupling held under a toroidal trap. Front. Phys., 2025, 20(2): 022202 https://doi.org/10.15302/frontphys.2025.022202

References

[1]
I. Žutić , J. Fabian , and S. Das Sarma , Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76(2), 323 (2004)
CrossRef ADS Google scholar
[2]
J. Wunderlich , B. Kaestner , J. Sinova , and T. Jungwirth , Experimental observation of the spin-Hall effect in a two-dimensional spin–orbit coupled semiconductor system, Phys. Rev. Lett. 94(4), 047204 (2005)
CrossRef ADS Google scholar
[3]
S. Murakami , Quantum spin Hall effect and enhanced magnetic response by spin–orbit coupling, Phys. Rev. Lett. 97(23), 236805 (2006)
CrossRef ADS Google scholar
[4]
M. Z. Hasan and C. L. Kane , Colloquium: Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)
CrossRef ADS Google scholar
[5]
X. L. Qi and S. C. Zhang , Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)
CrossRef ADS Google scholar
[6]
Y. J. Lin , K. Jiménez-García , and I. B. Spielman , Spin–orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011)
CrossRef ADS Google scholar
[7]
P. Wang , Z. Q. Yu , Z. Fu , J. Miao , L. Huang , S. Chai , H. Zhai , and J. Zhang , Spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett. 109(9), 095301 (2012)
CrossRef ADS Google scholar
[8]
L. Huang , Z. Meng , P. Wang , P. Peng , S. L. Zhang , L. Chen , D. Li , Q. Zhou , and J. Zhang , Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases, Nat. Phys. 12(6), 540 (2016)
CrossRef ADS Google scholar
[9]
J.R. LiJ.LeeW.HuangS.BurcheskyB.ShteynasF.Ç. TopA.O. JamisonW.Ketterle, A stripe phase with supersolid properties in spin−orbit-coupled Bose−Einstein condensates, Nature 543(7643), 91 (2017)
[10]
J. Zhong , B. Tang , X. Chen , and L. Zhou , Quantum gravimetry going toward real applications, Innovation 3(3), 100230 (2022)
CrossRef ADS Google scholar
[11]
S. C. Guo , Y. M. Xu , R. Cheng , J. S. Zhou , and X. Chen , Thermal Hall effect in insulating quantum materials, Innovation 3(5), 100290 (2022)
CrossRef ADS Google scholar
[12]
R.BarnettG.R. BoydV.Galitski, SU(3) spin–orbit coupling in systems of ultracold atoms, Phys. Rev. Lett. 109(23), 235308 (2012)
[13]
W. Han , X. F. Zhang , S. W. Song , H. Saito , W. Zhang , W. M. Liu , and S. G. Zhang , Double-quantum spin vortices in SU(3) spin−orbit-coupled Bose gases, Phys. Rev. A 94(3), 033629 (2016)
CrossRef ADS Google scholar
[14]
K. Sun , C. Qu , Y. Xu , Y. Zhang , and C. Zhang , Interacting spin–orbit-coupled spin-1 Bose–Einstein condensates, Phys. Rev. A 93(2), 023615 (2016)
CrossRef ADS Google scholar
[15]
C. Wu , I. Mondragon-Shem , and X. F. Zhou , Unconventional Bose–Einstein condensations from spin–orbit coupling, Chin. Phys. Lett. 28(9), 097102 (2011)
CrossRef ADS Google scholar
[16]
H. Hu , B. Ramachandhran , H. Pu , and X. J. Liu , Spin–orbit coupled weakly interacting Bose–Einstein condensates in harmonic traps, Phys. Rev. Lett. 108(1), 010402 (2012)
CrossRef ADS Google scholar
[17]
H. Sakaguchi , B. Li , and B. A. Malomed , Creation of two-dimensional composite solitons in spin–orbit-coupled self-attractive Bose–Einstein condensates in free space, Phys. Rev. E 89(3), 032920 (2014)
CrossRef ADS Google scholar
[18]
W. Han , G. Juzeliūnas , W. Zhang , and W. M. Liu , Supersolid with nontrivial topological spin textures in spin–orbit-coupled Bose gases, Phys. Rev. A 91(1), 013607 (2015)
CrossRef ADS Google scholar
[19]
H. Wang , L. H. Wen , H. Yang , C. X. Shi , and J. H. Li , Vortex states and spin textures of rotating spin–orbit-coupled Bose–Einstein condensates in a toroidal trap, J. Phys. At. Mol. Opt. Phys. 50(15), 155301 (2017)
CrossRef ADS Google scholar
[20]
G. I. Martone , Y. Li , L. P. Pitaevskii , and S. Stringari , Anisotropic dynamics of a spin–orbit-coupled Bose–Einstein condensate, Phys. Rev. A 86(6), 063621 (2012)
CrossRef ADS Google scholar
[21]
Z. Wu , L. Zhang , W. Sun , X. T. Xu , B. Z. Wang , S. C. Ji , Y. Deng , S. Chen , X. J. Liu , and J. W. Pan , Realization of two-dimensional spin–orbit coupling for Bose–Einstein condensates, Science 354(6308), 83 (2016)
CrossRef ADS Google scholar
[22]
Y. Xu , Y. Zhang , and B. Wu , Bright solitons in spin–orbit-coupled Bose–Einstein condensates, Phys. Rev. A 87(1), 013614 (2013)
CrossRef ADS Google scholar
[23]
T. Graß , R. W. Chhajlany , C. A. Muschik , and M. Lewenstein , Spiral spin textures of a bosonic Mott insu-9 lator with SU(3) spin–orbit coupling, Phys. Rev. B 90(19), 195127 (2014)
CrossRef ADS Google scholar
[24]
C. Ryu , M. Andersen , P. Cladé , V. Natarajan , K. Helmerson , and W. Phillips , Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap, Phys. Rev. Lett. 99(26), 260401 (2007)
CrossRef ADS Google scholar
[25]
X. F. Zhang , M. Kato , W. Han , S. G. Zhang , and H. Saito , Spin–orbit-coupled Bose–Einstein condensates held under a toroidal trap, Phys. Rev. A 95(3), 033620 (2017)
CrossRef ADS Google scholar
[26]
A. C. White , Y. P. Zhang , and T. Busch , Odd-petal-number states and persistent flows in spin–orbit coupled Bose–Einstein condensates, Phys. Rev. A 95(4), 041604(R) (2017)
CrossRef ADS Google scholar
[27]
J. G. Wang , L. L. Xu , and S. J. Yang , Ground-state phases of the spin–orbit-coupled spin-1 Bose gas in a toroidal trap, Phys. Rev. A 96(3), 033629 (2017)
CrossRef ADS Google scholar
[28]
K. Liu , H. He , C. Wang , Y. Chen , and Y. Zhang , Spin–orbit-coupled spin-1 Bose–Einstein condensates in a toroidal trap: Even-petal-number necklace-like state and persistent flow, Phys. Rev. A 105(1), 013323 (2022)
CrossRef ADS Google scholar
[29]
A. Griesmaier , J. Werner , S. Hensler , J. Stuhler , and T. Pfau , Bose–Einstein condensation of chromium, Phys. Rev. Lett. 94(16), 160401 (2005)
CrossRef ADS Google scholar
[30]
M. W. Ray , E. Ruokokoski , K. Tiurev , M. Möttönen , and D. S. Hall , Observation of isolated monopoles in a quantum field, Science 348(6234), 544 (2015)
CrossRef ADS Google scholar
[31]
L. Tanzi , E. Lucioni , F. Famà , J. Catani , A. Fioretti , C. Gabbanini , R. N. Bisset , L. Santos , and G. Modugno , Observation of a dipolar quantum gas with metastable supersolid properties, Phys. Rev. Lett. 122(13), 130405 (2019)
CrossRef ADS Google scholar
[32]
T. Lahaye , C. Menotti , L. Santos , M. Lewenstein , and T. Pfau , The physics of dipolar bosonic quantum gases, Rep. Prog. Phys. 72(12), 126401 (2009)
CrossRef ADS Google scholar
[33]
K. Góral , K. Rzążewski , and T. Pfau , Bose–Einstein condensation with magnetic dipole–dipole forces, Phys. Rev. A 61(5), 051601 (2000)
CrossRef ADS Google scholar
[34]
L. Santos , G. V. Shlyapnikov , and M. Lewenstein , Roton–maxon spectrum and stability of trapped dipolar Bose–Einstein condensates, Phys. Rev. Lett. 90(25), 250403 (2003)
CrossRef ADS Google scholar
[35]
F. Malet , T. Kristensen , S. M. Reimann , and G. M. Kavoulakis , Rotational properties of dipolar Bose–Einstein condensates confined in anisotropic harmonic potentials, Phys. Rev. A 83(3), 033628 (2011)
CrossRef ADS Google scholar
[36]
B. Liu , X. Li , L. Yin , and W. V. Liu , Weyl superfluidity in a three-dimensional dipolar fermi gas, Phys. Rev. Lett. 114(4), 045302 (2015)
CrossRef ADS Google scholar
[37]
S. Y. Chä and U. R. Fischer , Probing the scale invariance of the inflationary power spectrum in expanding quasitwo-dimensional dipolar condensates, Phys. Rev. Lett. 118(13), 130404 (2017)
CrossRef ADS Google scholar
[38]
M. O. Borgh , J. Lovegrove , and J. Ruostekoski , Internal structure and stability of vortices in a dipolar spinor Bose–Einstein condensate, Phys. Rev. A 95(5), 053601 (2017)
CrossRef ADS Google scholar
[39]
R. N. Bisset , P. B. Blakie , and S. Stringari , Staticresponse theory and the roton–maxon spectrum of a flattened dipolar Bose–Einstein condensate, Phys. Rev. A 100(1), 013620 (2019)
CrossRef ADS Google scholar
[40]
Y. Deng , J. Cheng , H. Jing , C. P. Sun , and S. Yi , Spin–orbit-coupled dipolar Bose–Einstein condensates, Phys. Rev. Lett. 108(12), 125301 (2012)
CrossRef ADS Google scholar
[41]
S. Gopalakrishnan , I. Martin , and E. A. Demler , Quantum quasicrystals of spin–orbit-coupled dipolar bosons, Phys. Rev. Lett. 111(18), 185304 (2013)
CrossRef ADS Google scholar
[42]
Y. Xu , Y. P. Zhang , and C. Zhang , Bright solitons in a two-dimensional spin–orbit-coupled dipolar Bose–Einstein condensate, Phys. Rev. Lett. 92(1), 013633 (2015)
[43]
R. M. Wilson , B. M. Anderson , and C. W. Clark , Meron ground state of Rashba spin–orbit-coupled dipolar bosons, Phys. Rev. Lett. 111(18), 185303 (2013)
CrossRef ADS Google scholar
[44]
G. Chen , J. Ma , and S. T. Jia , Long-range superfluid order in trapped Bose–Einstein condensates with spin–orbit coupling, Phys. Rev. A 86(4), 045601 (2012)
CrossRef ADS Google scholar
[45]
N. Q. Burdick , Y. Tang , and B. L. Lev , Long-lived spin–orbit-coupled degenerate dipolar Fermi gas, Phys. Rev. X 6(3), 031022 (2016)
CrossRef ADS Google scholar
[46]
X. J. Feng , J. X. Li , L. Qin , Y. Y. Zhang , S. Q. Xia , L. Zhou , C. J. Yang , Z. L. Zhu , W. M. Liu , and X. D. Zhao , Itinerant ferromagnetism entrenched by the anisotropy of spin–orbit coupling in a dipolar Fermi gas, Front. Phys. 18(5), 52303 (2023)
CrossRef ADS Google scholar
[47]
N. Su , Q. B. Wang , J. G. Hu , X. H. Su , and L. H. Wen , Topological defects in rotating spin–orbit-coupled dipolar spin-1 Bose−Einstein condensates, J. Phys. At. Mol. Opt. Phys. 53(21), 215301 (2020)
CrossRef ADS Google scholar
[48]
Y. Y. Li , Y. Liu , Z. W. Fan , W. Pang , S. H. Fu , and B. A. Malomed , Two-dimensional dipolar gap solitons in free space with spin–orbit coupling, Phys. Rev. A 95(6), 063613 (2017)
CrossRef ADS Google scholar
[49]
T. Oshima and Y. Kawaguchi , Spin Hall effect in a spinor dipolar Bose–Einstein condensate, Phys. Rev. A 93(5), 053605 (2016)
CrossRef ADS Google scholar
[50]
M. Kato , X. F. Zhang , D. Sasaki , and H. Saito , Twisted spin vortices in a spin-1 Bose–Einstein condensate with Rashba spin–orbit coupling and dipole–dipole interaction, Phys. Rev. A 94(4), 043633 (2016)
CrossRef ADS Google scholar
[51]
Y. Kawaguchi and M. Ueda , Spinor Bose–Einstein condensates, Phys. Rep. 520(5), 253 (2012)
CrossRef ADS Google scholar
[52]
Y. Kawaguchi , H. Saito , K. Kudo , and M. Ueda , Spontaneous magnetic ordering in a ferromagnetic spinor dipolar Bose–Einstein condensate, Phys. Rev. A 82(4), 043627 (2010)
CrossRef ADS Google scholar
[53]
D. M. Stamper-Kurn and M. Ueda , Spinor Bose gases: Symmetries, magnetism, and quantum dynamics, Rev. Mod. Phys. 85(3), 1191 (2013)
CrossRef ADS Google scholar
[54]
D. S. Wang , Y. R. Shi , K. W. Chow , Z. X. Yu , and X. G. Li , Matter-wave solitons in a spin-1 Bose–Einstein condensate with time-modulated external potential and scattering lengths, Eur. Phys. J. D 67(11), 242 (2013)
CrossRef ADS Google scholar
[55]
G.B. ArfkenH.J. WeberF.E. Harris, Mathematical Methods for Physicists, 7th Ed., Academic Press, New York, 2000
[56]
Z. F. Xu , Y. Kawaguchi , L. You , and M. Ueda , Symmetry classification of spin–orbit-coupled spinor Bose–Einstein condensates, Phys. Rev. A 86(3), 033628 (2012)
CrossRef ADS Google scholar
[57]
Z. Lan and P. Öhberg , Raman-dressed spin-1 spin–orbit coupled quantum gas, Phys. Rev. A 89(2), 023630 (2014)
CrossRef ADS Google scholar
[58]
Y. Zhang , L. Mao , and C. Zhang , Mean-field dynamics of spin–orbit coupled Bose–Einstein condensates, Phys. Rev. Lett. 108(3), 035302 (2012)
CrossRef ADS Google scholar
[59]
F. Dalfovo and S. Stringari , Bosons in anisotropic traps: Ground state and vortices, Phys. Rev. A 53(4), 2477 (1996)
CrossRef ADS Google scholar
[60]
M. L. Chiofalo , S. Succi , and M. P. Tosi , Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm, Phys. Rev. E 62(5), 7438 (2000)
CrossRef ADS Google scholar
[61]
W.BaoI.L. ChernF.Y. Lim, Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates, J. Comput. Phys. 219(2), 836 (2006)
[62]
C. Wang , C. Gao , C. M. Jian , and H. Zhai , Spin-orbit coupled spinor Bose–Einstein condensates, Phys. Rev. Lett. 105(16), 160403 (2010)
CrossRef ADS Google scholar
[63]
T. Mizushima , N. Kobayashi , and K. Machida , Coreless and singular vortex lattices in rotating spinor Bose–Einstein condensates, Phys. Rev. A 70(4), 043613 (2004)
CrossRef ADS Google scholar
[64]
K. Kasamatsu , M. Tsubota , and M. Ueda , Spin textures in rotating two-component Bose–Einstein condensates, Phys. Rev. A 71(4), 043611 (2005)
CrossRef ADS Google scholar
[65]
S. Heinze , K. von Bergmann , M. Menzel , J. Brede , A. Kubetzka , R. Wiesendanger , G. Bihlmayer , and S. Blügel , Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions, Nat. Phys. 7(9), 713 (2011)
CrossRef ADS Google scholar
[66]
S. Banerjee , J. Rowland , O. Erten , and M. Randeria , Enhanced stability of skyrmions in two-dimensional chiral magnets with Rashba spin–orbit coupling, Phys. Rev. X 4(3), 031045 (2014)
CrossRef ADS Google scholar
[67]
B. Dong , Q. Sun , W. M. Liu , A. C. Ji , X. F. Zhang , and S. G. Zhang , Multiply quantized and fractional skyrmions in a binary dipolar Bose–Einstein condensate under rotation, Phys. Rev. A 96(1), 013619 (2017)
CrossRef ADS Google scholar
[68]
H. Saito , Y. Kawaguchi , and M. Ueda , Breaking of chiral symmetry and spontaneous rotation in a spinor Bose–Einstein condensate, Phys. Rev. Lett. 96(6), 065302 (2006)
CrossRef ADS Google scholar
[69]
X. Z. Yu , W. Koshibae , Y. Tokunaga , K. Shibata , Y. Taguchi , N. Nagaosa , and Y. Tokura , Transformation between meron and skyrmion topological spin textures in a chiral magnet, Nature 564(7734), 95 (2018)
CrossRef ADS Google scholar
[70]
C. Chin , R. Grimm , P. Julienne , and E. Tiesinga , Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82(2), 1225 (2010)
CrossRef ADS Google scholar

Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12175129, 12475004, 12175027, and 12005125; the Key Research Program of Frontier Sciences of Chinese Academy of Sciences under Grant No. ZDBS-LY-7016; the Shaanxi Fundamental Science Research Project for Mathematics and Physics under Grant No. 22JSY034; the Scientific Research Program Funded by Shaanxi Provincial Education Department under Program No. 23JP020; the Natural Science Foundation of Chongqing under Grant Nos. cstc2019jcyj-msxmX0217 and cstc2021jcyjmsxmX0168; and the Youth Innovation Team of Shaanxi Universities.

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