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arxiv: 1907.02216 · v1 · pith:VW2ABEPRnew · submitted 2019-07-04 · ❄️ cond-mat.quant-gas · quant-ph

Topological spinor vortex matter on spherical surface induced by non-Abelian spin-orbital-angular-momentum coupling

Jia-Ming Cheng , Ming Gong , Guang-Can Guo , Zheng-Wei Zhou , Xiang-Fa Zhou This is my paper

Pith reviewed 2026-05-25 08:57 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas quant-ph
keywords spinor Bose-Einstein condensatesnon-Abelian SOAM couplingspherical surface traptopological spin vorticesmeta-ferromagnetic phasesmeta-polar statesThomson latticesangular momentum degeneracy
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The pith

Non-Abelian SOAM coupling on spherical traps produces tunable degenerate ground states with quantized angular momentum in spinor condensates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows an explicit implementation of non-Abelian spin-orbital-angular-momentum coupling in spinor Bose-Einstein condensates on a spherical surface using magnetic gradient coupling. This coupling supports multiple degenerate ground states that carry different total angular momenta, with the degeneracy level controlled by the coupling strength. For weakly interacting f=1 condensates the setup yields meta-ferromagnetic phases and meta-polar states indexed by the quantized value of total mean angular momentum. Polar states display Z2 symmetry and host Thomson lattices of spin-vortex defects. The construction supplies a route to stable topological spin-vortex states and a platform for studying strong correlations under tunable degeneracy.

Core claim

By realizing non-Abelian SOAM coupling through magnetic gradients on a spherical surface trap, the system supports various degenerate ground states carrying different total angular momenta J whose degeneracy is tuned by the SOAM strength; for f=1 condensates this produces meta-ferromagnetic and meta-polar phases characterized by quantized total mean angular momentum, together with Z2-symmetric polar states whose spin vortices form Thomson lattices.

What carries the argument

Non-Abelian SOAM coupling realized by magnetic gradient coupling on a spherical surface trap addressable by high-order Hermite-Gaussian beams, which enforces the required rotational symmetries and produces the angular-momentum degeneracy.

If this is right

  • Degeneracy of ground states can be tuned continuously by varying the SOAM coupling strength.
  • Meta-ferromagnetic phases appear for different quantized values of total mean angular momentum.
  • Meta-polar states with Z2 symmetry form and host spin vortices arranged in Thomson lattices.
  • The construction yields stable topological spin vortex states that can be prepared on demand.
  • The platform enables study of strong-correlated neutral-atom physics under controlled ground-state degeneracy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same spherical geometry and coupling scheme could be extended to higher spin values f>1 to generate additional lattice types or fractionalized excitations.
  • Because the degeneracy is tunable by a single parameter, the setup offers a clean route to explore quantum phase transitions between the meta-ferromagnetic and meta-polar regimes.
  • The topological character of the vortex defects suggests the system may host protected edge modes or anyonic statistics when interactions are increased.

Load-bearing premise

Magnetic gradient coupling on the spherical surface can be arranged to produce the desired non-Abelian SOAM term while preserving rotational symmetry and without adding uncontrolled perturbations.

What would settle it

Experimental failure to observe multiple degenerate ground states whose total mean angular momentum changes in discrete steps when the magnetic gradient strength is varied would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.02216 by Guang-Can Guo, Jia-Ming Cheng, Ming Gong, Xiang-Fa Zhou, Zheng-Wei Zhou.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic plot about the implementation of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The mean-field ground-states of the condensates in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spin vortex defects on the spherical surface in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Magnetic field modulation scheme of negative SOAM [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Orbital-angular-momentum quantum number [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Local spin-density vector [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 2
Figure 2. Figure 2: figure 2. The explicit form of [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Local spin-density vector [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Local spin-density vector [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Local spin-density [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Local spin-density [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

We provide an explicit way to implement non-Abelian spin-orbital-angular-momentum (SOAM) coupling in spinor Bose-Einstein condensates using magnetic gradient coupling. For a spherical surface trap addressable using high-order Hermite-Gaussian beams, we show that this system supports various degenerate ground states carrying different total angular momenta $\mathbf{J}$, and the degeneracy can be tuned by changing the strength of SOAM coupling. For weakly interacting spinor condensates with $f=1$, the system supports various meta-ferromagnetic phases and meta-polar states described by quantized total mean angular momentum $|\langle \mathbf{J} \rangle|$. Polar states with $Z_2$ symmetry and Thomson lattices formed by defects of spin vortices are also discussed. The system can be used to prepare various stable spin vortex states with nontrivial topology, and serve as a platform to investigate strong-correlated physics of neutral atoms with tunable ground-state degeneracy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes an explicit realization of non-Abelian spin-orbital-angular-momentum (SOAM) coupling in spinor Bose-Einstein condensates confined to a spherical surface trap, achieved via magnetic gradient coupling addressable by high-order Hermite-Gaussian beams. It claims this Hamiltonian supports tunable degeneracy among ground states carrying different total angular momenta J; for weakly interacting f=1 spinors, the system realizes meta-ferromagnetic and meta-polar phases characterized by quantized |<J>|, together with Z2-symmetric polar states whose spin-vortex defects form Thomson lattices. The setup is presented as a platform for stable topological spin vortices and tunable-degeneracy strong-correlation physics.

Significance. If the effective non-Abelian SOAM term can be realized without symmetry-breaking perturbations, the work supplies a concrete route to engineer tunable J-multiplet degeneracy and associated topological vortex lattices in neutral-atom spinor condensates, extending existing SOAM studies to spherical geometry and offering a falsifiable platform for meta-ferromagnetic/meta-polar phases.

major comments (1)
  1. [Implementation of the SOAM coupling (likely §2–3)] The headline claims (tunable J-degeneracy, quantized |<J>| plateaus, and Thomson lattices) rest on the effective Hamiltonian being exactly the desired non-Abelian SOAM operator on the sphere. The implementation via magnetic gradients plus high-order HG beams must be shown to introduce no uncontrolled position-dependent Zeeman or Abelian vector-potential terms that would split the J-multiplets; the manuscript should supply an explicit error analysis or symmetry argument demonstrating that deviations from ideal linear gradients and perfect beam profiles remain negligible within the reported parameter regime.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the single major comment below.

read point-by-point responses

  1. Referee: [Implementation of the SOAM coupling (likely §2–3)] The headline claims (tunable J-degeneracy, quantized |<J>| plateaus, and Thomson lattices) rest on the effective Hamiltonian being exactly the desired non-Abelian SOAM operator on the sphere. The implementation via magnetic gradients plus high-order HG beams must be shown to introduce no uncontrolled position-dependent Zeeman or Abelian vector-potential terms that would split the J-multiplets; the manuscript should supply an explicit error analysis or symmetry argument demonstrating that deviations from ideal linear gradients and perfect beam profiles remain negligible within the reported parameter regime.

    Authors: We agree that an explicit demonstration is required to confirm the absence of symmetry-breaking perturbations. In the revised manuscript we will add a new subsection (or appendix) that (i) uses the rotational symmetry of the spherical trap together with the angular-momentum selection rules of the chosen high-order Hermite-Gaussian modes to prove that any residual Abelian vector potential or position-dependent Zeeman term must vanish to leading order, and (ii) supplies a perturbative error estimate showing that realistic deviations from ideal linear gradients and perfect beam profiles remain below a few percent throughout the parameter regime used for the reported phases and do not lift the J-multiplet degeneracy. This addition directly addresses the referee’s concern. revision: yes

Circularity Check

0 steps flagged

No circularity: phases derived directly from constructed Hamiltonian

full rationale

The paper constructs an explicit effective Hamiltonian for non-Abelian SOAM coupling on the sphere via magnetic gradient terms, then derives the degenerate J-multiplets, meta-ferromagnetic/meta-polar phases, quantized |<J>|, Z2 symmetry, and Thomson vortex lattices by standard energy minimization or diagonalization of that Hamiltonian for f=1 spinors. No step reduces a prediction to a fitted input, renames a known result, or relies on a load-bearing self-citation whose content is itself unverified; the derivation chain is self-contained against the proposed model without circular reduction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the feasibility of the magnetic-gradient implementation and the validity of the mean-field description for weakly interacting f=1 atoms; no free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption Magnetic gradient coupling can be engineered to produce non-Abelian SOAM without breaking the required rotational symmetries on the sphere.
    Invoked in the first sentence of the abstract as the enabling step.
  • domain assumption The spherical surface trap is addressable by high-order Hermite-Gaussian beams while maintaining the ideal geometry.
    Stated as a prerequisite for the trap geometry.

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Reference graph

Works this paper leans on

75 extracted references · 75 canonical work pages · 2 internal anchors

  1. [1]

    In this case, the ground-state wavefunction reads ψl,f j,j (θ, φ)

    c1/c0 ∼ −1 with λ < 0 and j = l + f. In this case, the ground-state wavefunction reads ψl,f j,j (θ, φ). Sicne jz = j, this corresponds to the usual FM phases with maximized local vec- tor ⃗F(θ, φ) satisfying | ⃗F(θ, φ)|/n(θ, φ) = 1. In addition, the spin fluctuation defined by ∆ Fij = ⟨FiFj⟩−⟨F i⟩⟨Fj⟩ with ( i, j)∈ (x, y, z) also van- ishes. These states ar...

    work page

  2. [2]

    Here 5 the ground states also reads ψl,f j,jz=j(θ, φ)

    c1/c0 ∼ −1 with λ > 0 and j = |l− f|. Here 5 the ground states also reads ψl,f j,jz=j(θ, φ). Since j < l , the normalized vector | ⃗F(θ, φ)|/n(θ, φ) < 1 and changes its direction over the surface. There- fore, the state possesses nonzero the spin fluctua- tion ∆F̸ = 0, and is then called as the mFM phase

    work page

  3. [3]

    In this case, the system supports various polar states with ⃗F(θ, φ) = 0, which exhibits novel intrinsic topological proper- ties

    c1/c0 ∼ 1 for all λ. In this case, the system supports various polar states with ⃗F(θ, φ) = 0, which exhibits novel intrinsic topological proper- ties. To show this, we write the wavefunction us- ing the real nematic order ⃗d as ψ(θ, φ) = ⃗d·| ⃗ r⟩ = dx|x⟩ + dy|y⟩ + dz|z⟩, where {|x⟩,|y⟩,|z⟩} are the Cartesian basis formed by the eigenvectors ofFx,y,z wit...

    work page

  4. [4]

    The single-particle ground- state ψ1,1 0,0(θ, φ) (see Eq.B11) is non-degenerate, which should also be the ground-state for condensates with weak interaction strength

    In this case, spin and orbital-angular-momentum are along opposite directions. The single-particle ground- state ψ1,1 0,0(θ, φ) (see Eq.B11) is non-degenerate, which should also be the ground-state for condensates with weak interaction strength. The system possesses ho- mogeneous density distribution with its spin mean-value |F| = 0 and spin-densityFα(θ, ...

    work page

  5. [5]

    10 TABLE II

    There are two kinds of spin vortices with N+− N− = 16− 14 = 2. 10 TABLE II. Explicit information of different phases in figure 2 for λ > 0 within different regimes c1/c0. Here ”WF” is short for ”wavefunction”. ”D[a,b,c]” means a diagonal matrix with the diagonal elements {a, b, c}. Others are the same as those in figure 2. The explicit form of α, β, ηi, a and...

    work page

  6. [6]

    ( 31 48 ,∞) (−∞, η1) (η1, η2) (η2, η3) (η3,∞) WF ψ2,1 1,1 ψ2,1 1,0 ψ3,1 2,2 √ 2 3 ψ3,1 2,−1+√ 1 3 ψ3,1 2,2 ψ3,1 2,0 ψ4,1 3,3 ψ4,1 3,2 α [ ψ4,1 3,−3 + ψ4,1 3,3 ] + βψ 4,1 3,0 √ 1 2[ψ4,1 3,2 + ψ4,1 3,−2] |J| |J| = 1 |J| = 0 |J| = 2 |J| = 0 |J| = 0 |J| = 3 |J| = 2 |J| = 0 |J| = 0 |F| |F| = 1 2 |F| = 0 |F| = 2 3 |F| = 0 |F| = 0 |F| = 3 4 |F| = 1 2 |F| = 0 |F|...

    work page

  7. [7]

    0 2 4 6 0.5 1 1.5 2 2.5 3 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 -1 -1 -1 0z xy 00 1 1 1 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 FIG

    There are two kinds of spin vortices with N+− N− = 8− 6 = 2. 0 2 4 6 0.5 1 1.5 2 2.5 3 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 -1 -1 -1 0z xy 00 1 1 1 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 FIG. 10. Local spin-density vector ⃗F(θ, φ) in the mFM−(2) with SOAM coupling λ = 5 and weak interaction c0 = 1. Colorful symbols “+” in (a) represent spin vo...

    work page

  8. [8]

    There are two spin vortices with Q = 1

    work page

  9. [9]

    Creation of effective magnetic fields in optical lattices: the hofstadter but- terfly for cold neutral atoms,

    Dieter Jaksch and Peter Zoller, “Creation of effective magnetic fields in optical lattices: the hofstadter but- terfly for cold neutral atoms,” New Journal of Physics 5, 56 (2003)

    work page 2003

  10. [10]

    Simu- lation and detection of dirac fermions with cold atoms in an optical lattice,

    Shi-Liang Zhu, Baigeng Wang, and L-M Duan, “Simu- lation and detection of dirac fermions with cold atoms in an optical lattice,” Physical Review Letters 98, 260402 (2007)

    work page 2007

  11. [11]

    Spin- orbit-coupled bose-einstein condensates,

    Y.-J. Lin, K Jim´ enez-Garc´ ıa, and I.B. Spielman, “Spin- orbit-coupled bose-einstein condensates,” Nature 471, 83–86 (2011)

    work page 2011

  12. [12]

    Collective dipole oscillations of a spin-orbit coupled bose-einstein condensate,

    Jin-Yi Zhang, Si-Cong Ji, Zhu Chen, Long Zhang, Zhi- Dong Du, Bo Yan, Ge-Sheng Pan, Bo Zhao, You-Jin Deng, Hui Zhai, et al., “Collective dipole oscillations of a spin-orbit coupled bose-einstein condensate,” Physical Review Letters 109, 115301 (2012)

    work page 2012

  13. [13]

    Topological fulde-ferrell-larkin- ovchinnikov states in spin–orbit-coupled fermi gases,

    Wei Zhang and Wei Yi, “Topological fulde-ferrell-larkin- ovchinnikov states in spin–orbit-coupled fermi gases,” 11 0 2 4 6 0.5 1 1.5 2 2.5 3 0.01 0.02 0.03 0.04 0.05 0.06 -1 -1-1 0z xy 00 1 1 1 0.01 0.02 0.03 0.04 0.05 0.06 FIG. 11. Local spin-density ⃗F(θ, φ) in the mP −(3) with SOAM coupling λ = 7 and weak interaction c0 = 1. Col- orful symbols “+” in (...

    work page 2013

  14. [14]

    Experimental determination of the finite- temperature phase diagram of a spin-orbit coupled bose gas,

    Si-Cong Ji, Jin-Yi Zhang, Long Zhang, Zhi-Dong Du, Wei Zheng, You-Jin Deng, Hui Zhai, Shuai Chen, and Jian-Wei Pan, “Experimental determination of the finite- temperature phase diagram of a spin-orbit coupled bose gas,” Nature Physics 10, 314–320 (2014)

    work page 2014

  15. [15]

    Realization of two- dimensional spin-orbit coupling for bose-einstein conden- sates,

    Zhan Wu, Long Zhang, Wei Sun, Xiao-Tian Xu, Bao- Zong Wang, Si-Cong Ji, Youjin Deng, Shuai Chen, Xiong-Jun Liu, and Jian-Wei Pan, “Realization of two- dimensional spin-orbit coupling for bose-einstein conden- sates,” Science 354, 83–88 (2016)

    work page 2016

  16. [16]

    Experimental realization of two-dimensional synthetic spin-orbit coupling in ultra- cold fermi gases,

    Lianghui Huang, Zengming Meng, Pengjun Wang, Peng Peng, Shao-Liang Zhang, Liangchao Chen, Donghao Li, Qi Zhou, and Jing Zhang, “Experimental realization of two-dimensional synthetic spin-orbit coupling in ultra- cold fermi gases,” Nature Physics 12, 540–544 (2016)

    work page 2016

  17. [17]

    Spin-orbit coupling in quantum gases,

    Victor Galitski and Ian B. Spielman, “Spin-orbit coupling in quantum gases,” Nature 494, 49 (2013)

    work page 2013

  18. [18]

    Degenerate quantum gases with spin-orbit coupling: a review,

    Hui Zhai, “Degenerate quantum gases with spin-orbit coupling: a review,” Reports on Progress in Physics 78, 026001 (2015)

    work page 2015

  19. [19]

    Uncon- ventional states of bosons with the synthetic spin-orbit coupling,

    Xiangfa Zhou, Yi Li, Zi Cai, and Congjun Wu, “Uncon- ventional states of bosons with the synthetic spin-orbit coupling,” Journal of Physics B: Atomic, Molecular and Optical Physics 46, 134001 (2013)

    work page 2013

  20. [20]

    Spin-orbit coupled spinor bose-einstein condensates,

    Chunji Wang, Chao Gao, Chao-Ming Jian, and Hui Zhai, “Spin-orbit coupled spinor bose-einstein condensates,” Physical Review Letters 105, 160403 (2010)

    work page 2010

  21. [21]

    Unconventional bose-einstein condensations from spin-orbit coupling,

    Wu Cong-Jun, Ian Mondragon-Shem, and Zhou Xiang- Fa, “Unconventional bose-einstein condensations from spin-orbit coupling,” Chinese Physics Letters 28, 097102 (2011)

    work page 2011

  22. [22]

    Spin-orbit coupled weakly interacting bose-einstein con- densates in harmonic traps,

    Hui Hu, B. Ramachandhran, Han Pu, and Xia-Ji Liu, “Spin-orbit coupled weakly interacting bose-einstein con- densates in harmonic traps,” Physical Review Letters 108, 010402 (2012)

    work page 2012

  23. [23]

    Superstripes and the excitation spec- trum of a spin-orbit-coupled bose-einstein condensate,

    Yun Li, Giovanni I. Martone, Lev P. Pitaevskii, and Sandro Stringari, “Superstripes and the excitation spec- trum of a spin-orbit-coupled bose-einstein condensate,” Physical Review Letters 110, 235302 (2013)

    work page 2013

  24. [24]

    Stability of ultracold atomic bose condensates with rashba spin-orbit coupling against quantum and thermal fluctuations,

    Tomoki Ozawa and Gordon Baym, “Stability of ultracold atomic bose condensates with rashba spin-orbit coupling against quantum and thermal fluctuations,” Physical Re- view Letters 109, 025301 (2012)

    work page 2012

  25. [25]

    Fundamental, multipole, and half-vortex gap solitons in spin-orbit coupled bose- einstein condensates,

    Valery E. Lobanov, Yaroslav V. Kartashov, and Vladimir V. Konotop, “Fundamental, multipole, and half-vortex gap solitons in spin-orbit coupled bose- einstein condensates,” Physical Review Letters 112, 180403 (2014)

    work page 2014

  26. [26]

    Stable solitons in three dimensional free space without the ground state: Self-trapped bose- einstein condensates with spin-orbit coupling,

    Yong-Chang Zhang, Zheng-Wei Zhou, Boris A. Mal- omed, and Han Pu, “Stable solitons in three dimensional free space without the ground state: Self-trapped bose- einstein condensates with spin-orbit coupling,” Physical Review Letters 115, 253902 (2015)

    work page 2015

  27. [27]

    Spin- tensor–momentum-coupled bose-einstein condensates,

    Xi-Wang Luo, Kuei Sun, and Chuanwei Zhang, “Spin- tensor–momentum-coupled bose-einstein condensates,” Physical Review Letters 119, 193001 (2017)

    work page 2017

  28. [28]

    A stripe phase with supersolid prop- erties in spin-orbit-coupled bose-einstein condensates,

    Jun-Ru Li, Jeongwon Lee, Wujie Huang, Sean Burchesky, Boris Shteynas, Furkan C ¸ a˘ grı Top, Alan O Jamison, and Wolfgang Ketterle, “A stripe phase with supersolid prop- erties in spin-orbit-coupled bose-einstein condensates,” Nature 543, 91 (2017)

    work page 2017

  29. [29]

    Chiral super- solid in spin-orbit-coupled bose gases with soft-core long- range interactions,

    Wei Han, Xiao-Fei Zhang, Deng-Shan Wang, Hai-Feng Jiang, Wei Zhang, and Shou-Gang Zhang, “Chiral super- solid in spin-orbit-coupled bose gases with soft-core long- range interactions,” Physical review letters 121, 030404 (2018)

    work page 2018

  30. [30]

    Beliaev damping of a spin-orbit-coupled bose-einstein condensate,

    Rukuan Wu and Zhaoxin Liang, “Beliaev damping of a spin-orbit-coupled bose-einstein condensate,” Physical review letters 121, 180401 (2018)

    work page 2018

  31. [31]

    Searching for supersolidity in ultracold atomic bose condensates with rashba spin-orbit cou- pling,

    Renyuan Liao, “Searching for supersolidity in ultracold atomic bose condensates with rashba spin-orbit cou- pling,” Physical review letters 120, 140403 (2018)

    work page 2018

  32. [32]

    Angular momentum of a bose-einstein condensate in a synthetic rotational field,

    Chunlei Qu and Sandro Stringari, “Angular momentum of a bose-einstein condensate in a synthetic rotational field,” Physical review letters 120, 183202 (2018)

    work page 2018

  33. [33]

    Topo- logical superfluids with finite-momentum pairing and ma- jorana fermions,

    Chunlei Qu, Zhen Zheng, Ming Gong, Yong Xu, Li Mao, Xubo Zou, Guangcan Guo, and Chuanwei Zhang, “Topo- logical superfluids with finite-momentum pairing and ma- jorana fermions,” Nature Communications 4 (2013)

    work page 2013

  34. [34]

    Prob- ing anisotropic superfluidity in atomic fermi gases with rashba spin-orbit coupling,

    Hui Hu, Lei Jiang, Xia-Ji Liu, and Han Pu, “Prob- ing anisotropic superfluidity in atomic fermi gases with rashba spin-orbit coupling,” Physical Review Letters 107, 195304 (2011)

    work page 2011

  35. [35]

    Un- conventional superfluid in a two-dimensional fermi gas with anisotropic spin-orbit coupling and zeeman fields,

    Fan Wu, Guang-Can Guo, Wei Zhang, and Wei Yi, “Un- conventional superfluid in a two-dimensional fermi gas with anisotropic spin-orbit coupling and zeeman fields,” Physical Review Letters 110, 110401 (2013)

    work page 2013

  36. [36]

    Trapped two-dimensional condensates with synthetic spin-orbit coupling,

    Subhasis Sinha, Rejish Nath, and Luis Santos, “Trapped two-dimensional condensates with synthetic spin-orbit coupling,” Physical Review Letters 107, 270401 (2011)

    work page 2011

  37. [37]

    Three- dimensional quaternionic condensations, hopf invariants, and skyrmion lattices with synthetic spin-orbit cou- 12 pling,

    Yi Li, Xiangfa Zhou, and Congjun Wu, “Three- dimensional quaternionic condensations, hopf invariants, and skyrmion lattices with synthetic spin-orbit cou- 12 pling,” Physical Review A 93, 033628 (2016)

    work page 2016

  38. [38]

    Bose-hubbard models with syn- thetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity,

    William S Cole, Shizhong Zhang, Arun Paramekanti, and Nandini Trivedi, “Bose-hubbard models with syn- thetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity,” Physical Review Letters 109, 085302 (2012)

    work page 2012

  39. [39]

    Symmetry-enriched bose-einstein condensates in a spin-orbit-coupled bilayer system,

    Jia-Ming Cheng, Xiang-Fa Zhou, Zheng-Wei Zhou, Guang-Can Guo, and Ming Gong, “Symmetry-enriched bose-einstein condensates in a spin-orbit-coupled bilayer system,” Physical Review A 97, 013625 (2018)

    work page 2018

  40. [40]

    Vortex coupler for atomic bose-einstein conden- sates,

    Karl-Peter Marzlin, Weiping Zhang, and Ewan M. Wright, “Vortex coupler for atomic bose-einstein conden- sates,” Physical review letters 79, 4728 (1997)

    work page 1997

  41. [41]

    Optically induced spin-hall effect in atoms,

    Xiong-Jun Liu, Xin Liu, Leong Chuan Kwek, and Choo Hiap Oh, “Optically induced spin-hall effect in atoms,” Physical Review Letters 98, 026602 (2007)

    work page 2007

  42. [42]

    Spin– orbital-angular-momentum coupling in bose-einstein con- densates,

    Kuei Sun, Chunlei Qu, and Chuanwei Zhang, “Spin– orbital-angular-momentum coupling in bose-einstein con- densates,” Physical Review A 91, 063627 (2015)

    work page 2015

  43. [43]

    Quan- tum phases of bose-einstein condensates with synthetic spin–orbital-angular-momentum coupling,

    Chunlei Qu, Kuei Sun, and Chuanwei Zhang, “Quan- tum phases of bose-einstein condensates with synthetic spin–orbital-angular-momentum coupling,” Physical Re- view A 91, 053630 (2015)

    work page 2015

  44. [44]

    Half-skyrmion and vortex-antivortex pairs in spinor condensates,

    Yu-Xin Hu, Christian Miniatura, Benoˆ ıt Gr´ emaud,et al., “Half-skyrmion and vortex-antivortex pairs in spinor condensates,” Physical Review A 92, 033615 (2015)

    work page 2015

  45. [45]

    Angular spin-orbit cou- pling in cold atoms,

    Michael DeMarco and Han Pu, “Angular spin-orbit cou- pling in cold atoms,” Physical Review A 91, 033630 (2015)

    work page 2015

  46. [46]

    Spin-orbital-angular- momentum coupled bose-einstein condensates,

    H.-R. Chen, K.-Y. Lin, P.-K. Chen, N.-C. Chiu, J.-B. Wang, C.-A. Chen, P.-P. Huang, S.-K. Yip, Yuki Kawaguchi, and Y.-J. Lin, “Spin-orbital-angular- momentum coupled bose-einstein condensates,” Physical Review Letters 121, 113204 (2018)

    work page 2018

  47. [47]

    Ground- state phase diagram of a spin-orbital-angular-momentum coupled bose-einstein condensate,

    Dongfang Zhang, Tianyou Gao, Peng Zou, Lingran Kong, Ruizong Li, Xing Shen, Xiao-Long Chen, Shi-Guo Peng, Mingsheng Zhan, Han Pu, and Kaijun Jiang, “Ground- state phase diagram of a spin-orbital-angular-momentum coupled bose-einstein condensate,” Phys. Rev. Lett. 122, 110402 (2019)

    work page 2019

  48. [48]

    Rotating atomic quantum gases with light-induced az- imuthal gauge potentials and the observation of the hess- fairbank effect,

    P.-K. Chen, L.-R. Liu, M.-J. Tsai, N.-C. Chiu, Y. Kawaguchi, S.-K. Yip, M.-S. Chang, and Y.-J. Lin, “Rotating atomic quantum gases with light-induced az- imuthal gauge potentials and the observation of the hess- fairbank effect,” Physical Review Letters 121, 250401 (2018)

    work page 2018

  49. [49]

    Angular stripe phase in spin-orbital- angular-momentum coupled bose condensates,

    Xiao-Long Chen, Shi-Guo Peng, Peng Zou, Xia-Ji Liu, and Hui Hu, “Angular stripe phase in spin-orbital- angular-momentum coupled bose condensates,” arXiv preprint arXiv:1901.02595 (2019)

    work page arXiv 1901

  50. [50]

    Cowan, The theory of atomic structure and spectra, 3 (Univ of California Press, 1981)

    Robert D. Cowan, The theory of atomic structure and spectra, 3 (Univ of California Press, 1981)

    work page 1981

  51. [51]

    Topologi- cal insulators with su(2) landau levels,

    Yi Li, Shou-Cheng Zhang, and Congjun Wu, “Topologi- cal insulators with su(2) landau levels,” Physical Review Letters 111, 186803 (2013)

    work page 2013

  52. [52]

    High-dimensional topological in- sulators with quaternionic analytic landau levels,

    Yi Li and Congjun Wu, “High-dimensional topological in- sulators with quaternionic analytic landau levels,” Phys- ical Review Letters 110, 216802 (2013)

    work page 2013

  53. [53]

    Two-and three-dimensional topological insulators with isotropic and parity-breaking landau levels,

    Yi Li, Xiangfa Zhou, and Congjun Wu, “Two-and three-dimensional topological insulators with isotropic and parity-breaking landau levels,” Physical Review B 85, 125122 (2012)

    work page 2012

  54. [54]

    Spinor condensates on a cylindrical surface in synthetic gauge fields,

    Tin-Lun Ho and Biao Huang, “Spinor condensates on a cylindrical surface in synthetic gauge fields,” Physical Review Letters 115, 155304 (2015)

    work page 2015

  55. [55]

    Static and dy- namic properties of shell-shaped condensates,

    Kuei Sun, Karmela Padavi´ c, Frances Yang, Smitha Vishveshwara, and Courtney Lannert, “Static and dy- namic properties of shell-shaped condensates,” Physical Review A 98, 013609 (2018)

    work page 2018

  56. [56]

    Potential scattering on a spherical surface,

    Jian Zhang and Tin-Lun Ho, “Potential scattering on a spherical surface,” Journal of Physics B: Atomic, Molec- ular and Optical Physics 51, 115301 (2018)

    work page 2018

  57. [57]

    Bose-einstein conden- sation on the surface of a sphere,

    A Tononi and L Salasnich, “Bose-einstein conden- sation on the surface of a sphere,” arXiv preprint arXiv:1903.08453 (2019)

    work page arXiv 1903

  58. [58]

    Generalized thomson problem in arbitrary dimen- sions and non-euclidean geometries,

    J Batle, Armen Bagdasaryan, M Abdel-Aty, and S Ab- dalla, “Generalized thomson problem in arbitrary dimen- sions and non-euclidean geometries,” Physica A: Statisti- cal Mechanics and its Applications 451, 237–250 (2016)

    work page 2016

  59. [59]

    Tunable generation of correlated vortices in open superconductor tubes,

    Vladimir M Fomin, Roman O Rezaev, and Oliver G Schmidt, “Tunable generation of correlated vortices in open superconductor tubes,” Nano Letters 12, 1282–1287 (2012)

    work page 2012

  60. [60]

    Coupling of chiralities in spin and physi- cal spaces: The m¨ obius ring as a case study,

    Oleksandr V. Pylypovskyi, Volodymyr P. Kravchuk, De- nis D. Sheka, Denys Makarov, Oliver G. Schmidt, and Yuri Gaididei, “Coupling of chiralities in spin and physi- cal spaces: The m¨ obius ring as a case study,” Phys. Rev. Lett. 114, 197204 (2015)

    work page 2015

  61. [61]

    Spin connection and boundary states in a topological insulator,

    V Parente, P Lucignano, P Vitale, A Tagliacozzo, and F Guinea, “Spin connection and boundary states in a topological insulator,” Physical Review B 83, 075424 (2011)

    work page 2011

  62. [62]

    Topological nodal Cooper pairing in doped Weyl metals

    Yi Li and FDM Haldane, “Topological nodal cooper pairing in doped weyl metals,” arXiv preprint arXiv:1510.01730 (2015)

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  63. [63]

    Spherical topological insulator,

    Ken-Ichiro Imura, Yukinori Yoshimura, Yositake Takane, and Takahiro Fukui, “Spherical topological insulator,” Physical Review B 86, 235119 (2012)

    work page 2012

  64. [64]

    Testing for majorana zero modes in a px + ipy superconductor at high temperature by tunnel- ing spectroscopy,

    Yaacov E Kraus, Assa Auerbach, HA Fertig, and Steven H Simon, “Testing for majorana zero modes in a px + ipy superconductor at high temperature by tunnel- ing spectroscopy,” Physical Review Letters 101, 267002 (2008)

    work page 2008

  65. [65]

    Chi- ral p± ip superfluid on a sphere,

    Sergej Moroz, Carlos Hoyos, and Leo Radzihovsky, “Chi- ral p± ip superfluid on a sphere,” Physical Review B 93, 024521 (2016)

    work page 2016

  66. [66]

    Emergent Gauge Field for a Chiral Bound State on Curved Surface

    Zhe-Yu Shi and Hui Zhai, “Emergent gauge field for a chiral bound state on curved surface,” arXiv preprint arXiv:1510.05815 (2015)

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  67. [67]

    Synthetic lan- dau levels and spinor vortex matter on a haldane spheri- cal surface with a magnetic monopole,

    Xiang-Fa Zhou, Congjun Wu, Guang-Can Guo, Ruquan Wang, Han Pu, and Zheng-Wei Zhou, “Synthetic lan- dau levels and spinor vortex matter on a haldane spheri- cal surface with a magnetic monopole,” Physical Review Letters 120, 130402 (2018)

    work page 2018

  68. [68]

    Periodically driven quantum systems: effective hamiltonians and en- gineered gauge fields,

    Nathan Goldman and Jean Dalibard, “Periodically driven quantum systems: effective hamiltonians and en- gineered gauge fields,” Physical Review X 4, 031027 (2014)

    work page 2014

  69. [69]

    Spinor bose condensates in optical traps,

    Tin-Lun Ho, “Spinor bose condensates in optical traps,” Physical Review Letters 81, 742 (1998)

    work page 1998

  70. [70]

    Spinor bose– einstein condensates,

    Yuki Kawaguchi and Masahito Ueda, “Spinor bose– einstein condensates,” Physics Reports 520, 253–381 (2012)

    work page 2012

  71. [71]

    Joseph John Thomson, “Xxiv. on the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with ap- plication of the results to the theory of atomic structure,” 13 The London, Edinburgh, and Dublin Philosophical Mag- azine and Journal of...

    work page 1904

  72. [72]

    Spin- nematic order in antiferromagnetic spinor condensates,

    Tilman Zibold, Vincent Corre, Camille Frapolli, Andrea Invernizzi, Jean Dalibard, and Fabrice Gerbier, “Spin- nematic order in antiferromagnetic spinor condensates,” Physical Review A 93, 023614 (2016)

    work page 2016

  73. [73]

    Stability and internal structure of vortices in spin-1 bose-einstein condensates with conserved magne- tization,

    Justin Lovegrove, Magnus O Borgh, and Janne Ru- ostekoski, “Stability and internal structure of vortices in spin-1 bose-einstein condensates with conserved magne- tization,” Physical Review A 93, 033633 (2016)

    work page 2016

  74. [74]

    Morris Edgar Rose, Elementary theory of angular momentum (Courier Corporation, 1995)

    work page 1995

  75. [75]

    Coreless and singular vortex lattices in rotat- ing spinor bose-einstein condensates,

    Takeshi Mizushima, Naoko Kobayashi, and Kazushige Machida, “Coreless and singular vortex lattices in rotat- ing spinor bose-einstein condensates,” Physical Review A 70, 043613 (2004)

    work page 2004