Fig. 1. The ground-state density profiles of ferromagnetic spin-1 BECs with isotropic SU(3) SOC. The columns in every panel from left to right are the densities of the m_F = –1 component |Ψ₋₁|², the m_F = 0 component |Ψ₀|², the m_F = 1 component |Ψ₁|², and the total |Ψ|² = |Ψ₋₁|²+|Ψ₀|²+|Ψ₁|². The SOC strengths in (a)–(d) are γ = 0, 1, 3, and 5, respectively. The spin–spin interaction c₂ = −50.

Fig. 2. The ground-state density profiles of antiferromagnetic spin-1 BECs with isotropic SU(3) SOC. The columns in every panel from left to right are the densities of the m_F = –1 component |Ψ₋₁|², the m_F = 0 component |Ψ₀|², the m_F = 1 component |Ψ₁|², and the total |Ψ|² = |Ψ₋₁|²+|Ψ₀|²+|Ψ₁|². The SOC strengths in (a)–(d) are γ = 0, 1, 2, and 4, respectively. The spin–spin interaction c₂ = 100.

Fig. 3. The ground-state density profiles of antiferromagnetic spin-1 BECs with isotropic SU(3) SOC. The columns in every panel from left to right are the densities of the m_F = –1 component |Ψ₋₁|², the m_F = 0 component |Ψ₀|², the m_F = 1 component |Ψ₁|², and the total |Ψ|² = |Ψ₋₁|²+|Ψ₀|²+|Ψ₁|². The SOC strengths in (a)–(e) are γ = 0.50, 0.75, 1.10, 1.65, and 1.75, respectively. The spin–spin interaction c₂ = 2000.

Fig. 4. The ground-state density profiles of antiferromagnetic spin-1 BECs with isotropic SU(3) SOC. The columns in every panel from left to right are the densities of m_F = –1 component |Ψ₋₁|², m_F = 0 component |Ψ₀|², m_F = 1 component |Ψ₁|², and the total |Ψ|² = |Ψ₋₁|²+|Ψ₀|²+|Ψ₁|². The SOC strengths in (a)-(e) are γ = 2, 2.5, 3.5, 4, and 4.4, respectively. The spin–spin interaction c₂ = 2000.

Fig. 5. The parameters of (a)–(d) are the same as those of Figs. 2(d), 4(a), 4(b), and 4(e), respectively. The momentum distributions of (b1)–(d1) the m_F = –1 component |Ψ₋₁(k)|², (b2)–(d2) the m_F = 0 component |Ψ₀(k)|², and (b3)–(d3) the m_F = 1 component |Ψ₁(k)|².

Fig. 6. The ground-state phase diagram spanned by the SU(3) SOC strength γ and the spin–spin interaction strength c₂. Five ground-state phases can be identified on the phase diagram, including the PW phase, the ST phase, the KL phase, the SHL phase, and the HHL phase.

Fig. 7. The ground-state density profiles of spin-1 antiferromagnetic BECs with anisotropic SU(3) SOC. The columns in every panel from left to right are the densities of m_F = –1 component |Ψ₋₁|², m_F = 0 component |Ψ₀|², m_F = 1 component |Ψ₁|², and the total |Ψ|² = |Ψ₋₁|²+|Ψ₀|²+|Ψ₁|². The SOC ratios in (a)–(c) are ζ = 0.90, 0.99 and 1.1, respectively. The spin–spin interaction c₂ = 2000 and the SOC strength along the x direction γ_x = 5.