Lattice configurations in spin-1 Bose–Einstein condensates with the SU(3) spin–orbit coupling

doi:10.1088/1674-1056/abab72

Abstract

We consider the SU(3) spin–orbit coupled spin-1 Bose–Einstein condensates in a two-dimensional harmonic trap. The competition between the SU(3) spin–orbit coupling and the spin-exchange interaction results in a rich variety of lattice configurations. The ground-state phase diagram spanned by the isotropic SU(3) spin–orbit coupling and the spin–spin interaction is presented. Five ground-state phases can be identified on the phase diagram, including the plane wave phase, the stripe phase, the kagome lattice phase, the stripe-honeycomb lattice phase, and the honeycomb hexagonal lattice phase. The system undergoes a sequence of phase transitions from the rectangular lattice phase to the honeycomb hexagonal lattice phase, and to the triangular lattice phase in spin-1 Bose–Einstein condensates with anisotrpic SU(3) spin–orbit coupling.

Keywords: Bose-Einstein condensates lattice configurations SU(3) spin-orbit coupling

Received: 06 April 2020
Revised: 02 July 2020
Accepted manuscript online: 01 August 2020

PACS:	03.75.Lm	(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
	03.75.Mn	(Multicomponent condensates; spinor condensates)
	67.85.Hj	(Bose-Einstein condensates in optical potentials)
	67.80.K-	(Other supersolids)

Corresponding Authors: ^†Corresponding author. E-mail: wangjiguo@stdu.edu.cn

About author:

†Corresponding author. E-mail: wangjiguo@stdu.edu.cn

* Project supported by the National Natural Science Foundation of China (Grant No. 11904242) and the Natural Science Foundation of Hebei Province, China (Grant No. A2019210280).

Cite this article:

Ji-Guo Wang(王继国)†, Yue-Qing Li(李月晴), and Yu-Fei Dong(董雨菲) Lattice configurations in spin-1 Bose–Einstein condensates with the SU(3) spin–orbit coupling 2020 Chin. Phys. B 29 100304

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.

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Lattice configurations in spin-1 Bose–Einstein condensates with the SU(3) spin–orbit coupling

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