<p>We theoretically study the existence and stability of defect solitons in spin-orbit-coupled (SOC) Bose-Einstein condensate with PT-symmetric lattice. Defect modes bifurcate from the band edges and may conserve their energy or endure gain or loss upon propagating. By numerical calculations, it is found that the defect solitons exist in the semi-infinite gap and the first gap. A stationary nonlinear Schrödinger equation has been obtained using multi-scale techniques. The stability of defect solitons is significantly influenced by the SOC strength <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\kappa $</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> and Rabi coupling strength <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. For attractive defects or zero defects, the stability of defect solitons in the semi-infinite gap is enhanced with increasing <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\kappa $</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> or decreasing <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. However, weaker <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\kappa $</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> or stronger <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> strengths are more conducive to the stability of solitons in the first gap. For repulsive defects, weaker strengths of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\kappa $</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> are more favorable for the stability of solitons. It is also observed that decreasing the defect strength leads to an increase in the instability of solitons.</p>

Defect solitons in spin-orbit-coupled Bose-Einstein condensate with PT-symmetric optical lattice

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发表日期：

2026年7月21日

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Baolong Xi,
Jinping Ma,
Pu Tu,
Xi Zhao,
Kaihua Shao,
Yuren Shi

摘要

We theoretically study the existence and stability of defect solitons in spin-orbit-coupled (SOC) Bose-Einstein condensate with PT-symmetric lattice. Defect modes bifurcate from the band edges and may conserve their energy or endure gain or loss upon propagating. By numerical calculations, it is found that the defect solitons exist in the semi-infinite gap and the first gap. A stationary nonlinear Schrödinger equation has been obtained using multi-scale techniques. The stability of defect solitons is significantly influenced by the SOC strength $\kappa $ $κ$ and Rabi coupling strength $\gamma $ $γ$ . For attractive defects or zero defects, the stability of defect solitons in the semi-infinite gap is enhanced with increasing $\kappa $ $κ$ or decreasing $\gamma $ $γ$ . However, weaker $\kappa $ $κ$ or stronger $\gamma $ $γ$ strengths are more conducive to the stability of solitons in the first gap. For repulsive defects, weaker strengths of $\kappa $ $κ$ or $\gamma $ $γ$ are more favorable for the stability of solitons. It is also observed that decreasing the defect strength leads to an increase in the instability of solitons.