Abstract

<sec>Bessel optical lattice yields a non-spatially periodic column-symmetric optical lattice potential field, which has the characteristics of both infinite deep potential well and the ring-shaped potential well. A deep potential is formed in the center of the 0-order Bessel optical lattice. In the non-zero-order Beseel optical lattice, a ring-shaped shallow potential well with a central barrier can be formed. Exciton-polariton is a semi-light and semi-matter quasi-particle, which can achieve the Bose-Einstein condensate phase transition even at room temperature to form a polariton condensate. In addition, the polariton condensate is likely to realize sufficiently strong spin-orbit coupling due to the cavity-induced TE-TM splitting of the polariton energy levels. The polariton condensate can be realized at room temperature, and there can be spin-orbit coupling in it, which provides a new platform for the studying of quantum physics. </sec><sec>In this paper, the Bessel optical lattice is introduced into a polariton condensate. The stationary state structure of spinor two-component polariton condensate with spin-orbit coupling is investigated. By solving the Gross-Pitaevskii equation, we first give a stationary state structures of the polariton condensate both in the laboratory coordinate frame and in the rotating coordinate frame. Owing to the introduction of the Bessel optical lattice, the stationary state structures of polariton condensate are diverse. We dispaly the stationary state structures of the basic Gaussian solitons and multipole solitons in the central deep potential well in the laboratory coordinate frame, and the ring solitons and multipole solitons in the central shallow potential well. We also dispaly the vortex ring soliton that exists in the rotating coordinate frame, and the stationary state structure of the component separation caused by the spin-orbit interaction. We analyze not only the influences of the spin-orbit coupling on the stationary state structures in the two coordinate frames, but also the stability of the multipole solitons in the rotating coordinate frame. It is found that the multipole solitons formed in the ring-shaped shallow potential well have better stability than in the central deep potential well, and they can maintain the relative structure and spatial distribution for a long time in the rotation process. In the rotating coordinate frame, even if the two-component separation conditions are not satisfied, the introduction of spin-orbit coupling can cause the two components to separate.</sec>

Highlights

  • which has the characteristics of infinite deep potential well

  • A deep potential is formed in the center of the 0-order Bessel optical lattice

  • achieve the Bose-Einstein condensate phase transition even be at room temperature to form polariton condensates

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Summary

Bessel 型光晶格

式 是 −V0Jn2( 2br) , 其 中 V0 是 势√场 强 度 , Jn(r)是 n 阶 Bessel 函数, 径向半径 r = x2 + y2 , b 表示 径向收缩因子 . 可以看出, BL 整体呈环状分布, 每个环的深度和宽度随半径 r 变化, 0 阶 BL 的最 小值 −1在 BL 中央, 其它各环的深度远小于中央 势阱的深度, 因此 0 阶 BL 在势场中央形成深势 阱, 而且中央深势阱的深度和势场强度一致. 高阶 ( n ≥ 1)BL 的最小值分布在靠近势场中 央 (势场中央是势垒) 的第一圆环处 (图 1(b), (c), (d) 中黑色部分), 第一圆环的半径随阶数 n 的增大 而增加, 其深度随阶数 n 的增加而减小, 高阶 BL 在第一圆环处形成环状浅势阱, 其特点是在其 中央存在"倒钟形"势垒. 因此, 为 了维持相同的势阱深度, 高阶 BL 需要更大的势阱 强度. 宽度可以通过径向收缩因子 b 调节, 在没有特别指 出的情况下, 我们计算过程中取 b = 0.5. 另外, 高 阶 BL 的势阱深度和势场强度不一致, 势阱深度由 势场最小值和势场强度共同决定. 例如, n = 3时, 势场最小值为 −0.2, 为了使其维持和 n = 0时具有 相同的势阱深度, 其势场强度应取 V0 = 5

Gross-Pitaevskii 方程
SOC 作用对实验室坐标系中极化激元 凝聚稳态结构的影响
BL 的径向缩放因子对旋转系统稳态 结构的影响
BL 势场中多极孤立子的旋转稳定性
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