Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices
Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices
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DOI：
10.1103/physreva.75.063602
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发表时间：
2007-05
影响因子：
2.9
通讯作者：
A. Gubeskys;B. Malomed
中科院分区：
文献类型：
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作者：
A. Gubeskys;B. Malomed
我们研究了由两个平行的准一维陷阱(CORE)组成的系统中的自发对称性破缺，这些陷阱配有光学晶格(OL)并填充了玻色-爱因斯坦凝聚体(BEC)。该模型还可以用具有周期性折射率调制的平行平面光波导中的空间孤子来解释。对相应的线性耦合Gross-Pitaevskii方程组(GPES)的分析表明，单个GPE的光谱带隙分裂为多个子带隙。研究了两个陷阱中的吸引(AA)和排斥(RR)非线性情况下两分量BEC孤子的对称性破缺，并考虑了一个陷阱中的排斥和另一个中的吸引(RA)的混合情况。在所有情况下，分别在AA和RR系统中发现了稳定的非对称孤子，它们分别从对称或反对称孤子中分叉出来(并使它们失稳)。在任何一种情况下，都可以预测到双稳，非分叉的稳定分支，要么反对称，要么对称，与不对称分支共存。被分叉破坏稳定的孤子倾向于将自己重新排列成稳定的非对称孤子。除了基本孤子外，还发现了AA系统中扭曲(奇)孤子的分支，以及AA和RR系统中基本孤子的扭曲束缚态。还研究了两个磁芯中的OL之间的相位失配{Delta}的影响。结果表明，{Delta}={pi}/2只是轻微地改变了图像，而{Delta}={pi}则彻底改变了图像，用伪分叉取代了对称破缺分叉，不对称解的分支渐近接近其对称或反对称解的分支(分别在AA和RR系统中)，而不是脱离它。还考虑了一个相关的模型，假设两个物种(代表同一原子的不同自旋态)通过线性相互转换耦合在单核陷阱中的二元BEC。在这种情况下，如果物种间的非线性相互作用变得比物种内的非线性作用更强，AA和RR模型中的对称破缺分叉就会改变它们的特征。
We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral band gaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bistability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in bothmore » AA and RR systems, are found too. The impact of a phase mismatch, {delta}, between the OLs in the two cores is also studied. It is concluded that {delta}={pi}/2 only mildly deforms the picture, while {delta}={pi} changes it drastically, replacing the symmetry-breaking bifurcations by pseudobifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the interspecies nonlinear interaction becomes stronger than the intraspecies nonlinearity.« less