法拉第图案、自旋纹理、自旋-自旋相关性和竞争不稳定性在驱动的自旋1反铁磁玻色-爱因斯坦凝聚体中的研究
Faraday patterns, spin textures, spin-spin correlations and competing instabilities in a driven spin-1 antiferromagnetic Bose-Einstein condensate
AI总结：
研究通过调节自旋1反铁磁玻色-爱因斯坦凝聚体的散射长度，揭示法拉第图案、自旋纹理及竞争不稳定性现象，探讨其在不同维度下的行为差异。
摘要：
我们研究了在驱动的准一维和准二维自旋1玻色-爱因斯坦凝聚体中，通过周期性调节s波散射长度a0和a2，形成瞬态法拉第图案和自旋纹理的过程，从反铁磁相开始。该相特征由布里托夫谱组成，包括三种模式：一种是存在能隙的模式，另外两种是无能隙的模式。当调节a0且半周期频率低于存在能隙的模式时，密度和自旋法拉第图案出现。在准一维情况下，自旋纹理由周期性相反z极化域特征。当驱动超过能隙时，自旋纹理由沿凝聚体轴随机取向的自旋矢量特征。在驱动的准二维凝聚体中出现新的定性特征。例如，当驱动超过能隙时，自旋纹理由异常涡旋和反涡旋特征，这些涡旋在单个磁性分量中不表现出相位缠绕。在能隙以下，自旋纹理表现出不规则的铁磁斑块，具有相反的极化。在准一维空间中，自旋-自旋相关性表现出高斯包络，而在准二维中则具有贝塞尔函数依赖性。在a2调节下，密度图案主导，无论驱动频率如何，除非自旋依赖的相互作用强度足够小。当同时调节两种散射长度时，会出现竞争不稳定性的情景。最后，我们显示竞争不稳定性导致人口转移与二次泽曼场强度之间复杂的相互关系，同时保持其他参数不变。
英文摘要：
We study the formation of transient Faraday patterns and spin textures in driven quasi-one-dimensional and quasi-two-dimensional spin-1 Bose-Einstein condensates under the periodic modulation of $s$-wave scattering lengths $a_0$ and $a_2$, starting from the anti-ferromagnetic phase. This phase is characterized by a Bogoliubov spectrum consisting of three modes: one mode is gapped, while the other two are gapless. When $a_0$ is modulated and half of the modulation frequency lies below the gapped mode, density and spin Faraday patterns emerge. In that case, in quasi-one-dimension, the spin texture is characterized by periodic domains of opposite $z$-polarizations. When driven above the gap, the spin texture is characterized by random orientations of spin vectors along the condensate axis. Qualitatively new features appear in the driven quasi-two-dimensional condensate. For instance, when driven above the gap, the spin textures are characterized by anomalous vortices and antivortices that do not exhibit phase winding in individual magnetic components. Below the gap, the spin texture exhibits irregular ferromagnetic patches with opposite polarizations. The spatial spin-spin correlations in quasi-one-dimension exhibit a Gaussian envelope, whereas they possess a Bessel function dependence in quasi-two-dimension. Under the $a_2$-modulation, the density patterns dominate irrespective of the driving frequency, unless the spin-dependent interaction strength is sufficiently smaller than that of the spin-independent interaction. The intriguing scenario of competing instability can emerge when both scattering lengths are simultaneously modulated. Finally, we show that the competing instabilities result in a complex relationship between the population transfer and the strength of the quadratic Zeeman field, while keeping all other parameters constant.
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