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本文研究运动光格中非线性作用随时空变化的玻色-爱因斯坦凝聚体的混沌时空动力学。在运动光格势强度和非线性作用调制强度较小的情况下，系统满足微扰条件，将Melnikov函数法应用于理论分析，得到了系统的Melnikov时空混沌判据。当系统不满足微扰条件时，数值模拟表明，对于原子间呈吸引作用的玻色-爱因斯坦凝聚体，非线性作用调制强度的增大可以加深系统的时空混沌程度。在某些参数区域，非线性作用调制频率对系统时空动力学行为具有重要影响。进一步的数值研究结果揭示，较大的化学势不仅可以抑制吸引系统的时空混沌，还可以抑制排斥系统的时空混沌。基于以上研究结果，在实验中可以根据需要规避或引发玻色-爱因斯坦凝聚系统的时空混沌。
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关键词:
- 玻色-爱因斯坦凝聚 /
- 运动光格 /
- Melnikov混沌判据 /
- 混沌
The dynamical behaviors of Bose-Einstein condensates (BECs) depend largely on the nonlinear interactions between BEC atoms. The advancement of experimental techniques enables the rapid and effective modulation of the nonlinear interactions through Feshbach resonance technique. At present, both the time-varying nonlinear interaction and space-varying nonlinear interaction have been realized, respectively. This makes it possible to simultaneously modulate the nonlinear interactions in time and space through the combination of techniques. It will provide more options to conduct various studies by manipulating the BECs. Therefore, BECs with time- and space-varying interactions must possess unique advantages in studying BEC dynamics.
This paper studies the chaotic spatiotemporal dynamics of BECs with time- and space-varying nonlinear interactions in moving optical lattices. When the intensities of the moving optical lattice potential and the modulation of the nonlinear interaction are small, the system satisfies the perturbation conditions and the Melnikov-function method is used in the theoretical analyses to obtain the Melnikov spatiotemporal chaotic criterion of the system. When the system does not meet the perturbation conditions, numerical simulations show that, for a BEC with an attractive atomic interaction, increasing the modulation intensity of the nonlinear interaction can deepen the degree of spatiotemporal chaos in the system. In certain parameter regions, the modulation frequency of the nonlinear interaction can have a significant impact on the spatiotemporal dynamical behavior of the system. Further numerical research results show that larger chemical potentials can suppress the spatiotemporal chaos in not only the attractive but also the repulsive BECs. Based on the above research results, it is possible to avoid or trigger spatiotemporal chaos of BEC systems in experiments according to demand.-
Keywords:
- Bose-Einstein condensates /
- Travelling optical lattice /
- Melnikov chaotic criterion /
- chaos
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