可调三体相互作用下深光晶格中玻色-爱因斯坦凝聚体的离散呼吸子和孤子模集体激发
Discrete Breather and Soliton-Mode Collective Excitations in Bose-Einstein Condensates in a Deep Optical Lattice with Tunable Three-body Interactions
摘要：
我们研究了具有可调三体相互作用的深光晶格中玻色-爱因斯坦凝聚体集体激发的动态演化。它们的动力学由高阶离散非线性薛定谔方程（DNLSE）控制。用变分法得到了系统的动态相图。动力学演化显示出非常有趣的特征。在三体相互作用完全超过两体相互作用的情况下，离散呼吸相完全消失。只有当孤子线接近相图中的临界线时，才存在这种特殊区域中的孤子相。当弱两体相互作用重新引入到这个制度，离散呼吸解决方案重新出现，但占据一个非常小的域中的相空间。同样地，在这种情况下，如果两体和三体相互作用的符号相反，孤子以及离散呼吸相位完全消失。我们分析了具有可调相互作用的玻色-爱因斯坦凝聚体的集体激发这种不寻常的动力学演化的原因。我们还进行了直接的数值模拟的DNLS方程的离散孤子解的存在性预测的变分计算，并检查孤子解的长期稳定性。
英文摘要：
We have studied the dynamic evolution of the collective excitations in Bose-Einstein condensates in a deep optical lattice with tunable three-body interactions. Their dynamics is governed by a high order discrete nonlinear Schrodinger equation (DNLSE). The dynamical phase diagram of the system is obtained using the variational method. The dynamical evolution shows very interesting features. The discrete breather phase totally disappears in the regime where the three-body interaction completely dominates over the two-body interaction. The soliton phase in this particular regime exists only when the soliton line approaches the critical line in the phase diagram. When weak two-body interactions are reintroduced into this regime, the discrete breather solutions reappear, but occupies a very small domain in the phase space. Likewise, in this regime, the soliton as well as the discrete breather phases completely disappear if the signs of the two-and three-body interactions are opposite. We have analysed the causes of this unusual dynamical evolution of the collective excitations of the Bose-Einstein condensate with tunable interactions. We have also performed direct numerical simulations of the governing DNLS equation to show the existence of the discrete soliton solution as predicted by the variational calculations, and also to check the long term stability of the soliton solution.
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