电磁诱导重力下三维玻色凝聚体中紧束缚的孤子与涡旋
Tightly bound solitons and vortices in three-dimensional bosonic condensates with the electromagnetically-induced gravity
AI总结：
研究了激光诱导长程相互作用下三维玻色-爱因斯坦凝聚体的自陷态，发现紧自陷模式（TSTMs）及嵌入涡旋的稳定结构，并揭示了多体碰撞合并的非弹性动力学机制。
摘要：
激光照射诱导的 $1/r$ 长程相互作用，为在三维自由空间中实现 Bose-Einstein condensates (BECs，玻色-爱因斯坦凝聚体) 的稳定自陷提供了一种机制。利用变分近似和数值解，我们发现该设定下（具有吸引性非局域和排斥性局域相互作用）的自陷态类似于紧束缚的紧子。然而，它们并非真正的紧子，而是具有小幅非零尾部的紧自陷模式（TSTMs）。通过尾部解析解解释了这些自陷态的结构。此外，我们证明了嵌入涡旋的稳定 TSTMs 存在于同一设定中，其环绕数至少可达 $S=6$。在研究双 TSTM 相互作用时，我们发现基态对（GSs，$S=0$）、涡旋-涡旋对（$S_1=S_2$）和涡旋-反涡旋对（$S_1=-S_2$）均能形成稳定旋转的束缚态。由冲击引发慢速运动的涡旋 TSTMs 之间的对心碰撞是非弹性的，导致它们合并为一个 GS 孤子；该孤子可能停留在碰撞位置或侧向移动，通过辐射发射耗散角动量，或者导致形成一个同样侧向移动的涡旋。
英文摘要：
The $1/r$ long-range interaction, induced by laser illumination, offers a mechanism for the implementation of stable self-trapping in Bose-Einstein condensates (BECs) in the three-dimensional free space. Using the variational approximation and numerical solutions, we find that self-trapped states in this setting , with attractive nonlocal and repulsive local interactions, resemble tightly-bound compactons. However, these are not true compactons but rather \textit{tightly self-trapped modes} (TSTMs), with small-amplitude nonvanishing tails. The structure of the self-trapped states is explained by an analytical solution for their tails. Further, we demonstrate that stable % TSTMs with embedded vorticity, exist in the same setting, with winding numbers up to $S=6$ (at least). Addressing two-TSTM interactions, we find that pairs of ground states (GSs, with $S=0$), as well as vortex-vortex and vortex-antivortex pairs (with $S_1=S_2$ and $S_1=-S_2$, respectively), form stably rotating bound states. Head-on collisions between vortex TSTMs, set in slow motion by kicks, are inelastic, resulting in their merger into a GS soliton, that may either remain at the collision position or move aside, shedding the angular momentum with emitted radiation, or, alternatively, lead to the formation of a vortex that also moves aside.
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