雪茄状玻色-爱因斯坦凝聚体中的多原子暗孤子
Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
摘要：
研究了雪茄状玻色-爱因斯坦凝聚体中多重暗孤子的稳定性和动力学性质。我们的研究是出于这样一个事实，即多个物质波暗孤子可能会自然地形成在这样的设置，根据我们最近的工作[物理。101，130401（2008）]。首先，我们研究了暗孤子的相互作用，并表明，良好分离的孤子（即，以相对较低的速度进行碰撞的那些）可以通过类似粒子的运动方程来分析。后者考虑到孤立子之间的排斥（通过有效的排斥势）和系统的限制和维数（通过每个孤立子的有效抛物陷阱）。接下来，基于这样一个事实，即稳定的，分离良好的暗多孤子状态出现的量子谐振子的适当的激发本征值的非线性延续，我们使用Bogoliubov-de Gennes分析，系统地研究这种结构的稳定性。我们发现，对于一个足够大的原子数，多个孤子状态可能是动态稳定的，而对于一个小的原子数，我们预测的动态不稳定性出现的孤子模式的本征频率和固有的激发频率之间的共振效应的凝聚。最后，我们给出了多孤子态的实验实现，包括一个三孤子态，它由两个孤子围绕一个静止的孤子振荡组成。
英文摘要：
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multi-soliton states emerge as a nonlinear continuation of the appropriate excited eigensates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states may be dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally we present experimental realizations of multi-soliton states including a three-soliton state consisting of two solitons oscillating around a stationary one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
