标题： 孤子和耦合一维凝聚体中的行波解 显示英文标题

标题： Soliton and traveling wave solutions in coupled one-dimensional condensates

摘要： 超冷凝聚体为探索孤子物理提供了一个独特的平台。 受最近在分裂的一维（1D）玻色-爱因斯坦凝聚体中实现正弦-戈登模型的实验启发，我们证明该系统自然支持各种密度和相位孤子。 我们使用玻色化技术来探索这一物理现象，在该技术中，相位和密度是共轭对，并确定其有效语言方程和相应的运动方程。 我们表明，在两个凝聚体之间存在不对称性的情况下，会出现超出正弦-戈登模型的新解。 我们在该模型中计算了行波解和孤子解，并解析地确定了它们对应的能量密度。 最后，我们讨论了这些解与实验的相关性，并讨论了它们的观测情况。 该理论不依赖于准粒子激发机制，该机制在高维情况下产生Lee-Huang-Yang修正，因此更适用于描述一维系统的物理现象。 由于物理模型已经在实验中实现，这项工作为利用两个耦合凝聚体实现各种孤子和周期性解开辟了一个新的前沿。 显示英文摘要

摘要： Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports various density and phase solitons. We explore the physics using the bosonization technique, in which the phase and density are conjugate pairs, and determine its effective Language equation and the associated equation of motion. We show that in the presence of asymmetry between the two condensates, new solutions beyond those in the sine-Gordon model emerge. We calculate the traveling wave solutions and soliton solutions in this model and determine their corresponding energy densities analytically. Finally, we discuss the relevance of these solutions to the experiments and discuss their observations. This theory does not rely on the mechanism of quasi-particle excitation, which yields the Lee-Huang-Yang correction in higher dimensions, and is thus much more suitable to describe the physics in 1D systems. Since the physical models have already been realized in experiments, this work opens a new frontier for the realization of various soliton and periodic solutions using two coupled condensates.