玻色-爱因斯坦凝聚中的环状暗孤子动力学

郭慧; 王雅君; 王林雪; 张晓斐

doi:10.7498/aps.69.20191424

摘要

环状暗孤子最早是在非线性光学系统中理论预言并实验实现的一种二维孤子类型. 跟通常的二维孤子(如条纹孤子)相比, 环状暗孤子具有更好的稳定性和更加丰富的动力学行为. 玻色-爱因斯坦凝聚由于其高度可调控性为研究环状暗孤子提供了一个全新的平台. 本文结合玻色-爱因斯坦凝聚和孤子研究的现状, 综述玻色-爱因斯坦凝聚中环状暗孤子的解析解、稳定性调控及其衰变动力学等方面的研究进展. 首先介绍了一套变换方法将均匀系统中非线性系数不随时间变化的环状暗孤子解析解推广到谐振子外势下非线性系数随时间变化的环状暗孤子解析解; 然后讨论在形变扰动下环状暗孤子的稳定性相图, 并介绍了如何利用周期调制的非线性来增强环状暗孤子的稳定性; 此外, 还重点讨论了环状暗孤子衰变导致的涡旋极子动力学以及斑图形成.

关键词:

Abstract

Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.

Keywords:

作者及机构信息

1.
中国科学院国家授时中心时间频率基准重点实验室, 西安　710600

2.
中国科学院大学天文与空间科学学院, 北京　100049

3.
陕西科技大学文理学院, 西安　710021

通信作者: 张晓斐, xfzhang@ntsc.ac.cn

基金项目: 国家自然科学基金(批准号: 11775253, 11704383)和陕西省自然科学基础研究计划(批准号: 2019JQ-058)资助的课题

Authors and contacts

1.
Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China

2.
School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

3.
Department of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China

Corresponding author: Zhang Xiao-Fei, xfzhang@ntsc.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775253, 11704383) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2019JQ-058)

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参考文献

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施引文献

图 1 形变扰动下环状暗孤子的稳定性相图^[51]

Fig. 1. Stability phase diagram of ring dark solitons under deformation perturbation.

下载: 全尺寸图片幻灯片

图 2 单分量BEC中形变扰动下环状暗孤子的衰变行为^[51]

Fig. 2. Decay of the ring dark soliton under deformation perturbation in a single-component BEC.

下载: 全尺寸图片幻灯片

图 3 两分量BEC中相同深度环状暗孤子的衰变行为^[86]

Fig. 3. Decay of the ring dark solitons with the same depth in two-component BECs.

下载: 全尺寸图片幻灯片

图 4 四组涡旋极子在两分量BEC中的动力学演化^[86]

Fig. 4. Evolution of four vortex dipoles in two-component BECs.

下载: 全尺寸图片幻灯片

图 5 两分量BEC中不同深度环状暗孤子的衰变行为^[86]

Fig. 5. Decay of the ring dark solitons with different depths in two-component BECs.

下载: 全尺寸图片幻灯片

图 6 周期调制相互作用系统中环状暗孤子衰变引起的斑图形成^[94]

Fig. 6. Pattern formation induced by the decay of ring dark solitons in a system with periodically modulated interactions.

下载: 全尺寸图片幻灯片

图 7 斑图在周期调制相互作用系统中的演化^[94]

Fig. 7. Evolution of the pattern in a system with periodically modulated interactions.

下载: 全尺寸图片幻灯片

表 1 环状暗孤子寿命随相互作用振荡频率的变化^[51]

Table 1. Life of the ring dark soliton as a function of the interaction oscillation frequency.

相互作用振荡频率$\omega$/$\varOmega$	环状暗孤子寿命t/ms
$ < 0.5$	$ < 15$
0.6	17
0.8	43
1.0	45
1.5	16
$ > 1.7$	$ < 15$
注1: 原子间相互作用$g(t) = 1-\sin{\omega t}$, 环状暗孤子深度$\cos{\phi(0)} = 0.76$.

下载: 导出CSV

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