The dynamics of pseudo-spin-1/2 Bose-Einstein condensates with weak spin-orbit coupling through a moving obstacle potential are studied numerically. Four types of wakes are observed and the phase diagrams are determined for different spin-orbit coupling strengths. The conditions to form Bénard–von Kármán vortex street are rather rigorous, and we investigate in detail the dynamical characteristics of the vortex streets. The two point vortices in a pair rotate around their center, and the angular velocity and their distance oscillate periodically. The oscillation intensifies with increasing spin-orbit coupling strengths, and it makes part of the vortex pairs dissociate into separate vortices or combine into single ones and destroys the vortex street in the end. The width $b$ of the street and the distance $l$ between two consecutive vortex pairs of the same circulation are determined by the potential radius and its moving velocity, respectively. The $b/l$ ratios are independent of the spin-orbit coupling strength and fall in the range $0.19–0.27$, which is a little smaller than the stability criterion 0.28 for classical fluids. Proper $b/l$ ratios are necessary to form Bénard–von Kármán vortex street, but the spin-orbit coupling strength affects the stability of the street patterns. Finally, we propose a protocol to experimentally realize the vortex street in ${}^{87}\mathrm{Rb}$ spin-orbit-coupling Bose-Einstein condensates.

中文翻译：

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自旋轨道耦合的玻色-爱因斯坦凝结物中的贝纳德-冯·卡曼涡街

数值研究了通过自旋势垒耦合的弱自旋轨道耦合的准自旋1/2玻色-爱因斯坦凝聚体的动力学。观察到四种类型的尾波，并针对不同的自旋轨道耦合强度确定了相图。形成Bénard–vonKármán涡街的条件非常严格，我们将详细研究涡街的动力学特性。一对中的两个点涡绕其中心旋转，并且角速度及其距离周期性地振荡。随着自旋轨道耦合强度的增加，振荡加剧，这使部分涡对解离为单独的涡流或合并为单个涡流，并最终破坏了涡街。宽度$b$ 街道和距离 $升$同一循环的两个连续涡旋对之间的距离分别由势半径及其移动速度确定。的$b/升$ 比率与自旋轨道耦合强度无关，并且落在该范围内 $0.19–0.27$，它比经典流体的稳定度标准0.28小一些。正确$b/升$形成贝纳德－冯·卡尔曼涡街的比例是必要的，但是自旋-轨道耦合强度会影响街道格局的稳定性。最后，我们提出了一种协议，以通过实验实现${}^{87}b$ 自旋轨道耦合玻色-爱因斯坦凝聚物。