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基于数值求解定态与含时Gross-Pitaevskii方程,本文研究了一维拉曼型自旋-轨道耦合玻色气体中的静态特性与低能集体激发动力学性质.我们分析了凝聚体动量、自旋极化率和基态能量来分类三种基态物相(条纹相、平面波相和零动量相)以及对应的相变.在此基础上,通过设计不同的微扰激发方式,我们重点研究了四种典型的低能集体激发模式(偶极、呼吸、自旋-偶极和自旋-呼吸模式)的频率特性和动力学行为.我们发现,四种模式频率随拉比频率增加呈现非单调变化行为且不同物相中的集体激发模式表现出显著差异,尤其是自旋相关的两种模式在条纹相中呈现自旋自由度相关的独特振荡行为.这些发现将为理解自旋-轨道耦合玻色气体中新奇物相的量子多体动力学提供了重要参考和理论依据.By numerically solving the static and time-dependent Gross-Pitaevskii equations, we systematically investigate the ground-state properties and collective excitations of a weakly interacting Bose gas with the Raman-type spin-orbit coupling in one dimension. Our analysis focuses on three distinct quantum phases— the stripe phase, plane-wave phase, and zero-momentum phase—characterizing their key static properties, such as condensate momentum, spin polarization, and ground-state energy. Using time-dependent simulations, we explore the dynamics of total-density collective modes, including the dipole mode, which drives harmonic oscillations of the atomic cloud’ s center of mass, and the breathing mode, responsible for periodic expansion and contraction of the density profile. The modes’ frequencies exhibit a non-monotonic dependence on the Rabi frequency across the three phases and are significantly suppressed at the transition point between the plane-wave and the zero-momentum phases. Additionally, we study spin-dependent collective excitations, particularly the spin-dipole and spin-breathing modes, governed by the time-dependent spin density distribution $\left(\delta n(x, t) \equiv n_{\uparrow}(x, t)-n_{\downarrow}(x, t)\right)$ as shown in the following figure. Our results reveal that two spin oscillation modes exist only in the stripe and zero-momentum phases, with frequencies remarkably higher in the latter. Notably, in the stripe phase, mode frequencies decrease monotonically with increasing Rabi frequency, whereas they rise linearly in the zero-momentum phase. The spin-dipole mode induces rigid, out-of-phase oscillations of the two spin components, while the spin-breathing mode modulates the spin density distribution periodically. These findings offer fundamental theoretical insights into the dynamic behavior of spin-orbit-coupled quantum gases, particularly regarding spin-related collective excitations, and provide valuable guidance for future cold-atom experiments.
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