论文标题
一维费米气体的大型摩托车尾巴与自旋轨道耦合
Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
论文作者
论文摘要
我们研究了与自旋轨道耦合（SOC）的超低的一维（1D）两分量的Fermi气体（SOC）的超速一维（1D）两分量Fermi气体的接触，射频光谱和其他普遍关系。与以前的研究不同，我们发现动量分布矩阵的旋转混合（异形）项中的$ q^{ - 8} $尾巴取决于1D系统实验室框架中的两个SOC参数，其中$ q $是相对动量。可以通过飞行时间测量观察到这种尾巴，这是SOC对多体水平的影响的直接表现。除了传统的一维偶发散射长度外，我们发现必须由于SOC而引入两个新的物理量。因此，获得了两个有关两个SOC参数的新的绝热能量关系。此外，我们在该系统的短距离内得出了压力关系和病毒定理。为了找到SOC如何修改大型摩托车行为，我们将SOC参数视为扰动，因为SOC的强度应比原子间相互作用的相应强度尺度小得多。 In addition, by using the operator product expansion method, we derive the asymptotic behavior of the large-momentum distribution matrix up to the $q^{-8}$ order and find that the diagonal terms of the distribution matrix include the contact of traditional 1D even-wave scattering length as the leading term and the SOC modified terms beyond the leading term, the off-diagonal term is beyond the subleading term and is corrected by the SOC parameters.我们还发现，动量分布矩阵显示旋转依赖性和各向异性特征。此外，我们计算实验室框架中的动量分布矩阵，以实验意义。
We study the contacts, large-momentum tail, radio-frequency spectroscopy, and some other universal relations for an ultracold one-dimensional (1D) two-component Fermi gas with spin-orbit coupling (SOC). Different from previous studies, we find that the $q^{-8}$ tail in the spin-mixing (off-diagonal) terms of the momentum distribution matrix is dependent on the two SOC parameters in the laboratory frame for 1D systems, where $q$ is the relative momentum. This tail can be observed through time-of-flight measurement as a direct manifestation of the SOC effects on the many-body level. Besides the traditional 1D even-wave scattering length, we find that two new physical quantities must be introduced due to the SOC. Consequently, two new adiabatic energy relations with respect to the two SOC parameters are obtained. Furthermore, we derive the pressure relation and virial theorem at short distances for this system. To find how the SOC modifies the large-momentum behavior, we take the SOC parameters as perturbations since the strength of the SOC should be much smaller than the corresponding strength scale of the interatomic interactions. In addition, by using the operator product expansion method, we derive the asymptotic behavior of the large-momentum distribution matrix up to the $q^{-8}$ order and find that the diagonal terms of the distribution matrix include the contact of traditional 1D even-wave scattering length as the leading term and the SOC modified terms beyond the leading term, the off-diagonal term is beyond the subleading term and is corrected by the SOC parameters. We also find that the momentum distribution matrix shows spin-dependent and anisotropic features. Furthermore, we calculate the momentum distribution matrix in the laboratory frame for the experimental implication.
