自旋轨道耦合下杂化$s$ -和$p$ -波相互作用的普适关系
Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
摘要：
本文利用有效场论研究了一维自旋轨道耦合费米子在$s$波共振和$p$波共振附近的普适关系。由于自旋-轨道耦合混合了不同的分波，引入接触矩阵来捕捉二聚体之间的非平凡相关。我们发现自旋-轨道耦合的特征出现在动量分布矩阵的非对角分量的首阶，其与$1/q^{3}$成比例（$q$是相对动量）。我们进一步推导出拉曼光谱的大频率行为，它作为一个独立的可测量的接触量。最后，我们给出了一个明确的例子，考虑接触的两体问题。
英文摘要：
In this work, we study the universal relations for one-dimensional spin-orbital-coupled fermions near both $s$- and $p$-wave resonances using effective field theory. Since the spin-orbital coupling mixes different partial waves, a contact matrix is introduced to capture the non-trivial correlation between dimers. We find the signature of the spin-orbital coupling appears at the leading order for the off-diagonal components of the momentum distribution matrix, which is proportional to $1/q^{3}$ ($q$ is the relative momentum). We further derive the large frequency behavior of the Raman spectroscopy, which serves as an independent measurable quantity for contacts. Finally, we give an explicit example of contacts by considering a two-body problem.
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