The so-called quantum metric tensor is a band-structure invariant whose measure corresponds to the quantum distance between nearby states in the Hilbert space, characterizing the geometry of the underlying quantum states. In the context of spin–orbit coupled Fermi gases, we recently proposed that the quantum metric has a partial control over all those superfluid properties that depend explicitly on the mass of the superfluid carriers, i.e., the effective-mass tensor of the corresponding (two- or many-body) bound state. Here we scrutinize this finding by analyzing the collective phase and amplitude excitations at zero temperature. In particular to the Goldstone mode, we present extensive numerical calculations for the Weyl and Rashba spin–orbit couplings, revealing that, despite being small, the geometric contribution is solely responsible for the nonmonotonic evolution of the sound velocity in the BCS–BEC crossover.

所谓的量子度量张量是一种带结构不变量，其量度对应于希尔伯特空间中邻近状态之间的量子距离，表征了基础量子态的几何形状。在自旋轨道耦合费米气体的背景下，我们最近提出，量子度量对所有这些超流体特性都具有部分控制权，这些特性明确取决于超流体载流子的质量，即相应的（两个）的有效质量张量。 -或多体）约束状态。在这里，我们通过分析零温度下的集体相位和振幅激励来仔细检查这一发现。特别是对于Goldstone模式，我们对Weyl和Rashba自旋-轨道耦合进行了广泛的数值计算，结果表明，尽管它很小，