论文标题
伪时间 - 逆转对称性对称性拓扑拓扑的bogoliubov激发光学晶格中的Bose-Einstein冷凝物
Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices
论文作者
论文摘要
光学晶格中Bose-Einstein冷凝物的Bogoliubov激发可能具有类似于Fermions级AII的拓扑绝缘子中的带拓扑。使用克雷因空间理论的语言，这种拓扑特性被证明是受伪时间 - 反转对称性的保护，该对称是伪半统治，正方形为$ -1 $，相关的散装拓扑不变性也是$ \ m athbb z_2 $ index。我们为其构建了三个等效表达式，与Pfaffian，伪时间 - 反转极化以及最实际的，Wannier Center Flow ast the Wannier Center Flow ast as the Fermionic Case所采用，此处定义了相对于伪内部产品。在存在额外的伪独立和伪缓冲反面对称性的情况下，得出了更简单的表达。然后，我们研究了在冷原子平台上可行的两个玩具模型，以在数值上确认散装的对应关系。这项工作中开发的克雷因空间方法是一种普遍的形式主义，可以研究各种对称对称性保护的拓扑骨化骨bogoliubov频段。
Bogoliubov excitations of Bose-Einstein condensates in optical lattices may possess band topology in analogous to topological insulators in class AII of fermions. Using the language of the Krein-space theory, this topological property is shown to be protected by a pseudo-time-reversal symmetry that is pseudo-antiunitary and squares to $-1$, with the associated bulk topological invariant also being a $\mathbb Z_2$ index. We construct three equivalent expressions for it, relating to the Pfaffian, the pseudo-time-reversal polarization, and most practically, the Wannier center flow, all adopted from the fermionic case, defined here with respect to the pseudo inner product. In the presence of an additional pseudo-unitary and pseudo-Hermitian inversion symmetry, a simpler expression is derived. We then study two toy models feasible on cold atom platforms to numerically confirm the bulk-boundary correspondence. The Krein-space approach developed in this work is a universal formalism to study all kinds of symmetry-protected topological bosonic Bogoliubov bands.
