Li Fude, Xue Kang, Yi Xuexi
Center for Quantum Sciences and School of Physics, Northeast Normal University, Renmin Street 5268, Changchun 130024, China.
Entropy (Basel). 2021 Oct 26;23(11):1404. doi: 10.3390/e23111404.
Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson-hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.
近年来，光学晶格中的拓扑物理受到了广泛关注。对这类光学系统的非线性效应仍在深入研究，并已取得了大量进展。在本文中，对于一个非线性光学耦合玻色子 - 六角晶格系统，在平均场近似下，我们计算了非线性狄拉克锥，并讨论了其对系统参数的依赖性。由于该锥的特殊结构，围绕这些狄拉克锥获得的贝里相位（二维扎克相位）是量子化的，并且临界值可以通过不同晶格点之间的相互作用进行调制。我们通过数值计算了整体阿哈罗诺夫 - 玻姆（AB）相位，发现它也是量子化的，这提供了一个可能的拓扑数，借此我们可以表征量子相。此外，我们发现当非线性狄拉克点处的带隙关闭时会发生拓扑相变。这与线性系统不同，在线性系统中，相变发生在狄拉克点处带隙关闭并重新打开时。
